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    Smoothing the payoff for efficient computation of Basket option prices

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    Type
    Article
    Authors
    Bayer, Christian
    Siebenmorgen, Markus
    Tempone, Raul cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2017-07-22
    Permanent link to this record
    http://hdl.handle.net/10754/626067
    
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    Abstract
    We consider the problem of pricing basket options in a multivariate Black–Scholes or Variance-Gamma model. From a numerical point of view, pricing such options corresponds to moderate and high-dimensional numerical integration problems with non-smooth integrands. Due to this lack of regularity, higher order numerical integration techniques may not be directly available, requiring the use of methods like Monte Carlo specifically designed to work for non-regular problems. We propose to use the inherent smoothing property of the density of the underlying in the above models to mollify the payoff function by means of an exact conditional expectation. The resulting conditional expectation is unbiased and yields a smooth integrand, which is amenable to the efficient use of adaptive sparse-grid cubature. Numerical examples indicate that the high-order method may perform orders of magnitude faster than Monte Carlo or Quasi Monte Carlo methods in dimensions up to 35.
    Citation
    Bayer C, Siebenmorgen M, Tempone R (2017) Smoothing the payoff for efficient computation of Basket option prices. Quantitative Finance: 1–15. Available: http://dx.doi.org/10.1080/14697688.2017.1308003.
    Sponsors
    King Abdullah University of Science and Technology[CEMSE]
    Publisher
    Informa UK Limited
    Journal
    Quantitative Finance
    DOI
    10.1080/14697688.2017.1308003
    arXiv
    1607.05572
    Additional Links
    http://www.tandfonline.com/doi/abs/10.1080/14697688.2017.1308003
    ae974a485f413a2113503eed53cd6c53
    10.1080/14697688.2017.1308003
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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