Polynomial chaos solution to the Black Scholes equation with a random volatility

Kyoung Sook Moon, Hongjoong Kim

Research output: Contribution to journalArticle


In this study, the Black Scholes equation with uncertainty in its volatility is considered. A numerical algorithm for option pricing based on the orthonormal polynomials from the Askey scheme is derived. Then dependence of polynomial chaos on the distribution type of the volatility is investigated. Numerical experiments show that when appropriate polynomial chaos is chosen as a basis in the random space for the volatility, the solution to the Black Scholes equation converges significantly fast.

Original languageEnglish
JournalEconomic Computation and Economic Cybernetics Studies and Research
Publication statusPublished - 2012 Oct 5



  • Black Scholes equation
  • Option pricing
  • Polynomial chaos
  • Spectral method
  • Stochastic differential equation

ASJC Scopus subject areas

  • Economics and Econometrics
  • Computer Science Applications
  • Applied Mathematics

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