Efficient Pricing of CMS Spread Options in a Stochastic Volatility LMM

Abstract

In this paper we develop a fast yet accurate formula for pricing CMS spread options in a popular class of Libor market models with stochastic volatility. This formula makes it feasible to include quoted CMS spread option prices in the general calibration procedure and by this means to recover the correlation information contained in the market. Our approach is based on a new method for the fast evaluation of the density of an integrated Cox-Ingersoll-Ross (CIR) process. Combined with approximations for the swap-rate dynamics, this results in a semi-analytical formula for CMS spread option prices. Numerical experiments demonstrate the accuracy this formula.

Keywords: Libor market model, stochastic volatility, displaced Heston, integrated CIR, Laplace transform, optimal contour, CMS spread options, correlation calibration.

JEL Classification: G12, G13