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 study a new class of three-factor affine option pricing models with interdependent volatility dynamics and a … stochastic skewness component unrelated to volatility shocks. These properties are useful in order (i) to model a term structure … of implied volatility skews more consistent with the data and (ii) to capture comovements of short and long term skews …

volatility jump diffusion model …

Financial markets exhibit high levels of volatility. Volatile markets are usually associated with high risks and … high volatility using a suitable hedging structure. One particular volatility hedge, involves taking a position in an …

This paper provides an empirical study on the predictability of implied volatility using dataset collected from the … implied volatility characteristics across various maturities. We applied both in and out-of-sample tests that include the … provides evidence of non-random movement in the implied volatility series and indicates predictability of implied volatility …

, and the corresponding implied volatility surfaces have been analyzed in some detail. In the non-asymptotic regimes, option … trivially expressed in terms of their implied volatility. Recently, attempts at calculating the asymptotic limits of the implied … volatility have yielded several expressions for the short-time, long-time, and wing asymptotics. In order to study the volatility …

between stock returns and idiosyncratic return volatility at the firm level. By allowing for the volatility of the underlying … idiosyncratic choice variables to exhibit independent switches between a high and low volatility regime, we show that the options …' constant expected returns are composed of (i) a state dependent drift term that relates positively with the volatility regime …