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Smoothing the payoff for efficient computation of Basket option prices

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  • Christian Bayer
  • Markus Siebenmorgen
  • Raul Tempone

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 compared to Monte Carlo or Quasi Monte Carlo in dimensions up to 35.

Suggested Citation

  • Christian Bayer & Markus Siebenmorgen & Raul Tempone, 2016. "Smoothing the payoff for efficient computation of Basket option prices," Papers 1607.05572, arXiv.org, revised Feb 2017.
    • Handle: RePEc:arx:papers:1607.05572
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    References listed on IDEAS

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    5. Marc Romano & Nizar Touzi, 1997. "Contingent Claims and Market Completeness in a Stochastic Volatility Model," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 399-412, October.
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