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A New Scheme for Static Hedging of European Derivatives under Stochastic Volatility Models

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  • Akihiko Takahashi

    (Faculty of Economics, University of Tokyo)

  • Akira Yamazaki

    (Mizuho-DL Financial Technology Co., Ltd.)

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    Abstract

    This paper proposes a new scheme for static hedging of European path-independent derivatives under stochastic volatility models. First, we show that pricing European path-independent derivatives under stochastic volatility models is transformed to pricing those under one-factor local volatility models. Next, applying an efficient static replication method for one-dimensional price processes developed by Takahashi and Yamazaki[2007], we present a static hedging scheme for European path-independent derivatives. Finally, a numerical example comparing our method with a dynamic hedging method under the Heston[1993]'s stochastic volatility model is used to demonstrate that our hedging scheme is effective in practice.

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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2008/2008cf567.pdf
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    Bibliographic Info

    Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-567.

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    Length: 22 pages
    Date of creation: Jun 2008
    Date of revision:
    Handle: RePEc:tky:fseres:2008cf567

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    1. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm65, Yale School of Management.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Peter Carr & Liuren Wu, 2004. "Stochastic Skew in Currency Options," Finance 0409014, EconWPA.
    5. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
    6. Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
    7. Peter Carr & Katrina Ellis & Vishal Gupta, 1998. "Static Hedging of Exotic Options," Journal of Finance, American Finance Association, vol. 53(3), pages 1165-1190, 06.
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