# Hull john k options. Hull–White model

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This does not matter — the volatility is all that matters and is measure-independent.

Jamshidian's trick applies to Hull—White as today's value of a swaption in the Hull—White model is a monotonic function of today's short rate. Thus knowing how to price caps is also sufficient for pricing swaptions.

In the even that the underlying is a compounded backward-looking rate rather than a forward-looking LIBOR term rate, Turfus shows how this formula can be straightforwardly modified to take into account the additional convexity. Swaptions can also be priced directly as described in Henrard Direct implementations are usually more efficient.

Monte-Carlo simulation, trees and lattices[ edit ] However, valuing vanilla instruments such as caps and swaptions is useful primarily for calibration. The real use of the model is to value somewhat more exotic derivatives such as bermudan swaptions on a latticeor other derivatives in a multi-currency context such as Quanto Constant Maturity Swaps, as explained for example in Brigo and Mercurio The efficient and exact Monte-Carlo simulation of the Hull—White model with time dependent parameters can be easily performed, see Ostrovski and