A Financial Metric for Comparing Volatility Models: Do Better Models Make Money?

This paper proposes a fully-specified equilibrium approach which provides both financial and utility metrics for comparing alternative beliefs about the conditional distribution of a stock price. In this paper we focus on differences in volatility dynamics which are inputs to investors' assessments of a derivative security. We construct equilibria in which different investors (models) trade a derivative that is sensitive to the volatility of the underlying asset. Our approach can be used to assess the economic importance of parameter uncertainty and model misspecification. Examples using simulated data demonstrate that informed investors (investors with better models) make money and utility gains against uninformed investors. Parameter uncertainty and model uncertainty in general both lead to lower profits. Using historical data we find that GARCH models make significant gains against constant and exponentially weighted moving average specifications of volatility.