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

31 Pages Posted: 5 Aug 2014 Last revised: 11 Feb 2016

Akira Yamazaki

Hosei University - Graduate School of Business Administration

Date Written: September 18, 2014

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

Suggested Citation

Yamazaki, Akira, Generalized Barndorff-Nielsen and Shephard Model and Discretely Monitored Option Pricing (September 18, 2014). International Journal of Theoretical and Applied Finance, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2476223 or http://dx.doi.org/10.2139/ssrn.2476223

Akira Yamazaki (Contact Author)

Hosei University - Graduate School of Business Administration ( email )

Japan

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