Can Tests Based on Option Hedging Errors Correctly Identify Volatility Risk Premia?

Tests for the existence and the sign of the volatility risk premium are often based on expected option hedging errors. When the hedge is performed under the ideal conditions of continuous trading and correct model specification, the sign of the premium is the same as the sign of the mean hedging error for a large class of stochastic volatility option pricing models. We show, however, that the problems of discrete trading and model mis-specification, which are necessarily present in an empirical study, may cause the standard test to yield unreliable results. In particular, ignoring a possible jump risk premium can lead to incorrect conclusions about the volatility risk premium. We also show that delta-gamma hedges do not increase the reliability of the test compared to simple delta hedges.