positions. The framework starts with the near-term dynamics of the implied volatility surface and derives no … volatilities can also be constructed specific to, and different across, option contracts. Applying the new theory to the S&P 500 … index time series and options data, we extract volatility risk and risk premium from the volatility surfaces, and find that …

This paper documents the fact that in options markets, the (percentage) implied volatility bid-ask spread increases at … risk in an incomplete market with both directional and volatility risk. We extend this model to multi-periods and show that … the same phenomenon occurs there as well. Two new implications are generated: a volatility level effect and a volatility …

between catastrophe risk and the implied volatility smile of insurance stock options. We find that the slope is significantly …

skew swaps be used to explore the relationship between the skew in implied volatility and realized skew. Like the variance … almost half of the implied volatility skew can be explained by the skew risk premium. We provide evidence that skew and …

We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the … time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility … volatility and volatility-of-volatility risks. Volatility and volatility of volatility significantly and negatively predict …

We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the … time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility … which are more exposed to volatility and volatility-of-volatility risks. Volatility and volatility of volatility …

, such as the market excess return, size, book-to-market, momentum, liquidity, market volatility, and the variance risk …

We show that time-varying volatility of volatility is a significant risk factor which affects the cross-section and the … time-series of index and VIX option returns, beyond volatility risk itself. Volatility and volatility-of-volatility … are more exposed to volatility and volatility-of-volatility risks. Volatility and volatility of volatility significantly …

variance premium, the prices of equity index options, and the prices of volatility related derivatives in a long-run risks …