On the complete model with stochastic volatility by Hobson and Rogers

Abstract

We examine a recent model, proposed by Hobson and Rogers, which generalizes the classical one by Black and Scholes for pricing derivative securities such as options and futures. We treat the numerical solution of some degenerate partial differential equations governing this financial problem and propose some new numerical schemes which naturally apply in this degenerate setting. Then we aim to emphasize the mathematical tractability of the Hobson-Rogers model by presenting analytical and numerical results comparable with the known ones in the classical Black-Scholes environment.Black-Scholes model, stochastic volatility, path-dependent option, hypoelliptic equation