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...

Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a very difficult task for investors. This article recovers...

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...

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...

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LLM 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 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...