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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Christoph Aistleitner & Markus Hofer & Robert Tichy, 2012. "A Central Limit Theorem For Latin Hypercube Sampling With Dependence And Application To Exotic Basket Option Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-20.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:07:n:s021902491250046x
    DOI: 10.1142/S021902491250046X
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    Cited by:

    1. Su, Ziyi & Li, Xiaofeng, 2022. "Extraction of key parameters and simplification of sub-system energy models using sensitivity analysis in subway stations," Energy, Elsevier, vol. 261(PA).
    2. Lindsay Beevers & Lila Collet & Gordon Aitken & Claire Maravat & Annie Visser, 2020. "The influence of climate model uncertainty on fluvial flood hazard estimation," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 104(3), pages 2489-2510, December.
    3. Markus Hofer & Maria Rita Iacò, 2014. "Optimal Bounds for Integrals with Respect to Copulas and Applications," Journal of Optimization Theory and Applications, Springer, vol. 161(3), pages 999-1011, June.
    4. Boubalou Meriem & Ourbih-Tari Megdouda & Aloui Abdelouhab & Zioui Arezki, 2019. "Comparing M/G/1 queue estimators in Monte Carlo simulation through the tested generator “getRDS” and the proposed “getLHS” using variance reduction," Monte Carlo Methods and Applications, De Gruyter, vol. 25(2), pages 177-186, June.

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