Modelling Asymmetric Dependence in Stochastic Volatility and Option Pricing: A Conditional Copula Approach

Abstract

In this paper, stochastic volatility models with asymmetric dependence were presented and applied to pricing options. A dynamic conditional copula approach was proposed to capture this dependence asymmetry. This approach offered simplicity and flexibility, and yielded closed-form solutions for option pricing under different model constructions for the stochastic volatility based on a mean-reverting Gaussian, a square-root and a lognormal process. Empirical experimentation based on S&P 500 options showed that the developed dynamic option pricing models under asymmetric stochastic volatility significantly and consistently outperformed the basic Heston model across option maturities, strike prices and various copula function specifications. The square-root model combined with a Joe copula was the best ranked, having achieved 32.33% overall performance improvement. This superior empirical performance in option pricing, the unique flexibility to various dependence asymmetry considerations, and the analytical tractability added to the benefits of the proposed models framework.

Keywords

• Stochastic volatility
• Asymmetric dependence
• Copula h-function
• Dynamic conditional copula
• Option pricing