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A Moment Matching Approach To The Valuation Of A Volume Weighted Average Price Option

  • ANTONY WILLIAM STACE

    ()

    (Department of Mathematics, University of Queensland, Brisbane, Queensland 4072, Australia)

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    In this paper we develop a method to find the price of several options whose payoff depends on a volume weighted average price (VWAP). Fixed and floating strike VWAP, together with digital VWAP contracts are considered. Throughout we assume that the stock follows a geometric Brownian motion and the rate of trades evolves as a mean reverting process. It is assumed that the VWAP at the final time has a lognormal distribution. The parameters of the approximating lognormal distribution are obtained by matching the first two moments of the volume weighted average price with a lognormal process. A price is then obtained for the fixed strike and digital options when the market price of risk is a constant. We concentrate on the price for calls, prices for puts can be obtained in an analogous manner.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

    Volume (Year): 10 (2007)
    Issue (Month): 01 ()
    Pages: 95-110

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    Handle: RePEc:wsi:ijtafx:v:10:y:2007:i:01:p:95-110
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