Pure Mathematics
E-print 11, 2006
Author(s):
F. E. Benth, M. Groth, and R. Kufakunesu
Title:
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.
A pdf version of the entire e-print.