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Hedging lookback and partial lookback options using Malliavin calculus

  • Hans-Peter Bermin
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    The paper considers a Black and Scholes economy with constant coefficients. A contingent claim is said to be simple if the payoff at maturity is a function of the value of the underlying security at maturity. To replicate a simple contingent claim one uses so called delta-hedging, and the well-known strategy is derived from Ito calculus and the theory of partial differentiable equations. However, hedging path-dependent options require other tools since the price processes, in general, no longer have smooth stochastic differentials. It is shown how Malliavin calculus can be used to derive the hedging strategy for any kind of path-dependent options, and in particular for lookback and partial lookback options.

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    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 7 (2000)
    Issue (Month): 2 ()
    Pages: 75-100

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    Handle: RePEc:taf:apmtfi:v:7:y:2000:i:2:p:75-100
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    1. Jérôme B. Detemple & René Garcia & Marcel Rindisbacher, 2000. "A Monte-Carlo Method for Optimal Portfolios," CIRANO Working Papers 2000s-05, CIRANO.
    2. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-27, December.
    3. P. Carr, 1995. "Two extensions to barrier option valuation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 173-209.
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