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\begin{document}
\title{The Behavior of Emerging Market Sovereigns' Credit Default Swap Premiums and Bond Yield Spreads}
\author{Michael Adler}
\affil {Graduate School of Business, Columbia University}
\author{Jeong Song}
\affil {Morgan Stanley\footnote{The views, opinions, and content of this article do not necessarily reflect the views of Morgan Stanley but remain solely those of the author.}}
\date{}
\maketitle
\doublespace
\begin{abstract}
We test whether credit risk for Emerging Market Sovereigns is priced equally in the credit default swap (CDS) and bond markets.
The parity relationship between CDS premiums and bond yield spreads, that was tested and largely confirmed in the literature, is mostly rejected.
Prices below par can result in positive basis, i.e. CDS premiums that are greater than bond yield spreads and vice versa.
To adjust for the non-par price, we construct the bond yield spreads implied by the term structure of CDS premiums for various maturities.
We are able to restore the parity relation and confirm the equivalence of credit risk pricing in the CDS and bond markets for many countries
that have bonds with non-par prices and time varying credit quality.
We detect non-parity even after the adjustment mainly in countries in Latin America, where the bases are larger than the bid-ask spreads in the market.
We also find that the repo rate of bonds decreases around episodes of credit quality deterioration, which helps the basis remain positive.
\end{abstract}
\newpage
\section{Introduction}
Credit default swaps (CDS) have become increasingly popular in
recent years for providing a way to trade credit risk.\footnote{
Important theoretical work on credit risk and derivatives includes
\cite{Jarrow/Turnbull:95, Jarrow/Turnbull:00},
\cite{Longstaff/Schwartz:95a, Longstaff/Schwartz:95b},
\cite{Das/Tufano:96}, \cite{Duffie:98, Duffie:99}, \cite{Lando:98},
\cite{Duffie/Singleton:99}, \cite{Hull/White:00, Hull/White:01},
\cite{Das/Sundaram:00}, \cite{Jarrow/Yildirim:02},
\cite{Archarya/Das/Sundaram:02}, \cite{Das/Sundaram/Sundaresan:03},
and many others. } Studies of the pricing of CDS (\cite{Duffie:99},
\cite{Hull/White:00}) show that CDS premiums should be almost equal
to the bond yield spreads of a given reference entity. This
theoretical parity condition is largely confirmed by empirical
studies that find that CDS premiums and bond yield spreads for high
grade US corporates are generally cointegrated.\footnote{
\cite{Blanko/Brennan/Marsh:05} test the
equivalence of CDS premiums and bond yield spreads, finding support
for the parity as an equilibrium condition.
\cite{Houweling/Vorst:05} compare the credit risk pricing between
the bond market and the CDS market and find the price discrepancies
between CDS premia and bond yield spreads are quite small (about 10
basis points). \cite{Zhu:04} shows that CDS spreads and bonds yield
spreads of U.S. corporate are cointegrated in the long run. In the
short run, he finds negative basis when they use the swap rate or
tax-adjusted treasury rate. }
In contrast, our study finds that for Emerging Market (EM)
Sovereigns, there are fairly long periods during which the basis
turns strongly positive with the result that the cointegration and
parity relationships between CDS premiums and bond yield spreads
are mostly rejected. The reason is that the parity relationship
holds only when the reference bond is a floating rate note (FRN) and
its price is at par. When the perceived credit quality of a
reference entity changes, the price of a reference bond moves away
from par.
Furthermore, the fact that most traded bonds are not FRNs but fixed-rate,
coupon-paying bonds is another reason the cointegration
relationship between CDS premiums and bond yield spreads fails. The
bond yield spread of a fixed coupon bond is the same as the spread
of a FRN when both are at par. However, as mentioned earlier,
variations of perceived credit quality cause prices to deviate from
par. Changes in the riskless rate may also cause the prices of fixed
coupon bonds to vary, which is not the case for FRNs. When prices
are not at par, the fixed coupon bond yield spread is a poor
approximation of the FRN spread.
In recent years, the perceived credit quality of EM Sovereigns has
been improving with narrowing credit spreads compared with the
1990's. This improvement in credit quality has resulted in prices
above par and negative basis for countries such as South Korea,
Poland and Malaysia. On the other hand, such countries as Argentina,
Brazil, Venezuela, Colombia, Russia and Turkey experienced default
or major deteriorations in their credit quality during the early
2000s. The difference between maximum and minimum bond yield spreads
for these countries exceeded 10\% in our sample period. In
particular,
Argentina defaulted in December 2001 and Brazil's bond yield spreads rose above 30\% during
the election crisis of 2002 and 2003. For these countries our data show that bases turned
deeply positive before and during the credit event periods and came back to near zero level
only after the crises had passed.
The prevalence of non-zero bases and the rejection of cointegration
between CDS premiums and bond yield spreads do not, in and of
themselves, indicate a different price for credit risk.
Our pricing model shows that
deeply discounted bond prices account for positive
bases. The non-zero basis does persist, however, during
periods of deteriorating credit quality. This could arise naturally
as providers of credit insurance not only raise their prices but
also, as happens elsewhere in the insurance markets, become increasingly reluctant to write
new contracts.
We attempt to explain the remaining basis in this paper.
Our technique is basically to remove the bias in the basis caused by
below-par prices.
The availability of CDS premiums for various
maturities makes it possible to estimate default probabilities for various terms.\footnote{Unlike CDS for corporates, CDS
contracts for sovereigns trade actively for various maturities: see
\cite{Packer/Suthiphongchai:03}.} With an estimated term structure
of the default probability, we can adjust for the effect on the basis of deeply discounted
bond prices and extract what we call ``implied bond yield spreads".
To do so, we calculate the implied price of fixed coupon paying
bonds. Then we construct the implied yield spreads using the
calculated bond prices. Finally we use the implied bond yield spreads
instead of CDS premiums to test whether the CDS market and bond
market price credit risk equally.
We find that this procedure restores the parity relationship between
the implied bond yield spreads (IBYS) and the actual bond yield
spreads (BYS) in some cases. The parity relation is no longer rejected for
countries such as Mexico, Malaysia, Russia, and Turkey.
This result shows that in these cases the CDS and bond markets were fairly well integrated with respect to pricing credit risk.
However, Argentina, which provides the actual default event and
Brazil, which reached a very high credit event likelihood - more
than 30\% BYS in our sample period - do reject the revised parity
relations. For Argentina, sub-period analysis confirms that the
break down of the parity relation occurred near the default. After
the default, CDS did not trade at all while the bonds continued to
trade sporadically, albeit at long intervals and low volumes. For Brazil, the
difference between the IBYS and the BYS was negative in the early
period of parity break-down. It changed to positive later.
We also find evidence of contagion when we document regional
co-movements of the CDS premiums and BYS. When the CDS premiums and
the BYS in Brazil increased during 2002 and 2003, all the Latin
American countries in our sample showed increases in both their CDS
premiums and BYS. In all the countries in our sample including
Brazil, the increase of CDS premiums were larger than the increase
of the implied BYS. This results in the rejection of the parity relations for countries in Latin America.
However, the arbitrage opportunity was limited.
We find that a decreasing repo rate prevented CDS protection by selling and bond short selling for these countries.
Overall, we believe the contributions of this paper are as follows.
We derive pricing equations for the basis and explain how, and by
how much, factors such as accrued payments and price discounts can
affect the basis. We also offer a new explanation of the recently
empirically observed `basis smile'. This paper augments previous
empirical studies in other respects as well. Ours is the first paper
to use the term structure of the CDS premiums to correct the bias in
the basis that is introduced by non-par prices. Unlike previous
studies that dealt only with investment grade US corporates, we
investigate EM Sovereigns with various credit qualities. We are even able to include a case of actual default in our sample. Our study provides
evidence regarding the equivalence of credit risk pricing in the CDS
and bond markets for EM sovereigns and, using the new measure
`implied bond yield spreads'.
Furthermore we document that (reverse) repo rates decreased during the crisis for the bonds,
which limited the arbitrage from the positive basis.
The remainder of this paper is organized as follows.
Section 2 presents pricing models for CDS premiums and the basis. We
add to the basic model extensions for the payment of accrued CDS
premiums, riskless interest rate movements, non-par FRN bond prices and
fixed-coupon bonds. Section 3 presents the empirical tests and
results. Section 4 summarizes the results and offers concluding
remarks.
\section{Pricing Model}
\cite{Duffie:99} provides the basic CDS pricing equation.\footnote{
\cite{Duffie:99} shows that the spread on a par risky floating rate note over a par default risk free floating rate note equals the CDS premium.
He extends his basic model and shows the relation between bond yield spreads and CDS premiums when the bond price is not at par.
\cite{Hull/White:00} show that, with a flat risk free yield curve and constant interest rates,
the bond yield spread is exactly equal to the CDS premium
when the payout from a CDS on default is the sum of the principal amount plus accrued interest on a risky par yield bond times one minus the recovery rate.
\cite{Houweling/Vorst:05} show that the spread on a par risky fixed coupon bond over a par default risk free fixed coupon bond exactly equals the CDS premium
if the payment dates on the CDS and bond coincide, and recovery on default is a constant fraction of face value.
} Our interest focuses on the basis and we develop the necessary
extensions below. Based on \cite{Duffie:99}, we derive the relation
between CDS premiums and bond yield spreads. Because simple replication arguments
do not hold exactly, we solve independently for the CDS premiums and
the bond spreads and compare them. Basis is defined as the
difference between the CDS premiums and the bond spreads.
Fiirst, we set up the common notations to be used in this paper.
A probability space $(\Omega, \mathcal{F}, \mathbb{Q})$ is well defined,
where the filtration $\mathcal{F} = \{\mathcal{F}_t| 0\leq t \leq T\}$ satisfies $\mathcal{F}_T=\mathcal{F}$ and it is complete, increasing and right continuous
where $\mathbb{Q}$ is the equivalent martingale measure.
Suppose also a locally risk-free short rate process $r$.
Let $\chi(\tau)=1_{\xi\geq \tau}$ be a default indicator function of a reference entity, where $\xi$ is the stopping time that characterizes the time of default by the reference entity.
A risk neutral default intensity process $\lambda(\tau)$ for a stopping time $\xi$ is characterized by the property that the following is the martingale,
\begin{eqnarray*}
\chi(\tau) - \int_0^\tau \big(1-\chi(\mu)\big) \lambda(\mu) d\mu
\end{eqnarray*}
We shall use $L$ to denote the risk-neutral fractional loss of face value on a reference obligation in the event of a default.
\subsection{Case I: Base Model}
In this section, we derive a pricing model for CDSs and their replicating portfolio.
Suppose that two parties make a spot CDS contract at time $t$ with maturity of $\tau_c$.
A buyer of protection periodically pays premiums, $s_{t, \tau_{_c}}$, to a seller.
The payment is made $M_c$ times per year until any one of the following events happens:
the underlying reference entity defaults on its reference obligation or the maturity of the CDS contract comes.
The payment begins at $t+ \frac{1}{M_c}$.
The seller of protection receives the premium payment and its present value at $t$ is
\begin{eqnarray*}
\frac{s_{_{t, \tau_c}}}{M_c}\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[\frac{B(t)}{B({t}+\frac{j}{M_c})} \left(1-\chi\left({t}+\frac{j}{M_c}\right)\right)\bigg|\mathcal{F}_t\right]
\end{eqnarray*}
where $B(\tau) = e^{-\int_t^{\tau}r(s)ds}$. Then the value of the `premium leg' is
\begin{eqnarray*}
\frac{s_{_{t, \tau_c}}}{M_c}\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]
\end{eqnarray*}
The buyer of protection will receive a unit face value of the reference obligation in exchange of the physical delivery of the obligation when a credit event happens.
The payoff process, D(t), follows
\begin{eqnarray*}
d D(t) = (1-\chi(t)) \lambda(t) L dt + dM_{_D}(t)
\end{eqnarray*}
where $M_{D}(t)$ s a martingale with respect to $\mathbb{Q}$.
Then the present value of the protection payment is
\begin{eqnarray*}
E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]
\end{eqnarray*}
Since the net present value of a spot CDS at its initiation be zero, the spot CDS premium can be obtained by equating the value of the two legs
\begin{eqnarray}
\frac{s_{_{t, \tau_c}}}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L \lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\label{base1}
\end{eqnarray}
Suppose a portfolio is constructed at time $t$, with a long
position in a par floating riskless note and a short position in a
par floating risky note. An investor will hold this position through
the maturity of the risky FRN or until any credit event triggering
the payment of the CDS protection payment, whichever is earlier. In
the meantime, she pays the coupons on the risky FRN and receives the
coupons from the riskless FRN. The net payoff is the cash outflow of
the (constant) spread $SPR$. If a credit event does not occur before
maturity, then both notes mature at par value, and there is no net
cash flow associated with the principal. If a credit event does occur
before maturity, then she unwinds her position at the first coupon
date, immediately after the event. She will sell the riskless FRN at
par.\footnote{For now, we ignore the accrued coupon payment from the default
free FRN. That coupon payment will be included in the calculation in
subsection \ref{subsection_acc_int}.} At the termination of the
short position in risky FRN, she needs to pay $1-L$. The net payoff
will be $L$. Note that the payoff from this portfolio replicates the
payoff from buying the CDS protection. The value of this portfolio
is zero at time $t$.
$$\frac{-SPR}{M_c} \cdot \sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right] = 0$$
Then
\begin{eqnarray}
\frac{SPR}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\label{base2}
\end{eqnarray}
>From equation (\ref{base1}) and (\ref{base2}),
\begin{eqnarray}
basis = s - SPR = 0\label{base3}
\end{eqnarray}
Equation (\ref{base3}) shows that the basis between CDS premiums and
the spread of the par risky FRN is zero. This result confirms the
conclusion reached in \cite{Duffie:99}, based on his replication arguments.
\subsection{Case II: Payment of Accrued CDS Premiums at Default}
In this section, we extend \cite{Duffie:99} and show that the
accrued CDS premiums at default cause the basis to become negative.
In practice, a CDS protection buyer pays the accrued CDS
premiums to the protection seller when a credit event
occurs.\footnote{CDS premiums are paid quarterly before a credit
event happens. When a credit event occurs, the CDS contract is
physically settled within 30 days from the event's occurrence.} As a
result, the protection buyer's payoff is reduced by the accrued CDS
premiums. The value of the premium leg is the same as the base case.
\begin{eqnarray}
\frac{s_{_{t, \tau_c}}}{M_c}\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]
\end{eqnarray}
The value of the protection leg is, however, reduced by the payment of
accrued premiums. The value of the protection leg is:
\begin{eqnarray*}
E^\mathbb{Q}\left[\int_{t}^{\tau_c} \left(L-\frac{s_{_{t, \tau_c}}}{M_c}\cdot h(\mu) \right)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]
\end{eqnarray*}
where $h(\mu)$ is the deterministic function of time $\mu$ that accounts for the accrued CDS premiums.
\begin{eqnarray}
h(\mu) = \frac{\mu-t_{k-1}}{t_{k}-t_{k-1}}\;\;\mbox{where}\;\; t_{k-1} \leq \mu < t_{k},\;\; t_{k} = t + \frac{k}{M_c}
\end{eqnarray}
Since the CDS is a zero cost contract at its initiation,
\begin{eqnarray}
&&\frac{s_{_{t, \tau_c}}}{M_c}\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
=&&E^\mathbb{Q}\left[\int_{t}^{\tau_c} \left(L-\frac{s_{_{t, \tau_c}}}{M_c}\cdot h(\mu) \right)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]
\end{eqnarray}
Then
\begin{eqnarray}
\frac{s_{_{t, \tau_c}}}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\\label{ac_prem1}
\end{eqnarray}
Note that in equation (\ref{ac_prem1}), $E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]>0$ and this will cause the basis to be negative due to the payment of accrued CDS premiums at default.
Suppose a portfolio is constructed at time $t$, with a long
position in a par floating riskless note and a short position in a
par floating risky note. The value of this synthetic position is
zero at time $t$.
\begin{eqnarray*}
\frac{-SPR}{M_c} \cdot \sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right] = 0
\end{eqnarray*}
Then
\begin{eqnarray}
\frac{SPR}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\label{ac_prem2}
\end{eqnarray}
>From equations (\ref{ac_prem1}) and (\ref{ac_prem2}),
\begin{eqnarray}
\frac{basis}{M_c} &=&\frac{s - SPR}{M_c}\nonumber\\
&=& \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\
&&- \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\nonumber\\
&<& 0 \label{ac_prem3}
\end{eqnarray}
This result shows that the basis is negative when accrued CDS
premiums are paid upon default and extends the explanations of
negative basis in the current literature.
\subsection{Case III: Coupon Payments from Riskless Bonds at Default}\label{subsection_acc_int}
In this section, we add the coupon payment from the riskless FRN at
default and show that it causes the basis to become more negative.
With a portfolio that replicates the payoffs from a CDS, there will be a coupon payment from the riskless FRN
when the position is closed due to the default of the risky FRN.
Since it does not directly affect either the cashflow of the CDS
premium leg or that of CDS protection leg, CDS premiums do not
change. For CDS premiums,
\begin{eqnarray}
\frac{s_{_{t, \tau_c}}}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\\label{ac_rf1}
\end{eqnarray}
However, the coupon spreads for the risky FRN do change. Suppose a
synthetic CDS is constructed at time $t$ by a long position in a
par floating riskless note and a short position in a par floating
risky note. The value of this synthetic position is zero at time
$t$.
The value of the accrued interest from the riskless FRN is
\begin{eqnarray}
E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]\nonumber
\end{eqnarray}
where
\begin{eqnarray}
g(\mu) = R(t_{k-1},t_{k})\cdot \frac{\mu-t_{k-1}}{t_{k}-t_{k-1}}\;\;\mbox{where}\;\; t_{k-1} \leq \mu < t_{k},\;\; t_{k} = t + \frac{k}{M_c}
\end{eqnarray}
$ R(t_{k-1},t_{k})$ is a risk free interest rate from $t_{k-1}$ to $t_{k}$ at time $t_{k-1}$.
Then
\begin{eqnarray}
&&\frac{-SPR}{M_c} \cdot \sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
&&+E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]\nonumber\\
&&+E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]\nonumber\\
&=& 0
\nonumber
\end{eqnarray}
Then
\begin{eqnarray}
\frac{SPR}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]+ E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\nonumber\\\label{ac_rf2}
\end{eqnarray}
>From equations (\ref{ac_rf1}) and (\ref{ac_rf2}),
\begin{eqnarray}
\frac{basis}{M_c} &=&\frac{s - SPR}{M_c}\nonumber\\
&=& \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\
&&- \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}- \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\nonumber\\
&<& 0
\label{ac_rf3}
\end{eqnarray}
Equation (\ref{ac_rf3}) shows that the basis becomes more negative when
accrued interest from the riskless bond is to be paid.
\subsection{Case IV: Non Par Floating Rate Risky Bond}
In this section, we incorporate the possibility that risky FRN
prices deviate from par and show that a discounted bond price may
lead to a positive basis. In addition to that, we consider the time
series and cross-section movements of the basis as credit quality
changes. When we consider a single bond, the basis increases as the
credit quality of the reference entity deteriorates. However, in
cross-section, this is not always the case. We need to consider the
price and credit quality jointly. Our analysis enables us to provide
a new explanation of the `basis smile' based on the cross-sectional
properties of the basis.
Risky EM FRNs mostly trade away from par, occasionally above but
more frequently below. Suppose that the price of a risky FRN, $P_B
\neq 1$. Since the loss at default is a fraction of the face value,
a non par price for the reference bond does not affect the CDS
premiums. Therefore, the CDS premiums are as before:
\begin{eqnarray}
\frac{s_{_{t, \tau_c}}}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\\label{non_par1}
\end{eqnarray}
Suppose a portfolio is constructed at time $t$ with a long
position in a par floating riskless note and a short position in a
non-par floating rate risky note. The value of this synthetic position is
$(1-P_B)$ at time $t$.
Then
\begin{eqnarray}
&&\frac{-SPR}{M_c} \cdot \sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
&&+E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]\nonumber\\
&&+E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]\nonumber\\
&=& 1-P_{_B}
\nonumber
\end{eqnarray}
Then
\begin{eqnarray}
\frac{SPR}{M_c} &=& \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]+ E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\nonumber\\
&&- \frac{1-P_{_B}}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\label{non_par2}
\end{eqnarray}
>From equations (\ref{non_par1}) and (\ref{non_par2})
\begin{eqnarray}
\frac{basis}{M_c} &=&\frac{s - SPR}{M_c}\nonumber\\
&=& \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\
&&- \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}- \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} g(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}\nonumber\\
&&+ \frac{1-P_{_B}}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]}
\label{non_par3}
\end{eqnarray}
Note that a bond price that is discounted below par increases the
basis. As the discount gets deeper, the relative significance of the
`discount effect' can dominate the `accrued payment effect' and
result in the basis becoming positive. A deterioration of the credit
quality of a reference entity causes not only $P_B$ but also $\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]$ to
decline, which reinforces the `discount effect.'\footnote{
\cite{Norden/Weber:04} analyses the empirical relationship between
CDS, bonds and stocks for U.S. and European corporates during the
period 2000-2002. They find that changes in CDS premiums Granger
cause changes in bond yield spreads for a higher number of firms
than vice versa. They also find that the CDS market is significantly
more sensitive to the stock market than the bond market and that the
magnitude of this sensitivity increases as credit quality
deteriorates.}
Equation (\ref{non_par3}) has another
interesting implication for the cross-sectional variation of the
basis.
Is the basis of low credit quality bonds always positive?
The answer is, `not necessarily.'
The sign of the basis depends not only on $\lambda$ but also on the
price level. A low credit quality does not necessarily cause the
basis to be positive; and, similarly, a high credit quality does
not necessarily cause the basis to be negative. For example,
regardless of credit quality, if a bond is at par, the basis is negative as shown in the equation (\ref{ac_rf3}).
Note that when the credit quality changes, the price also changes,
the basis becomes as shown in the equation (\ref{non_par3}). The
sign of the basis is jointly determined by $\lambda$ and the price.
Suppose a bond is issued at par. When its credit quality does not
change, the basis is negative regardless of the credit quality at the time of issuance.\footnote{
In practice, coupon rates are picked in most cases to match the issue price of a bond as
closely to par as possible.} When its credit quality deteriorates,
the basis will increase. It may become positive when the magnitude of the deterioration is big
enough to make the `discount effect' sufficiently significant.
When its credit quality improves, the basis will decrease.
The sign of the basis is dependent on the relative credit quality compared to the credit quality when the bond was issued.
\begin{center}
\mbox{[Insert figure (\ref{non_par_fig1}) here]}
\end{center}
To illustrate, we provide as an example a plot of the basis in
Figure(\ref{non_par_fig1}), fixing $\Delta t = 0.25$, $r=0.05$,
$L=0.5$ and $T=5$. We vary $\lambda$ and $P_B$. $\lambda \in [0.0
,\; 0.5]$ and $P_B \in [0.8 ,\; 1.2]$ in Figure(\ref{non_par_fig1}).
\subsection{Smiles or Not?}
Non-monotonicity in the average basis across credit ratings can be
explained by transitions of credit ratings in each rating
class.\footnote{A `basis smile' was recently documented in
\cite{DeWit:06}. He explained the `basis smile' citing
\cite{Hjort/McLiesh/Dulake/Engineer:02}. They argued that the
zero-floor for CDS premiums mainly drives the basis upwards for
very high grade credits, while other factors, such as the
cheapest-to-deliver option, mainly affect credits with low ratings.
De Wit himself found that the basis for the portfolio of entities
with `AA' credit ratings was larger than that for `A' rated
entities. But the basis for `BBB' rating entities was bigger than
that for `A' rating entities. The basis smile was also observed by
\cite{Blanko/Brennan/Marsh:05} and \cite{Longstaff/Mithal/Neis:05}.
The average basis was $-41.4$ bp, $-44.8$ bp and $-30.8$ bp for `AAA
- AA', `A' and `BBB' credit rated entities in
\cite{Blanko/Brennan/Marsh:05}. It was -53.1 bp, -70.4 bp, -72.9 bp
and -70.1 bp for `AAA-AA', `A', `BBB' and `BB' credit rated entities
in \cite{Longstaff/Mithal/Neis:05}.} A rating class, which contains
down-graded bonds rather than up-graded bonds will tend to have a less negative or positive
basis. This is because the prices of down-graded bonds move below par.
Bonds with a current rating of `AAA-AA' will previously have had an `AAA-AA'
rating or below. Up-graded bonds in this rating class will acquire a
negative basis, as their prices move above par. On average, the basis in
the `AAA-AA' rating class will, therefore, be negative. Bonds with current
ratings of `A' can previously have been down-graded from `AAA-AA'; maintained an `A' rating; or have been up-graded from `BBB' ratings or below. If there are more up-graded bonds than down-graded bonds in the `A' class, it will have a negative basis.
The average basis of the `A' ratings class can be smaller, i.e. more negative than the
average basis of `AAA-AA' if it contains more bonds that have been
up-graded than down-graded. The average basis in the `BBB' class can
simultaneously be larger than that of the `A' category if it contains
a preponderance of down-graded bonds whose prices have moved to a
discount and whose bases have become positive. Whether the average basis of `A' is
smaller than either that of `AAA-AA' or `BBB-B' depends on the relative proportion of
up-graded bonds to down-graded bonds in each rating class. The same
argument holds for other rating classes as well. The composition is determined by the transitions
across credit ratings, and it can differ from period to period. By this token,
`smiles' in other periods could be flat or reversed (`frowns').
\subsection{Case V: Risky Bonds with Fixed Rate Coupons}
Most of the traded bonds are fixed rate coupon paying bonds and
coupons are paid semi-annually. \cite{Duffie/Liu:01} examine the
term structure of yield spreads between par floating-rate and par
fixed-rate notes of the same credit quality and maturity. They show
that spreads over default-free rates on par-fixed-rate and
par-floating-rate notes are approximately equal. When prices deviate
from par, bond yield spreads become poor approximations of the
par-floating-rate. We examine how the use of bond yield spreads
affects the basis.
Our previous result for the CDS premiums still holds, as follows:
\begin{eqnarray*}
\frac{s_{_{t, \tau_c}}}{M_c} = \frac{E^\mathbb{Q}\left[\int_{t}^{\tau_c} L\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}{\sum_{j=1}^{M_c\cdot (\tau_c - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_c}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[\int_{t}^{\tau_c} h(\mu)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]}\nonumber\\
\label{fixed_cds}
\end{eqnarray*}
Here `$s$' is the quoted CDS premiums for the year period and
`$\frac{s}{M}$' is CDS premiums per one premium payment period.
Suppose a reference bond with a per period coupon `$\frac{C_B}{M_B}$' and maturity of $\tau_B$ is
traded at $P_B$. The basis in the previous empirical studies is
defined as:
$$basis = s - BYS$$
$$s.t.$$
\begin{eqnarray}
P_B&=& \frac{C_B}{M_B}
\sum_{j=1}^{M_B\cdot (\tau_B - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_B}}(r(s) + BYS) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[e^{-\int_{t}^{\tau_B}(r(s) + BYS) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
&=&\frac{C_B}{M_B}\sum_{j=1}^{M_B\cdot (\tau_B - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_B}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right] + E^\mathbb{Q}\left[e^{-\int_{t}^{{\tau_B}}r(s) \lambda(s) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
&&+ E^\mathbb{Q}\left[\int_{t}^{\tau_c} (1-L)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]
\label{fixed_1}
\end{eqnarray}
There is no closed form solution for the basis in this case, as
there was when all bonds were FRNs. Nonetheless, we can still
explore how the basis changes when the credit quality of the
reference entity changes for fixed coupon paying bonds and how it
differs from that for FRNs. For simplicity, we assume flat
term structures of default-free zero-coupon rates and default intensities.
The basis increases in $\lambda$ for fixed coupon bonds as
well, but the magnitude of the change is smaller than in the
case of FRNs.
\begin{center}
\mbox{[Insert figure (\ref{non_par_fixed_fig1}) here]}
\end{center}
\section{Dynamic Relations between Bonds and CDS}
\subsection{Data}
In the previous section, we showed that the basis increases in
$\lambda$, i.e. the basis increases as the credit quality
deteriorates both for FRNs and fixed coupon paying bonds. Unless the
credit quality remains at the same level, the basis fluctuates as
prices vary. With a (quasi) permanent credit quality shift, the
level of the basis also shifts. The credit quality of Emerging
Market Sovereigns has not been stable in our sample and we need to
develop new empirical methods to deal with that. We describe our data
and explain how we construct our new measure, `implied bond yield
spreads' to test whether credit risk is priced equivalently in the
CDS market and bond market for EM sovereigns.
For riskless rates, we collect data for the constant maturity rate
for six-month, one-year, two-year, three-year, five-year,
seven-year, and ten-year rates from the Federal Reserve and construct zero rates. We then use a
standard cubic spline algorithm to interpolate these zero rates at
semiannual intervals. We use a linear interpolation of the
corresponding adjacent rates to obtain the discount rate for
other maturities.
Daily data for CDS premiums were supplied by J.P. Morgan Securities,
one of the leading players in the CDS market. These CDS contracts
are standard ISDA contracts for physical settlement for Emerging
Market (EM) Sovereigns. The notional value of contract (lot size) is
between five to ten million USD for a large market like Brazil,
while it is typically between two to five million for small markets.
The prices hold at `close of business.'
Daily data for EM Sovereign
bonds were also supplied by J.P. Morgan. Our sample ends in early January, 2006. We excluded all Brady bonds
and bonds with embedded options, step-up coupons, sinking funds, or any other special feature which may affect the price of bonds.
We excluded FRNs since we had only four FRNs and they had short samples, of about one and a half years from June, 2004.
Furthermore, we excluded bonds with maturities of less than one year.
\subsection{Term Structure of CDS premiums}
A noticeable pattern in CDS premiums is that CDS premiums usually increase with maturity as shown in figure(\ref{term_all}).
However, CDS premiums with short maturities are often higher than ones with long maturities, especially when the credit quality has been severely deteriorating.
It results in the inverted CDS premiums curve during the high credit risk period.
\begin{center}
\mbox{[Insert figure (\ref{term_all}) here]}
\end{center}
We first adapt the standard reduced-from model such as \cite{Duffie/Singleton:99}, \cite{Jarrow/Turnbull:95}, \cite{Lando:98}, \cite{Madan/Unal:98}, and \cite{Duffee:99}.
Following \cite{Pearson/Sun:94}, \cite{Duffee:99}, and \cite{Zhang:04}, we specify that the default intensity process $\lambda_t$ follows a CIR type squared-root process:
\begin{eqnarray}
d\lambda_{t} &=& \kappa (\theta - \lambda_{t})dt + \sigma \sqrt{\lambda_{t}}dB_{t}^\mathbb{P}\label{e_intensity1}
\end{eqnarray}
where $B_{t}^\mathbb{P}$ is a standard Brownian motion.
The market price of risk is assumed as $\frac{\xi}{\sigma}\sqrt{\lambda_{t}}$.
Then the default intensity $\lambda_{t}$ under the equivalent risk neutral measure, follows:
\begin{eqnarray}
d\lambda_{t} &=& \left[\kappa \theta - \left(\kappa + \xi \right) \lambda_{t} \right]dt + \sigma \sqrt{\lambda_{t}}dB_{t}^\mathbb{Q}\label{e_intensity2}
\end{eqnarray}
where $B_t^\mathbb{Q}$ is a standard Brownian motion under the equivalent martingale measure $Q$.\footnote{
In the literature on corporate CDS spreads, default intensity was modeled as a square-root process in \cite{Zhang:04} and \cite{Longstaff/Mithal/Neis:05}.}
We estimate the parameters with a standard quasi-maximum likelihood (QML) method widely used in the empirical term structure of interest rate literature
(for similar treatments, see \cite{Chen/Scott:93}, \cite{Pearson/Sun:94}, \cite{Duffie/Singleton:97}, \cite{Duffee:02}, \cite{Zhang:04} and \cite{Pan/Singleton:06}).
Since the default intensity $\lambda_{t}$ is unobservable, we assume that the 5-year CDS premiums are measured without error.
Given the parameter set, the implied default intensity vector $\lambda_t$ can be inverted numerically.
In addition, We assume that the nonzero measurement errors $\{\epsilon_t\}$ of 1-, 3-, and 10-year default swap contracts are serially uncorrelated,
but normally distributed with zero mean and variance-covariance matrix $\Omega_\epsilon$.
Under these above assumptions, the conditional maximum likelihood is,
\begin{eqnarray*}
L &=& \sum_{t=2}^T \ln f_{\lambda} (\lambda_t|\lambda_{t-1}) - \sum_{t=2}^T \ln |J_t^S| - \frac{3(T-1)}{2} \ln(2\pi) - \frac{T-1}{2} \ln|\Omega_\epsilon| - \frac{1}{2} \sum_{t=2}^T \epsilon_t' \Omega_\epsilon^{-1} \epsilon_t
\end{eqnarray*}
where $f_\lambda(\lambda_t|\lambda_{t-1})$ is the probability density of state vector $\lambda_t$ conditional on $\lambda_{t-1}$ and $J_t^S$ is the Jacobian of the transformation at time $t$.
$\Omega_\epsilon$ is decomposed into lower and upper triangular matrices. We denote the $(i,j)th$ element of the lower triangular matrix as $\{c_{i,j}\}$.
The conditional densities, $f_\lambda(\lambda_t|\lambda_{t-1})$, are non-central chi-square, as shown in \cite{Cox/Ingersoll/Ross:85}.
For $t = 2, \cdots, T$, the exact non-central chi-square density of $\lambda_t$ conditional on $\lambda_{t-1}$ is
\begin{eqnarray*}
f_\lambda(\lambda_t|\lambda_{t-1}) &=& d e^{-(u + v)} \left(\frac{v}{u}\right)^{\frac{1}{2}q} \cdot I_{q}\left(2 \sqrt{u\cdot v}\right)\\
d &=& \frac{2\kappa}{\sigma^2 \left[1- e^{- \kappa \Delta t}\right]}\\
u &=& d \lambda_{t-1}e^{- \kappa \Delta t}\\
v &=& d \lambda_{t}\\
q &=& \frac{2 \kappa \theta}{\sigma^2}-1
\end{eqnarray*}
$\Delta t$ is the time interval between $t$ and $t-1$, and $I_q(\cdot)$ is the modified Bessel function of the first kind of order $q$.
The modified Bessel function is approximated by the normal (see \cite{Zhang:04} for details.)
For the estimation using CDS data, we first assume independence between the short rate process and default intensity in equation (\ref{non_par1}).\footnote{
See \cite{Longstaff/Mithal/Neis:05} and \cite{Pan/Singleton:06} for similar approach.}
Upon estimating the parameters, we can construct a bond price following equation (\ref{fixed_1}).
We provide the estimation results in Table (\ref{mle_result}).
\begin{center}
\mbox{[Insert Table (\ref{mle_result}) here]}
\end{center}
In contrast to time series approaches, we also use a cross-sectional approach as used in \cite{Singh:03b}, \cite{Chan-Lau/03}, \cite{Andritzky/Singh:06}, \cite{Das/Hanouna:06} and \cite{Nashikkar/Subrahmanyam/Mahanti:07}.
The development of the CDS market makes it possible to extract the default probability without relying on a particular model of credit risk and specific parameterizations.
Using the term structure of CDS premiums on a given day, we can calibrate the default probability without statistical parameter estimation.
CDS premiums are a function of the short rate process, the default probability and the loss given default.
With pre-specified level of loss given default and zero rate from the market, we can effectively extract the default probability.
Only information on a given trading day is used, which is the common way traders would calibrate any derivatives pricing model in actual practice.\footnote{
See \cite{Das/Hanouna:06} and \cite{Nashikkar/Subrahmanyam/Mahanti:07} for more details.}
This approach is especially applicable for the purpose of this study,
since the default probability and discount rate prevailing each day are sufficient for the pricing of CDS premiums and bond as in equation (\ref{non_par1}) and (\ref{fixed_1}).
As in equation (\ref{e_intensity1}) and (\ref{e_intensity2}), time series approaches impose restrictions on the evolution of the default probability, which are redundant for the purpose of this study.
It is well known that the time series approach cannot match the all cross section of prices.
Its performance gets poor especially when the stationarity of the parameters and models become weak and it coincide with the period of crisis.
We use the results from the cross-sectional approach for the remainder of the paper.
\subsection{Bond Yield Spreads and Implied Bond Yield Spreads}
Bond yield spreads are defined as follows:
\begin{eqnarray*}
P_B&=& \frac{C_B}{M_B}
\sum_{j=1}^{M_B\cdot (\tau_B - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_B}}(r(s) + BYS) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[e^{-\int_{t}^{\tau_B}(r(s) + BYS) ds}\bigg|\mathcal{F}_t\right]
\end{eqnarray*}
As shown before, bond yield spreads are not equal to CDS premiums.
They can be negatively or positively biased depending on accrued
payments and bond prices. The disparity between CDS premiums and
bond yields spreads (BYS) gets bigger as the credit quality of a
reference entity deteriorates.
To adjust the disparity between CDS premiums and bond yield spreads,
we construct `implied bond yield spreads' (IBYS). Following estimation, we calculate the `implied price' of
a bond, $\widehat{P}_B$, via the following equation:
\begin{eqnarray*}
\widehat{P}_B&=& \frac{C_B}{M_B}\sum_{j=1}^{M_B\cdot (\tau_B - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_B}}r(s) + \lambda(s) ds}\bigg|\mathcal{F}_t\right] + E^\mathbb{Q}\left[e^{-\int_{t}^{{\tau_B}}r(s) \lambda(s) ds}\bigg|\mathcal{F}_t\right]\nonumber\\
&&+ E^\mathbb{Q}\left[\int_{t}^{\tau_c} (1-L)\lambda(\mu) e^{-\int_t^{\mu} r(s) + \lambda(s) ds} d\mu \bigg|\mathcal{F}_t\right]
\end{eqnarray*}
The implied bond yield spreads (IBYS), are then calculated from the
following equation.
\begin{eqnarray*}
\widehat{P}_B&=&\frac{C_B}{M_B}
\sum_{j=1}^{M_B\cdot (\tau_B - t)} E^\mathbb{Q}\left[e^{-\int_{t}^{{t}+\frac{j}{M_B}}(r(s) + IBYS) ds}\bigg|\mathcal{F}_t\right]+E^\mathbb{Q}\left[e^{-\int_{t}^{\tau_B}(r(s) + IBYS) ds}\bigg|\mathcal{F}_t\right]
\end{eqnarray*}
Implied bond yield spreads should be close to actual bond yield spreads.\footnote{ As the
significance of other factors such as liquidity, repo special and the value of CTD options becomes larger as credit quality deteriorates, the pricing equation for CDS premiums and
bond yield spreads may become less precise. These factors could induce the two measures not to be
exactly equal.} Our results presented below demonstrate that the
IBYS and BYS are indeed close to being equal during normal periods.
Equality is violated during severe crisis periods.\footnote{
There are multiple bonds outstanding for each EM sovereign. For the
analysis at the country level, we average the implied bond yield
spread of each bond in our sample. This averaging reduces the
bond-specific bias.}
We provide the basis statistics of bond yield spreads (BYS), implied
bond yield spreads (IBYS) and CDS in Table (\ref{basic_stat}).
\begin{center}
\mbox{[Insert Table (\ref{basic_stat}) here]}
\end{center}
\subsection{Dynamic Relations between CDS and Bonds}
We first run two regressions: between CDS premiums and bond yield spreads and between implied bond yield spreads and bond yields spreads.
\begin{eqnarray}
CDS_t &=& \alpha + \beta \cdot BYS_t + \epsilon_t \nonumber\\
IBYS_t &=& \alpha + \beta \cdot BYS_t + \epsilon_t
\end{eqnarray}
Results are provided in Table(\ref{regression}).
\begin{center}
\mbox{[Insert Table (\ref{regression}) here]}
\end{center}
Bond yield spreads are highly auto-correlated and close to being unit root processes.
Assuming a single mean, implied yield spreads and CDS premiums for Mexico are rejected at the 1\% significance level.
Assuming a trend, yield spreads, implied yield spreads and CDS premiums are rejected for Mexico at the 1\% significance
level. Turkey is rejected at the 5\% significance level.
\begin{center}
\mbox{[Insert Table (\ref{uint_root}) here]}
\end{center}
When two series are characterized by unit roots, we first perform a
cointegration rank test as proposed by \cite{Johansen:91}. Test
results are provided in the second column in Table \ref{coint_test}.
The null hypothesis is that pairs of two processes are not
cointegrated and it is rejected in most cases, implying that they
are cointegrated.\footnote{
\cite{Chan-Lau/Kim:04} study the relation between CDS, bonds and
equities for seven EM sovereigns. Cointegration between CDS premiums
and bond spreads is rejected for Mexico, Philippine and Turkey. The
countries in their study are Brazil, Venezuela, Mexico, Colombia,
Russia, Philippine and Turkey and the sample period is from March,
2001 to May, 2003. In their study, they use the JP Morgan Chase
Emerging Market Bond Index Plus (EMBI+) and do not match maturities.
The inclusion of Brady bonds in EMBI+ and/or the maturity mismatch
may cause the rejection of cointegration. }
\begin{center}
\mbox{[Insert Table (\ref{coint_test}) here]}
\end{center}
When the series pass the cointegration test, we impose the
restriction that the cointegration vector is [1 -1 d].
If implied bond yield spreads and actual bond yield spreads are not
cointegrated with [1 -1 d], then it implies that
the CDS and bond markets price credit risk differently in excess of a constant
amount or that there are time-varying non-transient factors differently affecting
prices in the CDS and bond markets.\footnote{\cite{Blanko/Brennan/Marsh:05} mention that time varying CTD option values and repo costs may be such time-varying non-transient factors.}
Test results are provided in the third column of Table (\ref{coint_test}). The
restriction on the CDS premiums and bond yield spreads is rejected
for Argentina, Brazil, Chile, Colombia, Peru, Russia and Venezuela
at the 1\% significance level. Mexico, Malaysia, Panama and Turkey
are rejected at the 5\% significance level. The rejection of 11
cases out of 16 is in sharp contrast with previous empirical studies
of investment grade corporates.\footnote{ In previous studies of high grade corporates, this
restriction on cointegration between CDS premiums and bond yield
spreads is rarely rejected. In Blanko et al.(2005), out of 16 U.S.
companies studied, only three reject the restriction at the $5\%$
level and none reject it at the $1\%$ level. For the 10 European
entities satisfying the cointegration restriction, the restriction
is rejected in only two cases at the $5\%$ level and none at the
$1\%$ level.} Note that the countries for which the restriction is
rejected are those which experienced a big credit quality change or, in
other words, a large price change.\footnote{ When sorted in terms of
the differences between maximum bond yield spreads and minimum bond
yield spreads during the sample period, the results are following.
The number in each parenthesis is the difference. AR (33.35):
rejected at 1\%, BR (25.23): rejected at 1\%, VE (15.44): rejected
at 1\%, RU (12.02): rejected at 5\%, TR (10.22): rejected at 1\%, CO
(10.05): rejected at 1\%, PE$_1$ (7.09): rejected at 1\%, MX (5.87):
not rejected, PA (5.39): rejected at 5\%, PH (5.12): not rejected,
ZA (3.15): not rejected, CL (2.21): rejected at 1\%, ID (2.16): NA,
PE$_2$ (1.59): not rejected, KR (1.54): not rejected, PL (1.34):
rejected at 5\%, MY (1.16): rejected at 5\%, CN (0.73): not
rejected.}
These results confirm that the parity relationship between CDS
premiums and bond yield spreads is not valid, especially when prices
are not near par. As in Figures (\ref{ar_all}) to
(\ref{ve_all}), which display plots of CDS premiums and bond yield
spreads for three countries with large differences of max-min bond
yield spreads during the sample period, the CDS premiums are bigger
than the bond yield spreads when the bond yield spreads are around
their peaks, as our pricing model suggests.\footnote{ Russia is the exception in that
it displays negative basis during 2001.}
\begin{center}
\mbox{[Insert figure (\ref{ar_all}) here]}
\end{center}
\begin{center}
\mbox{[Insert figure (\ref{br_all}) here]}
\end{center}
\begin{center}
\mbox{[Insert figure (\ref{ve_all}) here]}
\end{center}
These results show that it is difficult to test directly whether the CDS and bond markets for EM Sovereigns price credit risk equally by simply comparing CDS premiums and bond yield spreads.
By comparing the IBYS with the bond yield spreads (BYS), we can test more precisely whether the bond and CDS markets price credit risk equally.
As in Figures (\ref{ar_all}) to (\ref{ve_all}), the differences between IBYS and BYS are smaller than the differences between CDS premiums and BYS.
As a formal test, we impose the restriction that the cointegration
vector on the IBYS and the BYS is [1 -1 d]. 5 cases out of 16
reject the restriction at the 1\% significance level. Test results
are provided in the third column of Table \ref{coint_test}. The
parity relation is restored in the cases of Mexico, Malaysia, Russia and Turkey, which were formerly rejected at the 1\% and/or 5\% significance level.
The parity relationship is improved for most countries except Argentina.
However, Argentina, Brazil, Chile, Columbia, Panama, Peru and Venezuela still reject the restriction in our sample.
Interestingly, these are countries in Latin America, a region that suffered from an actual default by Argentina and credit crises in Brazil and Venezuela.
Disparity occurs mainly during the crisis with positive basis and the parity is restored when we exclude the crisis periods.
As shown in the figure (\ref{contagion}), CDS premiums for these countries move together.
Contagion in the CDS market may be a partial explanation for the break down of parity relationship in the region.
\begin{center}
\mbox{[Insert figure (\ref{contagion}) here]}
\end{center}
When we check the correlations of the IBYS among each pair of countries, they are very high.
This implies that CDS premiums are moving together.
In addition, we also find that the correlation of the BYS is also very high.
\cite{Longstaff/Pan/Pederson/Singleton:07} also find that Sovereign credit spreads are surprisingly highly correlated and there is little or no country-specific credit risk premium in their CDS data.
Our results complement the finding that the bond yield spreads are highly correlated as well.
The difference in the movement of the IBYS and BYS comes from the volatility, not the direction of the movement.
As shown in the table (\ref{corr_test}), the ratio of the covariance between the IBYS and BYS is generally greater than one.
This implies that the size of the movement is greater in the BYS, considering the similar magnitude of the correlation.
Differences in the liquidity or institutional features of each market may affect the price movement in each market.
\begin{center}
\mbox{[Insert Table (\ref{corr_test}) here]}
\end{center}
\subsection{Liquidity and the Limit of Arbitrage}
When we impose the more severe restriction that the cointegration vector is [1 -1 0], the restrictions are all rejected.
These test results are provided in the final column of Table \ref{coint_test}.
This is in sharp contrast with the test results with a cointegration vector of [1 -1 d].
We first find that the basis between the implied bond yield spread and bond yield spread is quite persistent with high auto correlation with high order as in Table (\ref{whitenoise}).
\begin{center}
\mbox{[Insert Table (\ref{whitenoise}) here]}
\end{center}
We also run two regressions: between the change of CDS premiums and the change of bond yield spreads; and between the change of implied bond yield spreads and the change of bond yields spreads.
\begin{eqnarray}
\Delta CDS_t &=& \alpha + \beta \cdot \Delta BYS_t + \epsilon_t \nonumber\\
\Delta IBYS_t &=& \alpha + \beta \cdot \Delta BYS_t + \epsilon_t
\end{eqnarray}
Results are provided in Table(\ref{regression2}). It is notable that $R^2$ is low and the coefficient is not around one.
\begin{center}
\mbox{[Insert Table (\ref{regression2}) here]}
\end{center}
\cite{Blanko/Brennan/Marsh:05}, mention that non-zero `d' may come from differences in the choice of the reference riskless rate.
However if this is the main reason for it, the magnitude and sign of `d' should be similar for each entity for similar periods, which is not the case in our study.
The sign and magnitude of the average basis are different as shown in Table (\ref{liquidity}).
Other than the choice of reference riskless rates, different liquidity and institutional features could also cause a non-zero `d.'
For investment grade U.S. corporates, the liquidity difference between the CDS and bond markets has been thought to be the main reason for the basis.
Let us check whether liquidity in each market can explain the sign and the magnitude of the difference here.\footnote{
\cite{Hull/Predescu/White:04} test if the difference between the 5-year bond par yield and the 5-year CDS quote equals the 5-year risk free rate.
They find that the implied risk-free rate rises as the credit quality of the reference entity declines in cross section.
They interpret this finding as the existence of counter party default risk in a CDS.
They conclude that the results may be influenced by other factors such as differences in the liquidities of the bonds issued by reference entities in different rating categories.
\cite{Longstaff/Mithal/Neis:05} find that the `basis' is time varying and strongly related to measures of
bond-specific illiquidity as well as to macroeconomic measures of bond-market liquidity.}
In Table \ref{liquidity}, we list the differences between the IBYS and the BYS, the bid-ask spreads of bonds and those of CDS premiums.
Bid-ask spreads for bonds are the spreads between the yields to maturity from bid and ask bond prices, respectively.
\begin{center}
\mbox{[Insert Table (\ref{liquidity}) here]}
\end{center}
In Brazil, Chile, Columbia, Panama and Peru, countries where cointegration was rejected,
the magnitude of the IBYS - BYS difference is bigger in many cases than the transaction cost measured by the sum of the bid-ask spread in both markets when those are at the maximum.
A similar pattern is observed for Mexico, Malaysia, Philippine, Turkey and South Africa.\footnote{
When it comes to the mean, Brazil, Columbia, Peru and Turkey show a similar pattern.}
Arbitrageurs might have been able to make profits by shorting bonds and CDS protection, exploiting the positive basis, had they been able to trade.
Traders typically use a reverse repo contract to short bonds.
Traders borrow a bond to short.
When they borrow the bond, they put up collateral in cashl.\footnote{
\cite{Nashikkar/Pedersen:07} find that the cash collateral is in excess of 100\% of the market value of the security to minimize counterparty credit risk.
That is, they find that cash collateral is often larger than the value of the borrowed security (usually 102\%).}
Interest is paid on the cash and it may be lower than the general interest rates.
This makes the shorting costly.
If there is an accompanying cost for the bond short sales, it may prevent the arbitrage.
We find that repo rates decrease as credit quality deteriorates.
The repo cost effectively eliminated the arbitrage opportunity in Chile and Panama.
Brazil, Venezuela and Peru, however, show a persistent positive basis above the bid-ask spread and repo cost during the crisis period.
\begin{center}
\mbox{[Insert figure (\ref{repo_cost}) here]}
\end{center}
There are other factors that
might affect the basis. The cheapest-to-deliver (CTD) option, new
issues of bonds and counter party risks are among
them. CTD options move deeper into the money and become more
valuable whenever the credit quality of a reference entity
deteriorates.\footnote{\cite{Singh/Andritzky:05} studied the extent of disparity by using the CTD bond.}
New issues of bonds may bring higher hedging demand,
resulting in a corresponding increase in demand for CDS protection and an
increase in premiums. New issues may also improve liquidity in the
bond market and reduce `liquidity' premiums in the bonds' yield
spreads. While the factors mentioned
above tend to increase the basis, counterparty risk may reduce it.
The possibility that the CDS protection seller might default may
cause protection buyers to require some compensation for that risk too
and reduce the CDS premiums that they would be willing to pay.
\section{Conclusion}
We show that most of the time the CDS and bond markets price credit
risk for the Emerging Market Sovereigns equally. The basis, defined
as the difference between the CDS premiums and bond yield spreads,
is biased away from zero when the price is not at par. To correct
the bias in bond yield spreads, we constructed `implied bond yield
spreads' using the CDS premiums for various maturities. Although
adjusted prices in the CDS and bond markets were fairly equal over a
wide range of changes in credit quality in each entity, we found
disparities in Argentina and Brazil when the likelihood of a credit
event was very high. During the high yield period in Brazil from
2002 to 2003, CDS premiums and bond yield spreads moved together and
affected all other regional Latin American countries. This
co-movement resulted in a disparity in other countries in the region.
We find that repo costs allowed the positive basis to persist by making short sales of bond costly.
Assessing the empirical impact of cheapest-to-deliver (CTD) options, of new issuance of bonds, of other transaction costs and counter party risks remain for further research.
\clearpage
\bibliographystyle{plainnat}
\bibliography{js_bib}
\clearpage
\begin{table}[t]
\caption{Maximum Likelihood Estimation Result} \label{mle_result} \hspace{0.5cm} {\par
This table provides the estimation results for the CIR specification parameters.
Standard deviations of the estimator are in parentheses.
\\
\par}
\centering
\scriptsize
% Table generated by Excel2LaTeX from sheet 'Sheet2'
\begin{tabular}{|r|rrrrrrr|}
\hline
& $\kappa$ & $\theta$ & $\eta$ & $\sigma$ & c11 & c22 & c33 \\
\hline
AR & 0.030 & 0.694 & -2.144 & 1.295 & 0.106 & 0.031 & 0.042 \\
& (0.000) & (0.004) & (0.017) & (0.005) & (0.004) & (0.002) & (0.003) \\
BR & 0.187 & 0.150 & -0.066 & 0.946 & 0.199 & 0.037 & 0.047 \\
& (0.007) & (0.005) & (0.141) & (0.047) & (0.003) & (0.001) & (0.002) \\
CL & 0.020 & 0.020 & -0.012 & 0.078 & 0.468 & 0.468 & 0.468 \\
& (0.007) & (0.008) & (0.048) & (0.004) & (0.035) & (0.035) & (0.035) \\
CN & 0.134 & 0.012 & -0.010 & 0.204 & 0.082 & 0.083 & 0.101 \\
& (0.001) & (0.000) & (0.005) & (0.007) & (0.006) & (0.006) & (0.009) \\
CO & 0.124 & 0.116 & -0.001 & 0.360 & 0.111 & 0.010 & 0.297 \\
& (0.002) & (0.001) & (0.000) & (0.012) & (0.002) & (0.000) & (0.017) \\
KR & 0.089 & 0.016 & 0.011 & 0.098 & 0.079 & 0.080 & 0.187 \\
& (0.002) & (0.000) & (0.011) & (0.005) & (0.006) & (0.006) & (0.014) \\
MY & 0.032 & 0.032 & -0.008 & 0.070 & 0.061 & 0.061 & 0.066 \\
& (0.001) & (0.001) & (0.017) & (0.004) & (0.005) & (0.005) & (0.006) \\
PA & 0.035 & 0.074 & -0.144 & 0.100 & 0.021 & 0.011 & 0.014 \\
& (0.001) & (0.001) & (0.001) & (0.001) & (0.001) & (0.001) & (0.001) \\
PE & 0.011 & 0.124 & -0.472 & 0.188 & 0.013 & -0.018 & 0.013 \\
& (0.000) & (0.002) & (0.006) & (0.001) & (0.001) & (0.001) & (0.001) \\
PH & 0.133 & 0.153 & -0.022 & 0.259 & 0.034 & -0.044 & 0.217 \\
& (0.000) & (0.002) & (0.000) & (0.000) & (0.002) & (0.003) & (0.014) \\
PL & 0.026 & 0.001 & -0.011 & 0.124 & 0.099 & 0.099 & 0.150 \\
& (0.068) & (0.010) & (0.090) & (0.013) & (0.009) & (0.009) & (0.015) \\
RU & 0.008 & 0.101 & -0.578 & 0.198 & 0.010 & 0.025 & 0.060 \\
& (0.001) & (0.007) & (0.010) & (0.002) & (0.000) & (0.001) & (0.003) \\
TR & 0.070 & 0.129 & -0.261 & 0.275 & 0.013 & 0.005 & 0.168 \\
& (0.001) & (0.001) & (0.003) & (0.002) & (0.000) & (0.000) & (0.008) \\
VE & 0.207 & 0.156 & -0.017 & 0.878 & 0.195 & 0.024 & 0.060 \\
& (0.062) & (0.007) & (0.117) & (0.000) & (0.003) & (0.001) & (0.002) \\
ZA & 0.130 & 0.007 & -0.009 & 0.345 & 0.089 & 0.090 & 0.135 \\
& (0.045) & (0.008) & (0.156) & (0.024) & (0.007) & (0.007) & (0.011) \\
\hline
\end{tabular}
\newline
\newline
\scriptsize
\par
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}\par
\end{table}
\clearpage
\begin{table}[t]
\caption{Basic Statistics} \label{basic_stat} \hspace{0.5cm} {\par
This table provides the basic statistics of yield spreads of
sovereign bonds, implied yield spreads and CDS premiums. Yield
spreads are averages of bid and ask spreads over riskless US
Treasury zero coupon rates. CDS premiums are averages of bid and ask
premiums. To calculate the implied yield spread, the prices of bonds
are estimated first. Using these prices, implied bond yield spreads
are then calculated.
\\
\par}
\scriptsize
\begin{tabular}{|c|rr|c|rrr|rrr|rrr|}
\hline
& \multicolumn{ 2}{c|}{Date} & N & \multicolumn{ 3}{c}{ BYS (\%) } & \multicolumn{ 3}{|c}{ IBYS (\%) } & \multicolumn{ 3}{|c|}{ CDS Premiums (\%) } \\
country & Begin & End & & Mean & MIN & MAX & Mean & MIN & MAX & Mean & MIN & MAX \\
\hline
AR & 3/29/1999 & 11/30/2001 & 667 & 9.26 & 4.93 & 36.62 & 9.44 & 4.63 & 31.44 & 9.92 & 4.08 & 53.61 \\
BR & 11/16/1998 & 1/13/2006 & 1788 & 7.73 & 1.34 & 25.57 & 7.95 & 1.46 & 28.22 & 8.20 & 1.43 & 37.48 \\
CL & 5/1/2002 & 1/13/2006 & 927 & 1.01 & 0.41 & 2.60 & 0.93 & 0.13 & 3.46 & 0.91 & 0.15 & 3.43 \\
CN & 4/10/2002 & 1/13/2006 & 942 & 0.61 & 0.03 & 1.02 & 0.36 & 0.19 & 0.65 & 0.35 & 0.20 & 0.57 \\
CO & 10/31/2000 & 1/13/2006 & 1297 & 4.44 & 1.22 & 11.00 & 5.43 & 1.44 & 13.19 & 5.26 & 1.41 & 13.31 \\
KR & 2/26/2002 & 1/13/2006 & 967 & 0.88 & 0.52 & 1.91 & 0.54 & 0.19 & 1.90 & 0.54 & 0.20 & 1.95 \\
MX & 11/16/1998 & 1/13/2006 & 1788 & 2.43 & 0.56 & 6.36 & 2.62 & 0.53 & 11.93 & 2.45 & 0.51 & 12.26 \\
MY & 1/29/2003 & 1/13/2006 & 741 & 0.79 & 0.47 & 1.64 & 0.56 & 0.20 & 1.88 & 0.54 & 0.20 & 1.80 \\
PA & 1/2/2001 & 1/13/2006 & 1255 & 3.25 & 1.18 & 6.14 & 3.46 & 1.29 & 7.11 & 3.38 & 1.28 & 7.05 \\
PE & 2/6/2002 & 1/13/2006 & 985 & 3.74 & 1.22 & 8.91 & 4.47 & 1.48 & 10.47 & 4.44 & 1.48 & 11.07 \\
PH & 1/11/2001 & 1/13/2006 & 1250 & 4.09 & 1.83 & 6.39 & 4.16 & 1.84 & 6.21 & 4.13 & 1.86 & 6.23 \\
PL & 6/28/2002 & 1/13/2006 & 886 & 0.93 & 0.38 & 2.29 & 0.42 & 0.11 & 1.12 & 0.43 & 0.12 & 1.02 \\
RU & 1/2/2001 & 1/13/2006 & 1255 & 3.87 & 0.58 & 12.36 & 3.62 & 0.37 & 10.87 & 3.51 & 0.43 & 10.82 \\
TR & 1/2/2001 & 1/13/2006 & 1255 & 5.30 & 1.11 & 11.16 & 6.23 & 1.22 & 13.69 & 5.99 & 1.18 & 13.91 \\
VE & 11/16/1998 & 1/13/2006 & 1788 & 8.24 & 1.58 & 18.40 & 8.45 & 1.64 & 21.65 & 8.41 & 1.62 & 22.72 \\
ZA & 3/25/2002 & 1/13/2006 & 948 & 1.41 & 0.54 & 3.73 & 1.27 & 0.42 & 2.83 & 1.27 & 0.41 & 2.73 \\
\hline
\end{tabular}
\newline
\newline
\scriptsize
\par
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\par
\end{table}
\clearpage
\begin{table}[t]
\caption{OLS estimation} \label{regression} \hspace{0.5cm} {\par This
table provides the regression coefficient and $R^2$ of two regression.$CDS_t = \alpha + \beta \cdot BYS_t + \epsilon_t$ and $IBYS_t = \alpha + \beta \cdot BYS_t + \epsilon_t$.
Number in the parenthesis is the OLS standard error of the estimator.
\\
\par}
\centering \scriptsize
\begin{tabular}{|r|rrr|rrr|}
\hline
country & \multicolumn{ 3}{c}{CDS Vs. BYS} & \multicolumn{ 3}{|c|}{ IBYS vs. BYS } \\
\hline
& $R^2$ & $\widehat{\alpha}$ & $\widehat{\beta}$ & $R^2$ & $\widehat{\alpha}$ & $\widehat{\beta}$ \\
\hline
AR & 0.97 & -0.038 & 1.475 & 0.97 & 0.005 & 0.968 \\
& & (0.001) & (0.010) & & (0.001) & (0.007) \\
BR & 0.97 & -0.014 & 1.347 & 0.98 & 0.003 & 1.083 \\
& & (0.000) & (0.006) & & (0.000) & (0.004) \\
CL & 0.95 & -0.006 & 1.530 & 0.95 & -0.007 & 1.584 \\
& & (0.000) & (0.011) & & (0.000) & (0.012) \\
CN & 0.83 & 0.000 & 0.712 & 0.90 & -0.002 & 0.952 \\
& & (0.000) & (0.011) & & (0.000) & (0.010) \\
CO & 0.95 & 0.003 & 1.136 & 0.96 & 0.003 & 1.162 \\
& & (0.000) & (0.007) & & (0.000) & (0.007) \\
KR & 0.80 & -0.001 & 0.846 & 0.84 & -0.001 & 0.919 \\
& & (0.000) & (0.014) & & (0.000) & (0.013) \\
MX & 0.83 & -0.001 & 0.981 & 0.87 & -0.002 & 1.094 \\
& & (0.000) & (0.011) & & (0.000) & (0.010) \\
MY & 0.85 & -0.005 & 1.340 & 0.86 & -0.005 & 1.391 \\
& & (0.000) & (0.021) & & (0.000) & (0.021) \\
PA & 0.89 & 0.001 & 1.017 & 0.91 & 0.000 & 1.083 \\
& & (0.000) & (0.010) & & (0.000) & (0.010) \\
PE & 0.96 & 0.001 & 1.219 & 0.96 & 0.001 & 1.226 \\
& & (0.000) & (0.008) & & (0.000) & (0.008) \\
PH & 0.86 & 0.010 & 0.866 & 0.88 & 0.010 & 0.925 \\
& & (0.000) & (0.010) & & (0.000) & (0.010) \\
PL & 0.89 & -0.001 & 0.797 & 0.88 & -0.002 & 0.938 \\
& & (0.000) & (0.009) & & (0.000) & (0.012) \\
RU & 0.98 & 0.002 & 0.910 & 0.98 & 0.001 & 0.956 \\
& & (0.000) & (0.004) & & (0.000) & (0.004) \\
TR & 0.94 & 0.001 & 1.080 & 0.95 & 0.002 & 1.117 \\
& & (0.000) & (0.008) & & (0.000) & (0.007) \\
VE & 0.98 & -0.002 & 1.130 & 0.98 & -0.001 & 1.117 \\
& & (0.000) & (0.007) & & (0.000) & (0.006) \\
ZA & 0.91 & 0.000 & 0.895 & 0.93 & -0.001 & 0.942 \\
& & (0.000) & (0.009) & & (0.000) & (0.008) \\
\hline
\end{tabular}
\newline
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{Unit Root Test} \label{uint_root} \hspace{0.5cm} {\par This
table provides the `Dickey Fuller Tau' statistics and unit root test
results. The null hypothesis is that each process follows a unit
root process with single mean or trend.
\\
\par}
\centering \scriptsize
\begin{tabular}{|c|cc|cc|cc|}
\hline
Country & \multicolumn{ 2}{c}{ Yield Spread } & \multicolumn{ 2}{|c}{ Implied Yield Spread } & \multicolumn{ 2}{|c|}{ CDS Premium } \\
& Single Mean & Trend & Single Mean & Trend & Single Mean & Trend \\
\hline
AR & 2.92 & 1.46 & 1.60 & 0.18 & 1.81 & 0.53 \\
BR & -1.63 & -1.89 & -0.99 & -1.27 & -1.35 & -1.52 \\
CL & -0.89 & -2.64 & -0.88 & -2.40 & -0.88 & -2.51 \\
CN & -1.85 & -2.19 & -1.47 & -2.42 & -1.11 & -2.77 \\
CO & -1.39 & -2.43 & -1.12 & -2.38 & -1.28 & -2.46 \\
KR & -1.70 & -3.39 & -2.09 & -3.27 & -1.95 & -3.09 \\
MX & -2.49 & -4.39** & -3.91** & -4.68** & -4.44** & -5.08** \\
MY & -2.28 & -2.68 & -2.31 & -1.88 & -2.02 & -1.68 \\
PA & -0.94 & -2.68 & -0.73 & -2.13 & -0.82 & -2.17 \\
PE & -0.95 & -2.27 & -0.98 & -2.46 & -1.06 & -2.49 \\
PH & -1.40 & -2.81 & -1.54 & -2.75 & -1.66 & -2.77 \\
PL & -2.40 & -2.20 & -1.79 & -1.77 & -1.58 & -1.99 \\
RU & -2.37 & -2.35 & -2.18 & -2.43 & -2.29 & -2.83 \\
TR & -1.07 & -3.48* & -1.26 & -3.09 & -1.50 & -3.30 \\
VE & -1.09 & -1.62 & -1.90 & -2.23 & -2.07 & -2.36 \\
ZA & -1.37 & -2.13 & -1.07 & -2.38 & -0.82 & -2.39 \\
\hline
\end{tabular}
\newline
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{Cointegration Test} \label{coint_test} \hspace{0.5cm} {\par
The second column provides the results for the Johansen Test, where
the null hypothesis is that no two process are cointegrated. The
third column contains results for the hypothesis that the
restriction on the cointegration vector is [1 -1 d]. The final
column provides results for the hypothesis that the restriction on
the cointegration vector is [1 -1 0].
\\
\par}
\begin{center} \scriptsize
\begin{tabular}{|c|ll|ll|l|}
\hline
& \multicolumn{ 2}{c}{ Johansen test } & \multicolumn{ 2}{|c}{ Restriction: [1 -1 d] } & \multicolumn{ 1}{|c|}{ Restriction: [1 -1 0] } \\
Country & BYS and IBYS & BYS and CDS & BYS and IBYS & BYS and CDS & BYS and IBYS \\
\hline
AR & 35.8 & 155.3 & 26.0** & 7.1** & 30.9** \\
BR & 66.2 & 57.8 & 15.7** & 20.0** & 26.1** \\
CL & 26.0 & 25.5 & 10.5** & 12.3** & 10.7** \\
CN & 73.6 & 41.2 & 0.5 & 0.9 & 18.6** \\
CO & 27.8 & 28.5 & 8.8** & 7.0** & 17.1** \\
KR & 31.1 & 26.5 & 0.0 & 0.0 & 7.3** \\
MX & 36.2 & 39.2 & 1.0 & 5.8* & 3.9** \\
MY & 19.9 & 22.2 & 0.3 & 2.9* & 10.2** \\
PA & 36.2 & 35.1 & 6.8* & 3.8* & 8.0** \\
PE & 72.3 & 77.6 & 30.3** & 32.4** & 38.5** \\
PH & 53.8 & 48.7 & 0.1 & 0.2 & 14.0** \\
PL & 66.3 & 78.0 & 0.6 & 1.1 & 6.3** \\
RU & 60.2 & 58.4 & 0.3 & 6.5** & 13.8** \\
TR & 29.3 & 25.1 & 5.9 & 2.8* & 7.0** \\
VE & 49.4 & 55.4 & 2.9* & 4.9** & 9.2** \\
ZA & 60.0 & 61.9 & 0.0 & 0.2 & 16.1** \\
\hline
\end{tabular}
\end{center}
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{Correlation and Covariance} \label{corr_test} \hspace{0.5cm} {\par
The first panel provides the correlation between the implied bond yield spread of each country,
while the second panel with the correlation between the bond yield spread.
The third panel show the ratio of covariance between implied bond yield spread and bond yield spread.
\\
\par}
\begin{center} \scriptsize
% Table generated by Excel2LaTeX from sheet 'Sheet2'
Panel A: Correlation between the IBYS
\\
\begin{tabular}{|c|rrrrrr|}
\hline
Country & BR & CL & CO & PA & PE & VE \\
\hline
BR & 1.00 & 0.97 & 0.88 & 0.92 & 0.97 & 0.78 \\
CL & 0.97 & 1.00 & 0.97 & 0.96 & 0.96 & 0.81 \\
CO & 0.88 & 0.97 & 1.00 & 0.95 & 0.96 & 0.79 \\
PA & 0.92 & 0.96 & 0.95 & 1.00 & 0.96 & 0.87 \\
PE & 0.97 & 0.96 & 0.96 & 0.96 & 1.00 & 0.84 \\
VE & 0.78 & 0.81 & 0.79 & 0.87 & 0.84 & 1.00 \\
\hline
\end{tabular}
\\
$ $\\
$ $\\
Panel B: Correlation between the BYS
\\
% Table generated by Excel2LaTeX from sheet 'Sheet2'
% Table generated by Excel2LaTeX from sheet 'Sheet2'
\begin{tabular}{|c|rrrrrr|}
\hline
Country & BR & CL & CO & PA & PE & VE \\
\hline
BR & 1.00 & 0.97 & 0.81 & 0.84 & 0.97 & 0.77 \\
CL & 0.97 & 1.00 & 0.95 & 0.96 & 0.97 & 0.90 \\
CO & 0.81 & 0.95 & 1.00 & 0.95 & 0.96 & 0.76 \\
PA & 0.84 & 0.96 & 0.95 & 1.00 & 0.96 & 0.81 \\
PE & 0.97 & 0.97 & 0.96 & 0.96 & 1.00 & 0.83 \\
VE & 0.77 & 0.90 & 0.76 & 0.81 & 0.83 & 1.00 \\
\hline
\end{tabular}
% Table generated by Excel2LaTeX from sheet 'Sheet2'
\\
$ $\\
$ $\\
Panel C: Covariance Ratio $({COV_{_{IBYS}}}/{COV_{_{BYS}}})$
\\
% Table generated by Excel2LaTeX from sheet 'Sheet2'
\begin{tabular}{|c|rrrrrr|}
\hline
Country & BR & CL & CO & PA & PE & VE \\
\hline
BR & 1.18 & 1.77 & 1.40 & 1.34 & 1.35 & 1.40 \\
CL & 1.77 & 2.63 & 2.06 & 1.95 & 2.00 & 1.70 \\
CO & 1.40 & 2.06 & 1.41 & 1.38 & 1.56 & 1.48 \\
PA & 1.34 & 1.95 & 1.38 & 1.26 & 1.49 & 1.46 \\
PE & 1.35 & 2.00 & 1.56 & 1.49 & 1.54 & 1.46 \\
VE & 1.40 & 1.70 & 1.48 & 1.46 & 1.46 & 1.63 \\
\hline
\end{tabular}
\end{center}
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. BR: Brazil,
CL: Chile, CO: Colombia, PA: Panama, PE: Peru, VE: Venezuela.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{Basis and Bid Ask Spreads} \label{liquidity}
\hspace{0.5cm} {\par The second column provides the differences
between implied bond yield spreads and bond yield spreads. The third
column is for the bid-ask spreads in bonds' yields-to-maturity. The final column is for the CDS contracts.
\\
\par}
\centering \scriptsize
% Table generated by Excel2LaTeX from sheet '1'
\begin{tabular}{|c|rrr|rrr|rrr|}
\hline
& \multicolumn{ 3}{|c|}{IBYS - BYS (bp)} & \multicolumn{ 3}{c}{Bond Bid Ask Spread(bp)} & \multicolumn{ 3}{|c|}{CDS Bid Ask Spread(bp)} \\
country & Mean & Min & Max & Mean & Min & Max & Mean & Min & Max \\
\hline
AR & 5.47 & -1011.57 & 403.42 & 26.56 & 1.79 & 357.62 & 50.00 & 40.00 & 110.00 \\
BR & 91.20 & -298.51 & 632.75 & 27.99 & 0.00 & 158.25 & 45.00 & 10.00 & 110.00 \\
CL & -10.48 & -60.01 & 155.83 & 11.11 & 5.00 & 22.84 & 13.00 & 10.00 & 46.00 \\
CO & 101.79 & -101.45 & 439.52 & 26.00 & 0.00 & 159.12 & 14.00 & 14.00 & 14.00 \\
PA & 21.51 & -126.03 & 200.92 & 21.75 & 0.00 & 104.04 & 30.00 & 30.00 & 30.00 \\
PE & 81.17 & -65.06 & 281.48 & 18.58 & 0.00 & 60.83 & 30.00 & 30.00 & 30.00 \\
VE & 81.76 & -282.86 & 712.50 & 64.94 & 0.00 & 451.31 & 50.00 & 20.00 & 120.00 \\
MX & 0.52 & -113.27 & 282.36 & 8.13 & 0.00 & 50.91 & 50.00 & 10.00 & 90.00 \\
CN & -20.27 & -40.12 & 11.77 & 8.54 & 3.43 & 13.56 & 10.00 & 10.00 & 10.00 \\
KR & -12.47 & -52.44 & 27.85 & 6.08 & 0.00 & 12.09 & 50.00 & 10.00 & 60.00 \\
MY & -22.83 & -51.54 & 36.55 & 5.83 & 2.00 & 12.93 & 15.00 & 10.00 & 15.00 \\
PH & 74.55 & -95.76 & 232.03 & 18.93 & 2.23 & 59.34 & N/A & N/A & N/A \\
PL & -28.31 & -56.00 & 10.99 & 11.38 & 1.37 & 27.52 & 22.00 & 6.00 & 60.00 \\
RU & -25.11 & -238.80 & 151.23 & 20.46 & 0.00 & 160.26 & 90.00 & 6.00 & 100.00 \\
TR & 90.80 & -124.18 & 502.49 & 25.17 & 0.00 & 165.30 & 55.00 & 30.00 & 60.00 \\
ZA & -16.05 & -268.82 & 264.89 & 17.50 & 0.00 & 218.45 & 20.00 & 20.00 & 20.00 \\
\hline
\end{tabular}
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{White Noise Test} \label{whitenoise} \hspace{0.5cm} {\par This
table provides the standard deviation of the basis at the second column.
Third column is the probability the basis is a white noise process for each country.
Following columns are the auto correlation coefficient.
\\
\par}
\centering \scriptsize
\begin{tabular}{|c|c|c|rrrrrr|}
\hline
Country & Std & Prob & One & Two & Three & Four & Five & Six \\
\hline
AR & 0.0102 & $<$0.0001 & 0.80 & 0.77 & 0.72 & 0.70 & 0.70 & 0.64 \\
BR & 0.0077 & $<$0.0001 & 0.95 & 0.93 & 0.91 & 0.89 & 0.87 & 0.84 \\
CL & 0.0036 & $<$0.0001 & 0.99 & 0.99 & 0.98 & 0.98 & 0.97 & 0.97 \\
CN & 0.0005 & $<$0.0001 & 0.89 & 0.82 & 0.77 & 0.71 & 0.66 & 0.62 \\
CO & 0.0069 & $<$0.0001 & 0.98 & 0.96 & 0.95 & 0.94 & 0.93 & 0.92 \\
KR & 0.0012 & $<$0.0001 & 0.95 & 0.91 & 0.88 & 0.86 & 0.83 & 0.81 \\
MX & 0.0050 & $<$0.0001 & 0.98 & 0.97 & 0.96 & 0.95 & 0.93 & 0.92 \\
MY & 0.0017 & $<$0.0001 & 0.98 & 0.98 & 0.97 & 0.96 & 0.95 & 0.95 \\
PA & 0.0047 & $<$0.0001 & 0.96 & 0.93 & 0.90 & 0.88 & 0.85 & 0.83 \\
PE & 0.0065 & $<$0.0001 & 0.98 & 0.96 & 0.95 & 0.93 & 0.92 & 0.91 \\
PH & 0.0040 & $<$0.0001 & 0.95 & 0.91 & 0.88 & 0.85 & 0.82 & 0.80 \\
PL & 0.0010 & $<$0.0001 & 0.86 & 0.84 & 0.82 & 0.81 & 0.79 & 0.80 \\
RU & 0.0044 & $<$0.0001 & 0.97 & 0.95 & 0.94 & 0.92 & 0.91 & 0.90 \\
TR & 0.0081 & $<$0.0001 & 0.98 & 0.97 & 0.96 & 0.95 & 0.94 & 0.94 \\
VE & 0.0050 & $<$0.0001 & 0.91 & 0.85 & 0.80 & 0.78 & 0.76 & 0.75 \\
ZA & 0.0019 & $<$0.0001 & 0.89 & 0.83 & 0.80 & 0.77 & 0.75 & 0.73 \\
\hline
\end{tabular}
\newline
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{table}[t]
\caption{OLS estimation} \label{regression2} \hspace{0.5cm} {\par This
table provides the regression coefficient and $R^2$ of two regression. $\Delta CDS_t = \alpha + \beta \cdot \Delta BYS_t + \epsilon_t$ and $\Delta IBYS_t = \alpha + \beta \cdot \Delta BYS_t + \epsilon_t$.
Number in the parenthesis is OLS standard error of the estimator.
\\
\par}
\centering \scriptsize
\begin{tabular}{|r|rrr|rrr|}
\hline
country & \multicolumn{ 3}{c}{CDS Vs. BYS} & \multicolumn{ 3}{|c|}{ IBYS vs. BYS } \\
\hline
& $R^2$ & $\widehat{\alpha}$ & $\widehat{\beta}$ & $R^2$ & $\widehat{\alpha}$ & $\widehat{\beta}$ \\
\hline
AR & 0.28 & 0.000 & 1.422 & 0.37 & 0.000 & 0.736 \\
& & (0.000) & (0.092) & & (0.000) & (0.039) \\
BR & 0.47 & 0.000 & 0.905 & 0.48 & 0.000 & 0.611 \\
& & (0.000) & (0.024) & & (0.000) & (0.015) \\
CL & 0.05 & 0.000 & 0.226 & 0.10 & 0.000 & 0.351 \\
& & (0.000) & (0.032) & & (0.000) & (0.036) \\
CN & 0.00 & 0.000 & 0.023 & 0.05 & 0.000 & 0.208 \\
& & (0.000) & (0.017) & & (0.000) & (0.031) \\
CO & 0.27 & 0.000 & 0.525 & 0.32 & 0.000 & 0.566 \\
& & (0.000) & (0.024) & & (0.000) & (0.023) \\
KR & 0.14 & 0.000 & 0.348 & 0.19 & 0.000 & 0.462 \\
& & (0.000) & (0.028) & & (0.000) & (0.031) \\
MX & 0.33 & 0.000 & 0.610 & 0.36 & 0.000 & 0.662 \\
& & (0.000) & (0.021) & & (0.000) & (0.021) \\
MY & 0.08 & 0.000 & 0.233 & 0.13 & 0.000 & 0.373 \\
& & (0.000) & (0.03) & & (0.000) & (0.037) \\
PA & 0.08 & 0.000 & 0.209 & 0.12 & 0.000 & 0.298 \\
& & (0.000) & (0.021) & & (0.000) & (0.023) \\
PE & 0.20 & 0.000 & 0.452 & 0.23 & 0.000 & 0.490 \\
& & (0.000) & (0.029) & & (0.000) & (0.028) \\
PH & 0.05 & 0.000 & 0.190 & 0.07 & 0.000 & 0.236 \\
& & (0.000) & (0.024) & & (0.000) & (0.024) \\
PL & 0.01 & 0.000 & 0.028 & 0.07 & 0.000 & 0.134 \\
& & (0.000) & (0.009) & & (0.000) & (0.017) \\
RU & 0.35 & 0.000 & 0.467 & 0.40 & 0.000 & 0.518 \\
& & (0.000) & (0.018) & & (0.000) & (0.018) \\
TR & 0.49 & 0.000 & 0.820 & 0.50 & 0.000 & 0.790 \\
& & (0.000) & (0.024) & & (0.000) & (0.022) \\
VE & 0.14 & 0.000 & 0.271 & 0.33 & 0.000 & 0.485 \\
& & (0.000) & (0.026) & & (0.000) & (0.027) \\
ZA & 0.03 & 0.000 & 0.060 & 0.10 & 0.000 & 0.160 \\
& & (0.000) & (0.011) & & (0.000) & (0.016) \\
\hline
\end{tabular}
\newline
\scriptsize
\begin{flushleft}
Acronyms for each country are as follows. AR: Argentina, BR: Brazil,
CL: Chile, CN: China, CO: Colombia, KR: Korea, MX:
Mexico, MY: Malaysia, PA: Panama, PE: Peru, PH: Philippines, PL:
Poland, RU: Russia, TR: Turkey,VE: Venezuela, ZA: South Africa.
\end{flushleft}
\end{table}
\clearpage
\begin{figure}[h]
\caption{Basis for $\lambda \in [0.0 ,\; 0.5]$ and $P_B \in [0.8 ,\;
1.2]$}\label{non_par_fig1}
\center
\includegraphics[width = 13cm]{non_par_fig1_1.eps}
\end{figure}
\clearpage
\begin{figure}[h]
\caption{$\frac{\partial}{\partial \lambda} (basis)$ for $\lambda
\in [0.001 ,\; 2]$ and $C \in [0.05 ,\;
0.14]$}\label{non_par_fixed_fig1}
\center
\includegraphics[width = 13cm]{non_par_fixed_fig1.eps}
\end{figure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Term Structure of CDS Premiums 1} \label{term_all}
\centering
\subfigure[Argentina]{\label{term_ar}\includegraphics[width=0.2\linewidth]{term_ar.eps}}\hfill
\subfigure[Brazil]{ \label{term_br}\includegraphics[width=0.2 \linewidth]{term_br.eps}} \hfill
\subfigure[Chile]{ \label{term_cl}\includegraphics[width=0.2\linewidth]{term_cl.eps}}\hfill
\subfigure[China]{ \label{term_cn}\includegraphics[width=0.2\linewidth]{term_cn.eps}}\hfill
\subfigure[Colombia]{ \label{term_co}\includegraphics[width=0.2\linewidth]{term_co.eps}}\hfill
\subfigure[Korea]{ \label{term_kr}\includegraphics[width=0.2\linewidth]{term_kr.eps}}\hfill
\subfigure[Mexico]{ \label{term_mx}\includegraphics[width=0.2\linewidth]{term_mx.eps}}\hfill
\subfigure[Malaysia]{ \label{term_my}\includegraphics[width=0.2\linewidth]{term_my.eps}}\hfill
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Term Structure of CDS Premiums 2}
\centering
\subfigure[Panama]{ \label{term_pa}\includegraphics[width=0.2\linewidth]{term_pa.eps}}\hfill
\subfigure[Peru]{ \label{term_pe}\includegraphics[width=0.2\linewidth]{term_pe.eps}}\hfill
\subfigure[Philippines]{ \label{term_ph}\includegraphics[width=0.2\linewidth]{term_ph.eps}}\hfill
\subfigure[Poland]{ \label{term_pl}\includegraphics[width=0.2\linewidth]{term_pl.eps}}\hfill
\subfigure[Russia]{ \label{term_ru}\includegraphics[width=0.2\linewidth]{term_ru.eps}}\hfill
\subfigure[Turkey]{ \label{term_tr}\includegraphics[width=0.2\linewidth]{term_tr.eps}}\hfill
\subfigure[Venezuela]{ \label{term_ve}\includegraphics[width=0.2\linewidth]{term_ve.eps}}\hfill
\subfigure[South Africa]{ \label{term_za}\includegraphics[width=0.2\linewidth]{term_za.eps}}\hfill
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Argentina} \label{ar_all}
\centering \subfigure[CDS cf. BYS]{
\label{ar_cds_bys}
\includegraphics[width=0.48\linewidth]{ar_cds_bys_75.eps}
} \hfill \subfigure[IBYS cf. BYS]{ \label{ar_iys_bys}
\includegraphics[width=0.48 \linewidth]{ar_iys_bys_75.eps}
}
%\hfill \subfigure[Basis]{ \label{ar_basis_bys}
%\includegraphics[width=0.48\linewidth]{ar_basis_75.eps}
%}
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Brazil} \label{br_all}
\centering \subfigure[CDS cf. BYS]{ \label{br_cds_bys}
\includegraphics[width=0.48\linewidth]{br_cds_bys_75.eps}
} \hfill \subfigure[IBYS cf. BYS]{ \label{br_iys_bys}
\includegraphics[width=0.48 \linewidth]{br_iys_bys_75.eps}
}
% \hfill \subfigure[Basis]{ \label{br_basis_bys}
%\includegraphics[width=0.48\linewidth]{br_basis_75.eps}
%}
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Venezuela} \label{ve_all}
\centering \subfigure[CDS cf. BYS]{ \label{ve_cds_bys}
\includegraphics[width=0.48\linewidth]{ve_cds_bys_50.eps}
} \hfill \subfigure[IBYS cf. BYS]{ \label{ve_iys_bys}
\includegraphics[width=0.48 \linewidth]{ve_iys_bys_50.eps}
}
%\hfill \subfigure[Basis]{ \label{ve_basis_bys}
%\includegraphics[width=0.48\linewidth]{ve_basis_50.eps}
%}
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{5 Year CDS Premiums for Latin Countries} \label{contagion}
\centering
\includegraphics[width=0.95\linewidth]{contagion.eps}
\end{sidewaysfigure}
\clearpage
\begin{sidewaysfigure}[h]
\caption{Basis and Repo Rate} \label{repo_cost}
\centering \subfigure[Argentina]{ \label{ar_repo}
\includegraphics[width=0.48\linewidth]{ar_repo.eps}
} \hfill \subfigure[Chile]{ \label{cl_repo}
\includegraphics[width=0.48 \linewidth]{cl_repo.eps}
}
\end{sidewaysfigure}
\end{document}