# Three Phase System

Topics: Credit default swap, Bond, Yield curve Pages: 27 (4550 words) Published: February 28, 2013
Bond Implied CDS Spread and CDS-Bond Basis
Richard Zhou†‡
August 15, 2008

Abstract
We derive a simple formula for calculating the CDS spread implied by the bond market price. Using no-arbitrage argument, the formula expresses the bond implied CDS spread as the sum of bond price, bond coupon and Libor zero curve weighted by risky annuities. We show that the bond implied CDS spread is consistent with the standard CDS pricing model if the survival probabilities and recovery are consistent with the bond price.

1. Introduction
A CDS contract is an OTC transaction between two parties in which the protection buyer pays a stream of coupon payment to the protection seller until the earlier of maturity or entity default in exchange for a default contingent payment. The common default settlement is the physical settlement where the protection buyer delivers a bond from a pool of eligible bonds to the protection seller in exchange for par. CDS contracts can also be cash settled where the protection buyer receives from the protection seller the cash amount of par less recovery.

With the physical settlement, the CDS protection buyer holds a delivery option where he can choose any bond from a pool of bonds to deliver into the CDS contract. Empirical evidence shows that bonds of the same entity do not necessarily have the same market value following default [1]. As a result, the standard CDS pricing with a flat recovery rate cannot properly price in the value of the delivery option embedded in the CDS contracts. Given the issuer default probability, the bond price is determined by the recovery and other fundamental and market technical factors such as supply and demand, and liquidity. From modeling perspective, it is difficult to separate recovery, default probability, and other market fundamental and technical factors since they are intertwined. The recovery swap prices can be used as the expected recovery rate but the market has not yet fully developed. Even if the recovery rate can be determined independently, the default probabilities calibrated to the market CDS spreads or bond prices are still contaminated by other factors such as supply and demand, funding cost, bond trading away from par (see [7] for a detailed exposition on factors impacting CDS and cash basis). Empirical studies show that the markets apears to price CDS based on Libor curve rather than the treasury curve [2]. CDS discounting should be based on Libor. Since the Libor

Risk Management, The Depository Trust & Clearing Corporation, Email: rzhou50@gmail.com. The opinions of this article are those of the author and do not reflect in any way the views or business of his employer. All errors are author’s own.

1

are the borrowing rates between banks of AA rating, the Libor curve is implicitly an AA rated yield curve. As a result, we use Libor as the risk free interest rate. An asset swap (ASW) is a package transaction between two parties in which the ASW buyer purchases a bond from the other party and simultaneously enters into an interest rate swap transaction, usually with the same counterparty, to exchange the coupon on the bond for Libor plus a spread. The spread is called the asset swap spread. A common asset swap is the par asset swap where the buyer pays par at the inception of the deal. Unlike CDS, ASW continues following bond default.

CDS-Bond basis is the difference between the CDS spread and the ASW spread on the same bond. It is a general indicator of relative value of CDS versus the cash bond. For example, when the CDS spread is higher than the ASW spread, i.e. the basis is positive, the CDS is generally considered to be more attractive than the bond. The reverse is true if the basis is negative.

Bond implied CDS spreads have been previously investigated. Davies and Pugachevsky proposed an approximation method for calculating the bond implied CDS spread based on the Z spread adjusted by the bond’s market price, duration,...