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Singular Perturbation Techniques Applied To Multiasset Option Pricing

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  • Peter W. Duck
  • Chao Yang
  • David P. Newton
  • Martin Widdicks

Abstract

It is well known that option valuation problems with multiple‐state variables are often problematic to solve. When valuing options using lattice‐type techniques such as finite‐difference methods, the curse of dimensionality ensures that additional‐state variables lead to exponential increases in computational effort. Monte Carlo methods are immune from this curse but, despite advances, require a great deal of adaptation to treat early exercise features. Here the multiunderlying asset Black–Scholes problem, including early exercise, is studied using the tools of singular perturbation analysis. This considerably simplifies the pricing problem by decomposing the multi‐dimensional problem into a series of lower‐dimensional problems that are far simpler and faster to solve than the full, high‐dimensional problem. This paper explains how to apply these singular perturbation techniques and explores the significant efficiency improvement from such an approach.

Suggested Citation

  • Peter W. Duck & Chao Yang & David P. Newton & Martin Widdicks, 2009. "Singular Perturbation Techniques Applied To Multiasset Option Pricing," Mathematical Finance, Wiley Blackwell, vol. 19(3), pages 457-486, July.
    • Handle: RePEc:bla:mathfi:v:19:y:2009:i:3:p:457-486
    DOI: 10.1111/j.1467-9965.2009.00373.x
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    3. Adi Ben-Meir & Jeremy Schiff, 2012. "The Variance of Standard Option Returns," Papers 1204.3452, arXiv.org.

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