We propose novel nonparametric estimators for stochastic volatility and the volatility of volatility. In doing so, we … relax the assumption of a constant volatility of volatility and therefore, we allow the volatility of volatility to vary … Standard & Poor´s 500 equity index, the estimates revealed strong evidence that both volatility and the volatility of …

We revisit the so-called Bergomi-Guyon expansion (Bergomi and Guyon, Stochastic volatility's orderly smiles, Risk, May … 2012). The expansion provides the smile of implied volatility at second order in the volatility of volatility for general … stochastic volatility models, including variance curve models. First, we present a new derivation of the price expansion which …

trade and hedge volatile swings in Bitcoin prices effectively. The violation of constant volatility and the log …-normality assumption of the Black-Scholes option pricing model led to the discovery of the volatility smile, smirk, or skew in options … markets. These stylized facts; that is, the volatility smile and implied volatilities implied by the option prices, are well …

pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier … stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic … volatility process which is assumed to follow Cox-Ingersoll-Ross ("CIR") model. …

log-returns and their volatility with the aim of analysing which risk factors and which distribution features provide a …-returns and volatility offer the best trade-off between model performance and parsimony …