Recovery of local volatility for financial assets with mean-reverting price processes

Abstract

This article is concerned with the model calibration for financial assets with mean-reverting price processes, which is an important topic in mathematical finance. The discussion focuses on the recovery of local volatility from market data for Schwartz(1997) model. It is formulated as an inverse parabolic problem, and the necessary condition for determining the local volatility is derived under the optimal control framework. An iterative algorithm is provided to solve the optimality system and a synthetic numerical example is provided to illustrate the effectiveness.