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CRIEFF Discussion Paper Number 0910

Pricing and Hedging of Asian Options: Quasi-Explicit Solutions via Malliavin Calculus

Zhaojun Yang,Christian-Oliver Ewald and Olaf Menkens

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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.

JEL codes: G2; G13
Keywords: Asian options, option pricing, hedging, Malliavin calculus

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