Pricing Barrier and Average Options under Stochastic Volatility Environment
AbstractThis paper proposes a new approximation method of pricing barrier and average options under stochastic volatility environment by applying an asymptotic expansion approach. In particular, a high-order expansion scheme for general multi-dimensional diffusion processes is effectively applied. Moreover, the paper combines a static hedging method with the asymptotic expansion method for pricing barrier options. Finally, numerical examples show that the fourth or fifth-order asymptotic expansion scheme provides sufficiently accurate approximations under the ƒÉ-SABR and SABR models.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-745.
Date of creation: May 2010
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-05-29 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Yoshifumi Muroi, 2005. "Pricing contingent claims with credit risk: Asymptotic expansion approach," Finance and Stochastics, Springer, vol. 9(3), pages 415-427, 07.
- Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
- Akihiko Takahashi & Nakahiro Yoshida, 2005. "Monte Carlo Simulation with Asymptotic Method," CIRJE F-Series CIRJE-F-335, CIRJE, Faculty of Economics, University of Tokyo.
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