A Unified Stochastic Volatility—Stochastic Correlation Model

Abstract

This paper has two main contributions. First, we build a simple but rigorous stochastic volatility-stochastic correlation model. Mean-reverting and locally stochastic with dependent Brownian motions, our model proves to fit both marginal and joint distributions of the option market implied volatility and correlation. Second, asset correlations are currently modeled exogenously and then ad hoc assigned to an asset price process such as the Geometric Brownian Motion (GBM). This is conceptually and mathematically unsatisfying. We apply our approach to build a unified asset price-asset correlation model, which outperforms the standard GBM significantly.