Pricing Default Swaps: Empirical Evidence

Abstract

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.

Estimation of the Term Structure of CDS-AdjustedRisk-Free Interest Rates

“…Bielecki and Rutkowski [2010] comprehensively surveyed both the structural and reduced-form approaches. In the framework of the reduced-form model, F ALL 2014 Longstaff et al [2005] and Houweling and Vorst [2005] gave the evaluation formula of default risk for corporate CDS as well as for corporate bonds.…”

“…Blanco et al [2005] used the swap rate as the risk-free rate. Houweling and Vorst [2005] noticed that the CDS market appears to use the swap rate rather than the Treasury rate as the riskfree rate. Fabozzi et al [2007] employed the 12-month LIBOR as a proxy for the risk-free rate.…”

“…Longstaff et al [2005] regarded the CDS spread as purely a result of default risk, and they used the CDS spread as a benchmark of default risk to identify the liquidity component in the corporate yield spread for cases in which the issuer of the corporate bond and the reference entity of the corporate bond are the same. Houweling and Vorst [2005] compared the default risk pricing between the bond market and CDS market and found that the price discrepancies between bond spreads and CDS spreads are quite small.…”

“…The empirical study is conducted by applying the cubic B-spline function to the forward rate curve (Fisher et al [1995]). The default risk is evaluated by the reduced-form model (Houweling and Vorst [2005]), where the default FALL 2014 intensity is assumed to be a deterministic piecewise constant function. The CDS-adjusted approach successfully estimates the term structure of forward rates and that of the default intensities.…”

“…Houweling and Vorst [2005] assumed that the default intensity is a constant, linear, quadratic, or cubic deterministic function with respect to the term to maturity. Longstaff et al [2005] assumed that the default intensity follows the Cox-Ingersoll-Ross (CIR) type of stochastic process.…”