A Unified Stochastic Volatility - Stochastic Correlation Model

Abstract

We propose a simple but rigorous stochastic volatility – stochastic correlation model, formulated as a pair of correlated CIRCEV and Jacobi processes. Our model proves to fit both marginal and joint distributions of implied volatility and correlation. When risk factors estimated from derivatives markets are accounted for, we show the model out-performance over GBM is substantial for index returns.