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A Central Limit Theorem For Latin Hypercube Sampling With Dependence And Application To Exotic Basket Option Pricing

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  • CHRISTOPH AISTLEITNER

    ()
    (Graz University of Technology, Institute of Mathematics A, Steyrergasse 30, 8010 Graz, Austria)

  • MARKUS HOFER

    ()
    (Graz University of Technology, Institute of Mathematics A, Steyrergasse 30, 8010 Graz, Austria)

  • ROBERT TICHY

    ()
    (Graz University of Technology, Institute of Mathematics A, Steyrergasse 30, 8010 Graz, Austria)

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    Abstract

    We consider the problem of estimating 𝔼[f(U1, …, Ud)], where (U1, …, Ud) denotes a random vector with uniformly distributed marginals. In general, Latin hypercube sampling (LHS) is a powerful tool for solving this kind of high-dimensional numerical integration problem. In the case of dependent components of the random vector (U1, …, Ud) one can achieve more accurate results by using Latin hypercube sampling with dependence (LHSD). We state a central limit theorem for the d-dimensional LHSD estimator, by this means generalising a result of Packham and Schmidt. Furthermore we give conditions on the function f and the distribution of (U1, …, Ud) under which a reduction of variance can be achieved. Finally we compare the effectiveness of Monte Carlo and LHSD estimators numerically in exotic basket option pricing problems.

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    Bibliographic Info

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

    Volume (Year): 15 (2012)
    Issue (Month): 07 ()
    Pages: 1250046-1-1250046-20

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    Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:07:p:1250046-1-1250046-20

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    Related research

    Keywords: Monte Carlo; variance reduction techniques; Latin hypercube sampling; option pricing; variance gamma; probabilistic methods;

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