Pricing Discrete Barrier Options Under Stochastic Volatility
AbstractThis 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 pricing barrier options with discrete monitoring. To the best of our knowledge, this paper is the first one that shows an analytical approximation for pricing discrete barrier options with stochastic volatility models. Furthermore, it provides numerical examples for pricing double barrier call options with discrete monitoring under Heston and λ-SABR models. Copyright Springer Science+Business Media, LLC. 2012
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Bibliographic InfoArticle provided by Springer in its journal Asia-Pacific Financial Markets.
Volume (Year): 19 (2012)
Issue (Month): 3 (September)
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Web page: http://springerlink.metapress.com/link.asp?id=102851
Discrete barrier option; Barrier option; Knock-out option; Double barrier option; Stochastic volatility; CEV model; Heston model; SABR model; λ-SABR model; Asymptotic expansion; Malliavin calculus;
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- Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
- Gianluca Fusai & I. Abrahams & Carlo Sgarra, 2006. "An exact analytical solution for discrete barrier options," Finance and Stochastics, Springer, vol. 10(1), pages 1-26, 01.
- Akihiko Takahashi & Nakahiro Yoshida, 2004. "An Asymptotic Expansion Scheme for Optimal Investment Problems," Statistical Inference for Stochastic Processes, Springer, vol. 7(2), pages 153-188, May.
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