POLYNOMIAL CHAOS SOLUTION TO THE BLACK SCHOLES EQUATION WITH A RANDOM VOLATILITY

초록

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.

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