In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

We introduce a discrete-time model for log-return dynamics with observable volatility and jumps. Our proposal extends … the class of Realized Volatility heterogeneous auto-regressive gamma (HARG) processes adding a jump component with time … compensating for equity, volatility, and jump risks, the generating function under the risk-neutral measure inherits analytical …

straddles; second, we estimate the PVR in a Heston (1993) stochastic-volatility model. In both cases, the estimation is … more negative and its term structure is steeper when volatility is high. These findings are inconsistent with calibrations …

This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to … parameters of GARCH-type time-series models measuring how conditional volatility responds to return shocks. Markets in which … return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in …

This paper builds a real-options model of the firm with stochastic volatility to shed new light on the value premium … options, such securities hedge against volatility risk and command lower volatility risk premia than the equities of value or … financially healthy firms. Conversely, corporate debt will tend to command large volatility risk premia, allowing the model to …

In recent years there has been a remarkable growth of volatility options. In particular, VIX options are among the most … actively trading contracts at CBOE. These options exhibit upward sloping volatility skew and the shape of the skew is largely … independent of the volatility level. To take into account these stylized facts, this article introduces a novel two …

distribution was found. The implied volatility dependencies for the equilibrium conditions and with predicted utility and liquidity …

We extend and generalize some results on bounding security prices under several stochastic volatility models that …

stochastically correlated default intensities, or multivariate dynamic portfolio choice with volatility and correlation jumps. We … implied volatility skew term structures that are largely unrelated to the level and composition of the spot volatility. This … options. Second, we find that volatility and correlation jumps can imply an economically relevant intertemporal hedging demand …