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Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus
Zhaojun Yang Hunan University - School of Economics and Trade Christian-Oliver Ewald Center for Dynamic Macroeconomic Analysis, University of St. Andrews, School of Economics and Finance; University of Sydney, School of Mathematics and Statistics Olaf Menkens Dublin City University - School of Mathematical Sciences June 29, 2009 Abstract: We use Malliavin calculus and the Clark-Ocone formula to derive the hedging strategy of an arithmetic Asian Call option in general terms. Furthermore we derive an expression for the density of the integral over time of a geometric Brownian motion, which allows us to express hedging strategy and price of the Asian option as an analytic, that is closed form, expression. Numerical computations which are based on this expression are provided.
Keywords: Asian options, option pricing, hedging, Malliavin calculus JEL Classifications: G11, G12, G13, C40, C61, C63 Working Paper SeriesDate posted: June 30, 2009 ; Last revised: September 01, 2009Suggested CitationContact Information
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