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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 expression. Numerical computations which are based on this expression are provided. Copyright Springer-Verlag 2011

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  • Zhaojun Yang & Christian-Oliver Ewald & Olaf Menkens, 2011. "Pricing and hedging of Asian options: quasi-explicit solutions via Malliavin calculus," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 93-120, August.
    • Handle: RePEc:spr:mathme:v:74:y:2011:i:1:p:93-120
    DOI: 10.1007/s00186-011-0352-7
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    References listed on IDEAS

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    Cited by:

    1. Gan, Lirong & Wang, Huamao & Yang, Zhaojun, 2020. "Machine learning solutions to challenges in finance: An application to the pricing of financial products," Technological Forecasting and Social Change, Elsevier, vol. 153(C).

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