A feature of credit markets is the large difference between probabilities of default calculated from historical data and probabilities of default implied from bond prices (or from credit default swaps). This paper illustrates and discusses the reasons for the difference between historical and...

Traditionally practitioners have used LIBOR and LIBOR-swap rates as proxies for risk-free rates when valuing derivatives. This practice has been called into question by the credit crisis that started in 2007. Many banks now consider that overnight indexed swap (OIS) rates should be used as the...

A company's credit default swap spread is the cost per annum for protection against a default by the company. In this paper we analyze data on credit default swap spreads collected by a credit derivatives broker. We first examine the relationship between credit default spreads and bond yields...

Regulatory changes are increasing the importance of collateral agreements and credit issues in over-the-counter derivatives transactions. This paper considers the nature of derivatives collateral agreements and examines the impact of collateral agreements, two-sided credit risk, funding costs,...

In 1976 Black and Cox proposed a structural model where an obligor defaults when the value of its assets hits a certain barrier. In 2001 Zhou showed how the model can be extended to two obligors whose assets are correlated. In this paper we show how the model can be extended to a large number of...

This paper presents a number of new ideas concerned with the implementation of theLIBOR market model and its extensions. It develops and tests an analytic approximationfor calculating the volatilities used by the market to price European swap options fromthe volatilities used to price interest...

Term structure models are widely used to price interest-rate derivatives such as swaps and bonds with embedded options. This paper describes how a general one-factor model of the short-rate can be implemented as a recombining trinomial tree and calibrated to market prices of actively traded...

This paper extends the analysis in Valuing Credit Default Swaps I: No Counter party Default Risk to provide a methodology for valuing credit default swaps that takesaccount of counterparty default risk and allows the payoff to be contingent on defaults by multiple reference entities. It develops...

This paper provides a methodology for valuing credit default swaps when the payoff is contingent on default by a single reference entity and there is no counterparty defaultrisk. The paper tests the sensitivity of credit default swap valuations to assumptions about the expected recovery rate. It...

The “practitioner Black-Scholes delta” for hedging options is a delta calculated from the Black-Scholes-Merton model (or one of its extensions) with the volatility parameter set equal to the implied volatility. As has been pointed out by a number of researchers, this delta does not minimize...