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...

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...

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.