one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use …

prices caused by stochastic volatility. -- option pricing ; autoregression ; heteroskedasticity ; GARCH ; leverage effect …

) and volatility (Theorem 2) swaps for stochastic volatilities driven by the semi-Markov processes. We also discuss some … extensions of the obtained results such as local semi-Markov volatility, Dupire formula for the local semi-Markov volatility and …

We introduce an asymptotic expansion for forward start options in a multi-factor local-stochastic volatility model. We … derive explicit approximation formulas for the so-called forward implied volatility which can be useful to price complex path … generalized to a wider class of local-stochastic volatility models. We illustrate the effectiveness of the technique through some …

We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive …

In this paper we propose a stochastic volatility model for crude oil markets that has the particularity to feature a … OVX volatility data. The model characterizes two states: a normal state with low volatility and negative variance premium … and acrisis state with high volatility and positive variance risk premium. The estimated states are consistent with GDP …

-affine volatility dynamics. We use extensive empirical data sets to study how infinite-activity Variance Gamma and Normal Inverse … Gaussian jumps with affine and non-affine volatility dynamics improve goodness of fit and option pricing performance. With …