double Wishart stochastic volatility model and its applications: Options with integral transforms Numerical schemes under diffusion models

This study considered Wishart affine diffusion processes, which are stochastic processes defined 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 constructed the double Wishart stochastic volatility model, through the generalization of Hestonmodel into a multifactor nature of implied volatilities, together with the associated properties.The partial differential equation associated to double Wishart volatility model was derived and solved through the application of Fourier techniques, combined with perturbation methods to obtain European call option pricing formula.