A Quadratic Volatility Cheyette Model

Abstract

In this paper we present an extension of the one factor blended Cheyette model for pricing single currency exotics, allowing for a more adequate fit to the swaption volatility smile. We first present a general framework based on the HJM model and then make a separability assumption on the instantaneous forward rate volatility, thus enabling a representation of the discount curve in a finite number of Markovian state variables. We show a practical application of this family of models by analyzing calibration and pricing in the case of a quadratic volatility function. By doing so, we provide a novel and parsimonious specification of the Cheyette model. Then for calibration purposes, we develop fast and accurate approximations for European swaptions, based on standard projection and averaging techniques. We also improve the usual naive mean state estimation by the use of Gaussian approximations. Last we present an efficient large step Monte-Carlo simulation for strongly path dependent exotics.