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Adaptive integration and approximation over hyper-rectangular regions with applications to basket option pricing

Author

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  • De Luigi Christophe

    (Université du Sud Toulon-Var, I.S.I.T.V., Avenue G. Pompidou BP 56, F-83162 La Valette du Var CEDEX, France. E-mail:)

  • Maire Sylvain

    (Université du Sud Toulon-Var, I.S.I.T.V., Avenue G. Pompidou BP 56, F-83162 La Valette du Var CEDEX, France. E-mail:)

Abstract

We describe an adaptive algorithm to compute piecewise sparse polynomial approximations and the integral of a multivariate function over hyper-rectangular regions in medium dimensions. The key ingredient is a quasi-Monte Carlo quadrature rule which can handle the numerical integration of both very regular and less regular functions. Numerical tests are performed on functions taken from Genz package in dimensions up to 5 and on basket options pricing.

Suggested Citation

  • De Luigi Christophe & Maire Sylvain, 2010. "Adaptive integration and approximation over hyper-rectangular regions with applications to basket option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 16(3-4), pages 265-282, January.
    • Handle: RePEc:bpj:mcmeap:v:16:y:2010:i:3-4:p:265-282:n:4
    DOI: 10.1515/mcma.2010.011
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    References listed on IDEAS

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    1. Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
    2. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
    3. Schürer, Rudolf, 2003. "A comparison between (quasi-)Monte Carlo and cubature rule based methods for solving high-dimensional integration problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 62(3), pages 509-517.
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