Modeling Tail Dependence Using Stochastic Volatility Model

As one can see in many previous well-known papers, an one-factor stochastic volatility model has its limitation to fit the market dynamics. Based on empirical facts that the market volatility can be well explained by the combination of short-term and long-term volatilities, a multi-scale stochastic volatility model that is governed by two factors evolving on different time-scales: a fast mean-reverting factor and a persistent, slow mean-reverting factor is applied to capture the dynamics of two assets in this paper. The validity of the model was tested by calibration against the market return distribution of the S&P 500 and Dow Jones Industrial Average Indices. Based on this multiscale model, an analytically approximate formula, in terms of the Gaussian copula, was obtained for the joint transition density and the parameters of this density were estimated using daily data from the S&P 500 and DAX Indices.