We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging...

Australian dollar bills futures are very particular, not only on the valuation at expiry but also for the maturity delivery option and the credit delivery option. This note consider only the interest rate part of the futures (marginning and maturity delivery option). An explicit formula for the...

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...

Based on Jarrow-Yildirim model for inflation derivatives, this note propose an explicit formula for option on inflation bonds. The formula is similar to the one for coupon-bond option in the HJM model.

In the framework of the Hull-White model we present a semi-explicit approach to compute the delta and the gamma. The method is faster and more accurate than classical approaches, specially when compared to the Hull-White tree implementation.

Two types of financial instruments including (overnight) compounding are studied in this note. The first one is overnight compounded instruments in the case where the settlement is delayed with respect to the end of the compounding period (floating leg of the OIS). The second is options on the...

A popular way to value (Bermudan) swaption in a Hull-White or extended Vasicek model is to use a tree approach. In this note we show that a more direct approach through iterated numerical integration is also possible. A brute force numerical integration would lead to a complexity exponential in...

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...