On the complete model with stochastic volatility by Hobson and Rogers

Abstract

In the complete model with stochastic volatility by Hobson and Rogers, preference independent options prices are solutions to degenerate partial differential equations obtained by including additional state variables describing the dependence on past prices of the underlying. In this paper, we aim to emphasize the mathematical tractability of the model by presenting analytical and numerical results comparable with the known ones in the classical Black–Scholes environment.