Stochastic volatility models for the implied correlation index. Evidence, properties and pricing

This paper studies the implied correlation index (CIX), revealing a new stylized fact: heteroscedasticity in correlation. A correlation stochastic volatility (C-SV) model is proposed and a consistent estimation methodology is implemented on CBOE S&P 500 CIX historical data. The impact of the SV parameters is studied for two types of crisis-motivated CIX derivatives, and the empirical study demonstrates that new parameters can have a significant influence of up to 60% on digital option prices.