Pricing Swaptions under the Libor Market Model of Interest Rates with Local-Stochastic Volatility Models

Abstract

This paper presents a new approximation formula for pricing swaptionsand caps/floors under the Libor market model of interest rates(LMM) with the local and affine-type stochastic volatility.In particular, two approximation methods are applied in pricing,one of which is so called “drift-freezing” that fixes parts of the underlyingstochastic processes at their initial values. Another approximationis based on an asymptotic expansion approach. An advantage of ourmethod is that those approximations can be applied in a unified mannerto a general class of local-stochastic volatility models of interestrates.To demonstrate effectiveness of our method, the paper takes CEVHestonLMM and Quadratic-Heston LMM as examples; it confirmssufficient flexibility of the models for calibration in a caplet market andenough accuracies of the approximation method for numerical evaluationof swaption values under the models.