On Pricing Barrier Options with Discrete Monitoring

Kenichiro Shiraya, Akihiko Takahashi and Toshihiro Yamada
Additional contact information
Kenichiro Shiraya: Mizuho-DL Financial Technology Co., Ltd.
Akihiko Takahashi: Faculty of Economics, University of Tokyo
Toshihiro Yamada: Mitsubishi UFJ Trust Investment Technology Institute Co.,Ltd. (MTEC)

No CIRJE-F-725, CIRJE F-Series from CIRJE, Faculty of Economics, 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 and the duality formula in Malliavin calculus are effectively applied in an asymptotic expansion approach. First, the paper derives an asymptotic expansion 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 approximation for pricing discrete barrier options with stochastic volatility models. Finally, it provides numerical examples for pricing double barrier call options with discrete monitoring under the Heston model.

Pages: 18pages
Date: 2010-03
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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2010cf725

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