Derivation of black Scholes equation using Heston’s model with dividend yielding asset

Abstract

Black Scholes formula is crucial in modern applied finance. Since the introduction of Black – Scholes concept model that assumes volatility is constant; several studies have proposed models that address the shortcomings of Black-Scholes model. Heston’s models stands out amongst most volatility models because the process of volatility is positive and is a process that obeys mean reversion and this is what is observed in the real market world. One of the shortcomings of Heston’s model is that it doesn’t incorporate dividend yielding asset. Black Scholes partial differential equation revolves around Geometric Brownian motion and its extensions. We, therefore, incorporate dividend yielding assets on Heston’s model and use it to model a new Black Scholes equation using the knowledge of partial differential equations.