Approximated Pricing of Swaptions in General Interest Rate Models

Abstract

The accurate pricing of swaption contracts is fundamental in interest rate markets, but modelling swaption payo may be relevant also beyond the standard setting. For example Basel III accords introduced the Credit Value Adjustment (C.V.A.) charge for over the counter contracts. It is interesting that for the most simple and popular kind of interest rate derivative, i.e. interest rate swap, the (unilateral) C.V.A. can be estimated as a portfolio of forward start European swaptions. We propose new bounds on the prices of European-style swaptions for a wide class of interest rate models. These bounds are computable whenever the joint characteristic function of the state variables is known in closed form or can be obtained numerically via some e cient procedure. In particular our lower bound involves the computation of one dimensional Fourier transform independently from the swap length.This allows a reduction of the computational cost, mainly when we have to price swaptions written on long-maturity swaps. We also show that methods put forward by Singleton and Umantsev [19] and Kim [13] are particular cases of our general framework. Indeed, we prove that their