### 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 |
---|---|

Journal | Economic Computation and Economic Cybernetics Studies and Research |

Volume | 6 |

Publication status | Published - 2012 Oct 5 |

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### 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

**Polynomial chaos solution to the Black Scholes equation with a random volatility.** / Moon, Kyoung Sook; Kim, Hongjoong.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Polynomial chaos solution to the Black Scholes equation with a random volatility

AU - Moon, Kyoung Sook

AU - Kim, Hongjoong

PY - 2012/10/5

Y1 - 2012/10/5

N2 - 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.

AB - 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.

KW - Black Scholes equation

KW - Option pricing

KW - Polynomial chaos

KW - Spectral method

KW - Stochastic differential equation

UR - http://www.scopus.com/inward/record.url?scp=84866952166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866952166&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84866952166

VL - 6

JO - The BMJ

JF - The BMJ

SN - 0730-6512

ER -