A Unified Theory of Option Pricing Assuming Stochastic Volatility

Abstract

Stochastic volatility models have grown in popularity in the past decade or two. However, for many stochastic volatility models, the functional form of volatility along with the description of the diffusion process for volatility have been posed with analytic convenience in mind. Here, we consider that analytic tractability may degenerate as realistic modelling improves and that a more general specification for the stock price and volatility processes may be necessary. This leads to an approximating polynomial for European option prices which is benchmarked to two popular stochastic volatility models, the Stein and Stein, and Heston models, before examining a more general specification which is compared to the corresponding Black Scholes price. Stochastic volatility and European option approximation and Heston and Stein and Stein and Black Scholes