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The Volatility Premium Risk: Valuation and Forecasting
Keywords
premium risk, volatility risk, stochastic volatility, option pricing, risk forecasting
Abstract
Empirical studies, such as Lamoureux and Lastrapes (1993), Guo (1998), Fouque et al. (2000) show that the market price of volatility risk is nonzero and time varying. This paper provides a theoretical investigation of the market price of volatility risk. We consider that the market price of volatility risk is a function of two variables: the price of underlying asset and its volatility. We suggest a closed-form solution for the price of volatility risk under the conditions of stochastic volatility and of correlation between the underlying asset price and its volatility. This formula involves in a direct way the unobservable market price of volatility risk. We prove that the correlation between underlying price and its volatility has no impact on the price of volatility risk. Finally, we present empirical results using the prices of CAC 40 index and of CAC 40 index call options from January 2006 to December 2007.