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.
Highlights
Introduction and MotivationAsset prices are typically modeled with the Geometric Brownian motion (GBM)of the form dSt = St μdt + σ dBt (1)where St is the asset price, μ is the drift, σ is the volatility, and dBt is a standard Brownian motion.Rapid developments in vanilla and exotic options markets, over the past several decades, have fundamentally challenged the static assumptions of μ and σ parameters in Geometric Brownian Motion (GBM)
Cox and Ross [2] create the constant elasticity of variance (CEV) model, where an exponential parameter α is added to the asset price
CBOE publishes both historical data series of the Implied Volatility, and the Implied Correlation, derived from standard 1-month options and dispersion trading strategies respectively, under the methodologies given by CBOE [24] and CBOE [25]
Summary
How to cite this paper: Lu, X., Meissner, G. and Sherwin, H. (2020) A Unified Stochastic Volatility—Stochastic Correlation Model. How to cite this paper: Lu, X., Meissner, G. and Sherwin, H. (2020) A Unified Stochastic Volatility—Stochastic Correlation Model. Received: September 11, 2020 Accepted: November 22, 2020 Published: November 25, 2020
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