and portfolios. We document that the SDF is dense in characteristics with the impliedrealized volatility spread, option …

function to maturity that satisfies the consistency condition, the European volatility smile is obtained. As an illustration of … the formalism, we show that when the underlying asset price changes at constant volatility (standard deviation), the … offer a parameterization of the volatility smile with a closed-form expression using pre-calculated tables. Comprehensive …

We propose model-free (nonparametric) estimators of the volatility of volatility and leverage effect using high … characteristic function of the price increment until the options’ expiration and we use these estimates to recover spot volatility …. Our volatility of volatility estimator is then formed from the sample variance and first-order autocovariance of the spot …

volatility measures and estimators applied in the process of valuation. We calculate the Black model with historical (BHV …), implied (BIV) and several different types of realized (BRV) volatility (additionally searching for the optimal interval Δ, and …. Applying different volatility processes for the same pricing model suggest strongly that point-estimate, not averaged process …

check the properties of option pricing models with different assumptions concerning the volatility process (historical … pricing and to check the robustness of our results. The Black model with implied volatility (BIV) comes as the best model and … the realized volatility model as the worst one. Moreover, we do not see any advantage of much complex and time …

) the statistical properties of the Korea's representative implied volatility index (VKOSPI) derived from the KOSPI 200 … options and (b) macroeconomic and financial variables that can predict the implied volatility process of the index, using … the VKOSPI. In addition, we find that the stock market return and implied volatility index of the US market (i.e., the S …