We consider the mixed AR(1) time series model <Equation ID="Equa"> <EquationSource Format="TEX">$$X_t=\left\{\begin{array}{ll}\alpha X_{t-1}+ \xi_t \quad {\rm w.p.} \qquad \frac{\alpha^p}{\alpha^p-\beta ^p},\\ \beta X_{t-1} + \xi_{t} \quad {\rm w.p.} \quad -\frac{\beta^p}{\alpha^p-\beta ^p} \end{array}\right.$$</EquationSource> </Equation>for −1  β <Superscript> p </Superscript> ≤ 0 ≤ α <Superscript>...</superscript></superscript></equationsource></equation>

In this paper, we propose a parametric model of implied variance which is a natural generalization of the SVI model. The model improves the SVI by allowing more flexibly the negative curvature in the tails which is justified both theoretically and empirically. The fitting of the model, comparing...

This paper studies fundamental aspects of modelling data using multivariate Watson distributions. Although these distributions are natural for modelling axially symmetric data (i.e., unit vectors where ±x are equivalent), for high-dimensions using them can be difficult—largely because for...