An Asymptotic Expansion with Malliavin Weights: An Application to Pricing Discrete Barrier Options

Akihiko Takahashi and Toshihiro Yamada
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Akihiko Takahashi: Faculty of Economics, University of Tokyo
Toshihiro Yamada: Mitsubishi UFJ Trust Investment Technology Institute Co.,Ltd. (MTEC)

No CARF-F-193, CARF F-Series from Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo

Abstract: This paper proposes a new approximation method for pricing barrier options with discrete monitoring under stochastic volatility environment. In particular, the integration-by-parts formula in Malliavin calculus is effectively applied in an asymptotic expansion approach. First, the paper derives an expansion formula for generalized Wiener functionals. After it is applied to pricing path-dependent derivatives with discrete monitoring, the paper presents an analytic (approximation) formula for valuation of discrete barrier options under stochastic volatility environment. To our knowledge, this paper is the first one that shows an analytical formula for pricing discrete barrier options with stochastic volatility models.

Pages: 13 pages
Date: 2009-12
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Persistent link: https://EconPapers.repec.org/RePEc:cfi:fseres:cf193

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