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

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  • AKIRA YAMAZAKI

    (Graduate School of Business Administration, Hosei University, The Research Institute for Innovation Management, 2-17-1 Fujimi, Chiyoda-ku, Tokyo 102-8160, Japan)

Abstract

This paper proposes a generalization of the Barndorff-Nielsen and Shephard model, in which the log return on an asset is governed by a Lévy process with stochastic volatility modeled by a non-Gaussian Ornstein–Uhlenbeck process. Under the generalized model, we derive a closed-form expression of 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.

Suggested Citation

  • Akira Yamazaki, 2016. "Generalized Barndorff-Nielsen And Shephard Model And Discretely Monitored Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-34, June.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:04:n:s0219024916500242
    DOI: 10.1142/S0219024916500242
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    References listed on IDEAS

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    Cited by:

    1. Kenichiro Shiraya & Cong Wang & Akira Yamazaki, 2021. "A general control variate method for time-changed Lévy processes: An application to options pricing," CARF F-Series CARF-F-499, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    2. Shiraya, Kenichiro & Uenishi, Hiroki & Yamazaki, Akira, 2020. "A general control variate method for Lévy models in finance," European Journal of Operational Research, Elsevier, vol. 284(3), pages 1190-1200.

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