A technique for calibrating derivative security pricing models: numerical solution of an inverse problem

Ronald Lagnado, Stanley Osher

Abstract

ABSTRACT

A technique is presented for calibrating derivative security pricing models with respect to observed market prices. This technique can be applied in a very general multifactor setting where model parameters such as volatilities and correlations are allowed to be functions of the underlying state variables. These functions are estimated from price observations by solving the inverse problem associated with the parabolic partial differential equation governing arbitrage-free derivative security prices. A detailed exposition is given for consistent pricing of equity index options under a stochastic model that treats index volatility as a deterministic function of index level and time.