Determining the Volatility in Option Pricing From Degenerate Parabolic Equation

Abstract

This contribution deals with the inverse volatility problem for a degenerate parabolic equation from numerical perspective. Being different from other inverse volatility problem in classical parabolic equations, the model in this paper is degenerate parabolic equation. Due to solve the deficiencies caused by artificial truncation and control the volatility risk with precision, the linearization method and variable substitutions are applied to transformed the inverse principal term coefficient problem for classical parabolic equation into the inverse source problem for degenerate parabolic equation in bounded region. An iteration algorithm of Landweber type is designed to obtain the numerical solution of the inverse problem. Some numerical experiments are performed to validate that the proposed algorithm is robust and the unknown coefficient is recovered quite well.