TITLE:
A Unified Stochastic Volatility—Stochastic Correlation Model
AUTHORS:
Xiang Lu, Gunter Meissner, Hong Sherwin
KEYWORDS:
Stochastic Volatility, Stochastic Correlation, Chan-Karolyi-Longstaff-Sanders (CKLS) Process, Constant Elasticity of Variance (CEV), Jacobi Process
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.10 No.4,
November
25,
2020
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.