On Black–Scholes option pricing model with stochastic volatility: an information theoretic approach

Abstract

In this article, we derive the risk-neutral measures of the stock options price and volatility by incorporating a simple constrained minimization of the Kullback measure of relative information. We obtain a second-order parabolic partial differential equation, the generalized Black–Scholes equation based on the theoretical analysis when the underlying financial asset is estimated using a stochastic volatility model. Also to investigate the analytical solution of this generalized Black–Scholes equation we have used Laplace transform homotopy perturbation method.

Keywords:

• Option pricing theory
• Black–Scholes equation
• Kullback measure of relative information
• stochastic volatility
• homotopy perturbation method
• Liouville–Caputo fractional derivative