Generalized Barndorff-Nielsen and Shephard Model and Discretely Monitored Option Pricing

Abstract

This paper proposes a generalization of the Generalized Barndorff-Nielsen and Shephard model, in which the log return on an asset price is governed by a Levy process with stochastic volatility modeled by a non-Gaussian Ornstein-Uhlenbeck process. Under the generalized model, we derive a closed-form expression for the multivariate characteristic function of the intertemporal joint distribution of the underlying log return. Then, we also investigate asymptotic behavior of the log return and its variance. Moreover, we evaluate discretely monitored path-dependent derivatives such as geometric Asian, forward start, barrier, fade-in, and lookback options as well as European options.

Keywords: Ornstein-Uhlenbeck process, Levy process, intertemporal joint distribution, multivariate characteristic function, asymptotic analysis, discretely monitored path-dependent option

JEL Classification: G13, C63