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

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  • Zhaojun Yang
  • Christian-Oliver Ewald
  • Olaf Menkens

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.

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Bibliographic Info

Paper provided by Centre for Research into Industry, Enterprise, Finance and the Firm in its series CRIEFF Discussion Papers with number 0910.

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Date of creation: Sep 2009
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Handle: RePEc:san:crieff:0910

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Keywords: Asian options; option pricing; hedging; Malliavin calculus.;

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  1. Carr, Peter & Ewald, Christian-Oliver & Xiao, Yajun, 2008. "On the qualitative effect of volatility and duration on prices of Asian options," Finance Research Letters, Elsevier, vol. 5(3), pages 162-171, September.
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