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...

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...

An explicit pricing formula for inflation bond options is proposed in the Jarrow-Yildirim model. The formula resembles that for coupon bond options in the HJM model.

Even if the name futures indicates a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can deliver the cheapest. This paper focuses...

Bond futures are liquid but complex instruments. Here they are analysed in a one-factor Gaussian HJM model. The in-the-model delta and out-of-the-model delta and gamma are studied. An explicit formula is provided for in-the-model delta. The out-of-the-model delta and gamma are equivalent to...

Constant maturity swaps (CMS) and CMS spread options are analysed in the multi-factor HJM framework. For Gaussian models, which include a version of the Libor Market Models and the G2++ model, explicit approximated pricing formulae are provided. Two approximating approaches are proposed: an...

This book presents a simple model (the simplest?) for the computation of the value-at-risk: the delta-normal approach. It doesn't explain the shortcomings and advantages of the method nor compares it with other models. Even on this single topic, by no way it pretends to be complete or in the...

In practice the option pricing models are calibrated to market prices of liquid instruments. Consequently for those instruments, all the models give the same price. But the computed risk can be widely different. The note proposes comparison on simple instruments (swaptions) on a simple risk...

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...

This note describes the problem arising from using a currency basket in the computation of value-at-risk. This applies mainly when the basket is used as base currency. A solution based on the modification of the historical time series is proposed. The solution is easy to implement and doesn't...