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...

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...

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...

Prior to 2007, derivatives practitioners used a zero curve that was bootstrapped from LIBOR swap rates to provide “risk-free” rates when pricing derivatives. In the last few years, when pricing fully collateralized transactions, practitioners have switched to using a zero curve bootstrapped...

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,...

The authors examine whether a bank should make a funding value adjustment (FVA) when valuing derivatives. They conclude that an FVA is justifiable only for the part of a company's credit spread that does not reflect default risk. They show that an FVA can lead to conflicts between traders and...

In this paper, we propose a way to construct a single forward-looking model for interest rates, which represents their evolution under both the Q-measure and P-measure (a joint measure model). As is well known, the market prices of contingent claims are independent of investor risk preferences....