Explicit Volatility Specification for the Linear Cheyette Model

18 Pages Posted: 30 Jan 2012

Date Written: January 29, 2012


In this paper we present an extension of the classical Hull-White framework for pricing single currency exotics, which allows 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 where the forward rate volatility is a linear function of the short rate. 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 technics. We also improve the usual naïve mean state approximation by the use of Gaussian approximations. We give numerical examples.

Keywords: HJM, Cheyette, Separable volatilities, Skew, Averaging Technics

JEL Classification: G12

Suggested Citation

Chibane, Messaoud, Explicit Volatility Specification for the Linear Cheyette Model (January 29, 2012). Available at SSRN: https://ssrn.com/abstract=1995214 or http://dx.doi.org/10.2139/ssrn.1995214

Messaoud Chibane (Contact Author)

Neoma Business School ( email )

1 Rue du Maréchal Juin
Mont Saint Aignan Cedex, 76825