State-of-the-art stochastic volatility models generate a 'volatility smirk' that explains why out-of-the-money index puts have high prices relative to the Black-Scholes benchmark. These models also adequately explain how the volatility smirk moves up and down in response to changes in risk....

We nest multiple volatility components, fat tails and a U-shaped pricing kernel in a single option model and compare their contribution to describing returns and option data. All three features lead to statistically significant model improvements. A U-shaped pricing kernel is economically most...