We present a discrete time stochastic volatility model in which the conditional distribution of the logreturns is a Variance-Gamma, that is a normal variance-mean mixture with Gamma mixing density. We assume that the Gamma mixing density is time varying and follows an affine Garch model, trying...

We study the dependence structure between the S&P500, the VIX Index, and implicit Interexpectile Differences, that are an alternative measure of implied volatility based on the notion of implicit expectile, recently introduced in Bellini et al. (2018). After filtering the time series of the...

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynamics. After risk neutralization by means of a Bilateral Esscher Transform, the model admits a recursive procedure for the computation of the characteristic...

We show how to compute the expectiles of the risk neutral distribution from the prices of European call and put options. Empirical properties of these implicit expectiles are studied on a dataset of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference Δ<sub>τ...

We investigate the possibility of approximating the variance gamma distribution with a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm

In this paper we present an option pricing model based on the assumption that the underlying asset price is an exponential Mixed Tempered Stable Lévy process. We also introduce a new R package called PricingMixedTS that allows the user to calibrate this model using procedures based on loss or...