. This BS-shaped option pricing formula allows us to derive interesting characterizations of the volatility smile, that is …

generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two … implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility …

Stochastic volatility models, aka SVOL, are more difficult to estimate than standard time-varying volatility models … volatility forecasts especially around crucial periods of high volatility. We extend the basic SVOL needs to allow for the … model diagnostics, such as the identification of outliers for stochastic volatility models or the assessment of the …

in a conditionally log-normal setting. Extensions to mixtures of log-normals lead to stochastic volatility models …, including models with leverage effect. We characterize implications of such models for volatility smiles and show that they are … fully similar to the ones derived from continuous-time stochastic volatility models. We then review usual continuous …