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Smoothing the payoff for efficient computation of basket option prices

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Titel: Smoothing the payoff for efficient computation of basket option prices
Autoren: Bayer, Christian, Siebenmorgen, Markus, Tempone, Raúl F.
Publikationsjahr: 2016
Bestand: Weierstrass Institute for Applied Analysis and Stochastics publication server
Schlagwörter: article, ddc:510, 91G60, 65D30, 65C20, Stochastische Algorithmen und Nichtparametrische Statistik, Volatilitätsschätzung und Risikobewertung, Computational Finance, European Option Pricing, Multivariate approximation and integration, Sparse grids, Stochastic Collocation methods, Monte Carlo and Quasi Monte Carlo methods
Beschreibung: 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 compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 25.
Publikationsart: report
Sprache: English
Relation: https://doi.org/10.20347/WIAS.PREPRINT.2280
DOI: 10.20347/WIAS.PREPRINT.2280
Verfügbarkeit: https://doi.org/10.20347/WIAS.PREPRINT.2280
https://archive.wias-berlin.de/receive/wias_mods_00002349
https://archive.wias-berlin.de/servlets/MCRFileNodeServlet/wias_derivate_00002262/wias_preprints_2280.pdf
http://www.wias-berlin.de/publications/wias-publ/run.jsp?template=abstract&type=Preprint&year=2016&number=2280
Rights: all rights reserved ; info:eu-repo/semantics/openAccess
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  Data: 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 compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 25.
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