European Option Pricing Under Double Wishart Stochastic Volatility Model

Abstract

This study considered Wishart affine diffusion processes, which are stochastic processes de fined as matrix-valued square root processes or as matrix generalization of a squared Bessel process. The aim of the study was to develop a double Wishart stochastic volatility model to price European option: A multifactor Heston model whose volatility components follow Wishart affine processes for a single risky asset, with two dependence matrices describing the correlations between the asset dynamic and the Wishart processes, making it more flexible enough to price options or describe the market prices for short or long maturities. We con structed the double Wishart stochastic volatility model, through the generalization of Heston model into a multifactor nature of implied volatilities, together with the associated properties. The partial differential equation describing the behavior of prices associated to the dynamics of stock price under double Wishart volatility model was derived and solved through the ap plication of Fourier techniques, combined with perturbation methods to obtain European call option pricing formula to confirm the applicability of the model in financial derivatives. Then the log asset return price dynamic under double Wishart model was derived using Ito lemma and its integrals are solved using corrected Euler-Maruyama discretization technique in order to obtain the numerical solution for the log-asset return in order to illustrate the behavior of the log asset returns. The numerical examples show that the call price predictions under double Wishart model exhibits similar pricing behavior with respect to the market price in short and long maturities due to the flexibility in the model. Additionally, the numerical illustrations on the log-asset price return shows the effect of model parameters more so the correlation matrices on the log-asset price return behavior under double Wishart volatility model in trading, which is of importance for investors to analyze the stock prices over time