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

Kyoung Sook Moon, Hongjoong Kim

Research output: Contribution to journalArticle

Abstract

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
Volume6
Publication statusPublished - 2012 Oct 5

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Black-Scholes Equation
Polynomial Chaos
Chaos theory
Volatility
Polynomials
Orthonormal Polynomials
Option Pricing
Numerical Algorithms
Numerical Experiment
Converge
Uncertainty
Black-Scholes equation
Chaos
Costs
Experiments

Keywords

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

ASJC Scopus subject areas

  • Economics and Econometrics
  • Computer Science Applications
  • Applied Mathematics

Cite this

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