Singular Perturbation Techniques Applied to Multiasset Option Pricing

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

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)457-486
Number of pages30
JournalMathematical Finance
Volume19
Issue number3
DOIs
StatePublished - Jul 1 2009
Externally publishedYes

Keywords

  • Implied volatilities
  • Multiple underlyings
  • Numerical techniques
  • Option valuation
  • Singular perturbation theory

ASJC Scopus subject areas

  • Accounting
  • Finance
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Applied Mathematics

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