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 …

, which is defined as the ratio between the realized volatility and trading volume and which refines the popular price impact … measure proposed by Amihud (2002). In our model, both price volatility and market liquidity are assumed to follow stochastic … processes in continuous time. In this setting, characterized by stochastic volatility and liquidity, we prove that the realized …

significant price jump component in variance swap rates. A model-based analysis shows that investors' willingness to ensure … against volatility risk increases after a market drop. This effect is stronger for short horizons and more persistent for long …

We derive analytic series representations for European option prices in polynomial stochastic volatility models. This … polynomial option price series expansion performs as efficiently and accurately as the Fourier transform based method in the …

The uncertainty of U.S. core inflation, measured by the stochastic volatility of forecast errors, has soared to a level …