### 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 language | English |
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Journal | Economic Computation and Economic Cybernetics Studies and Research |

Volume | 6 |

Publication status | Published - 2012 |

### 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

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## Cite this

Moon, K. S., & Kim, H. (2012). Polynomial chaos solution to the Black Scholes equation with a random volatility.

*Economic Computation and Economic Cybernetics Studies and Research*,*6*.