COLLEGE OF ARTS AND SCIENCES Department of Mathematics and Statistics

Seminars

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Applied Math Seminar: The Inverse Problem of Option Pricing in the Black-Scholes Model

2009-12-09

3:15 PM; Neill Hall 3W

Junjian Sun

Abstract: The inverse problem of Black-Scholes PDE is investigated where the implied volatility, a coefficient function of the second order partial derivative in the model, is unknown. An optimal control method is applied to determine the volatility function, then the convergence of the approximate optimal solutions is proved and the necessary conditions are discussed. The analysis sheds light onto the importance of the a priori knowledge of the unknown volatility and the nature of the illposedness of the inverse problem.