λ model. A partial differential equation is derived as the transformation between the implied volatility surface and … such risk neutral probability. Given a well-interpolated volatility surface from market data, the risk neutral probability … local volatility function can be derived from Fokker-Planck equation. Based on such solution, I discuss possible forms of …

such as the Variance Gamma and the Normal Inverse Gaussian models as well as their stochastic volatility counterparts, e …

volatility risk. While pointing out the joint pricing kernel is not identified nonparametrically, we propose model-free estimates … of marginal pricing kernels of the market return and volatility conditional on the VIX. We find that the pricing kernel … present a U-shape. Hence, stochastic volatility is the key state variable responsible for the U-shape puzzle documented in the …

We investigate the effects of return jumps on option bid-ask spreads measured in implied volatility. To explain bid … shows that bid-ask volatility spread increases by 0.742% for a one-standard-deviation increase in our defined nonlinear jump … factor and by 0.247% for the factor of diffusion volatility. We obtain a R² value above 80%, and the jump risk factor is …

volatility jump diffusion model …

the market diffusive risk have a higher option-implied volatility level while firms with a larger return compensation for … market jump risk have steeper option-implied volatility slope …

This paper analyzes the joint dynamics of S&P 500 jumps and volatility using option-implied information. Our results … indicate that volatility is not related to the evolution of jumps but the uncertainty about volatility is. More uncertainty … about future volatility shifts the return distribution to the left, such that negative price jumps are more likely and …

fanning effect generates pronounced volatility smirks …