Smooth ambiguity preferences and asset prices with a jump-diffusion process

Abstract

The present study extends the continuous-time smooth ambiguity preferences model by introducing a Poisson jump component into the agent's consumption process. Under this setting, we examine the effect of ambiguity with respect to both Brownian motion and a Poisson jump process on asset prices. Using reasonable values for preferences parameters, our model replicates historical moments of the U.S. asset returns, including the equity premium, equity volatility, and risk-free rate. Our model also generates substantial equity variance premium and a mildly downward sloping volatility curve of equity options that are consistent with the U.S. data. In addition, our model captures the predictive power of the variance premium with respect to equity returns.