VALUING VOLATILITY AND VARIANCE SWAPS FOR A NON-GAUSSIAN ORNSTEIN-UHLENBECK STOCHATISC VOLATILITY MODEL

Abstract

Following the increasing awareness of the risk from volatility fluctuations the markets for hedging contracts written on realised volatility has surged. Companies looking for means to secure against unexpected accumulation of market activity can find over-the-counter products written on volatility indices. Since the Black and Scholes model require a constant volatility the need to consider other models is obvious. We investigate swaps written on powers of realised volatility in the stochastic volatility model proposed by Barndorff-Nielsen and Shephard. We derive a key formula for the realised variance and are able to represent the swap price dynamics in terms of Laplace transforms, which makes fast numerical inversion methods viable. We show an example using the fast Fourier transform and compare with the approximation proposed by Brockhaus and Long.