In the framework of the Libor Market Model (LMM) an explicit pricing formula is obtained for European swaptions. The LLM used is a displaced diffusion also called Bond Market Model (BMM). The results are similar to the one obtained for the Gaussian HJM. The extension to bond futures and...

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LMM and HJM models is presented. The approximation used is a Taylor expansion on the swap rate as a function of a random variable which is intuitively similar to a (short) rate. This approach...

A simple and fundamental question in derivatives pricing is the way (contingent) cash-flows should be discounted. As cash can not be invested at Libor the curve is probably not the right discounting curve, even for Libor derivatives. The impact on derivative pricing of changing the discounting...

A simple exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is...

The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation...

An exotic option (floor on rolled deposit) is studied in the shifted log-normal Libor Market (LMM) and Gaussian HJM models. The shifted log-normal LMM exhibits a controllable volatility skew. An explicit approach is used for both models. Using approximations the price in the LMM is obtained...

In this study, one of the simplifying assumptions of the McConnell and Schwartz (1986) LYON pricing model is relaxed. We present a valuation model that incorporates stochastic interest rates. LYON prices are computed with the modified explicit finite differences method of Hull and White (1990)...

This paper tailors Monte Carlo simulations to the scope of binary options whose underlying dynamics obey jump-diffusion or jump-mean-reverting processes and may not be traded. In the process, we justify the existence of well-defined arbitrage prices notwithstanding a framework of incomplete...

We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon...

A simple and fundamental question in derivatives pricing is how (contingent) cash-flows should be discounted. As cash can generally not be invested at Libor, the Libor curve is probably not the right discounting curve, even for Libor derivatives. The impact on derivative pricing of changing the...