Modeling the Dynamics of Correlations among Implied Volatilities

Robert F. Engle · Stephen Figlewski

51 citations0/0 files storedEuropean Finance Review

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Market Dynamics and Volatility

Abstract

Abstract Implied volatility (IV) reflects both expected empirical volatility and also risk premia. Stochastic variation in either creates unhedged risk in a delta hedged options position. We develop EGARCH/DCC models for the dynamics of volatilities and correlations among daily IVs from options on twenty-eight large cap stocks. The data strongly support a general correlation structure and also a one-factor model with the VIX index as the common factor. Using IVs from stocks that are either highly correlated with the target stock’s IV or in the same industry together with the VIX can significantly improve hedging of individual IV changes.

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References

1973The Pricing of Options and Corporate Liabilities 1986Generalized autoregressive conditional heteroskedasticity 1982Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation 1991Conditional Heteroskedasticity in Asset Returns: A New Approach 1993On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 2002Dynamic Conditional Correlation 1987The Pricing of Options on Assets with Stochastic Volatilities

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