Essay About Recovery Value R And Implication Of Cds Spreads

Credit Default Swaps in Emerging Markets
Essay title: Credit Default Swaps in Emerging Markets
II. An Alternate Methodology: The Cheapest-to-Deliver Bonds for Argentina and Brazil …….4
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An Alternative Methodology for Proxying Recovery Value in Credit Default Swap Contracts
In times of distress when a country loses access to markets, there is evidence that credit default swap
(CDS) spreads are a leading indicator for sovereign risk than the EMBI+ sub-index for the country.
However, it is not easy to discern the variables that determine the level of CDS spreads in Emerging
Markets (EM); traders only quote the CDS spreads and not the inputs that are required to calculate
such spreads. This note provides some evidence from Argentina and Brazil that reveals inconsistency
between theory and practice in pricing CDS spreads in EM. This note suggests an alternate
methodology that links CTD (cheapest to deliver) bonds to recovery values assumed in CDS
contracts.
I. CORRELATION BETWEEN RECOVERY VALUE AND PROBABILITY OF DEFAULT
The assumptions underlying the correlation between recovery value r, and the probability of default p
is key to understanding CDS spreads. At a theoretical level, it is clear that CDS spreads are a joint
function of the r and the p where both r and p are determined jointly; in other words, the correlation
between r and p is not zero.2 Discussions with traders in EM reveal that in practice r is usually fixed
at roughly 20 cents of the face (or par) value. Mathematically, using r as a constant will result in the
correlation of r and p to be zero. Also, empirically evidence from the corporate literature has shown
(not surprising) that r is inversely correlated to p. The correlation between r and p cannot be zero in
EM when theory and corporate literature suggest that r and p are negatively correlated.
Figure 1. Credit Default Swap in Practice
Source: Bloomberg, L.P.
Figure 1 shows CDS spreads (s) =f (r, p) and explains how CDS works in 3 components:
r is the recovery value at default, p is the probability of default; and s is
2 Mathematically, the correlation between two variables, where one is a constant, is zero.
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the premium per dollar of notational protection from time zero to T that solves the following
equation:
Where
p(t) = risk-neutral default probability;
r = expected recovery rate on the reference obligation in a risk-neutral world;
s = premium per dollar of notational protection from time zero to T;
u(t) = the present value (PV ) of payments at the rate of $1 per year on payment dates between
zero and t
e(t) = PV on an accrual payment at time t, with