This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in Palmowski & Rolski (2002). With this generic approach, we first derive explicit...

In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is crucially important to financial institutions to properly account...

The VIX index is not only a volatility index but also a polynomial combination of all possible higher moments in market return distribution under the risk-neutral measure. This paper formulates the VIX as a linear decomposition of four fundamentally different elements: the realized variance...

The standard shifted lognormal model, defined by just two parameters, provides a remarkably good fit to the market implied volatilities of VIX options.Inspired by an analytic approximation derived by Lee and Wang, we propose a simple, intuitive extension that provides better empirical fits while...

We provide an efficient swaption volatility approximation for longer maturities and tenors, under the lognormal forward-LIBOR model. In particular, we approximate the swaption volatility with a mean update of the spanning forward rates. Since the joint distribution of the forward rates is not...

In this article, the Universal Approximation Theorem of Artificial Neural Networks (ANNs) is applied to the SABR stochastic volatility model in order to construct highly efficient representations. Initially, the SABR approximation of Hagan et al. [2002] is considered, then a more accurate...

Affine jump diffusion models in general and affine stochastic volatility models in particular are important modeling tools in finance. Their popularity resides in their exibility coupled with their analytical tractability, especially with respect to characteristic functions and polynomial...