The story of modelling financial markets with stochastic processes began in 1900 with the
study of Bachelier (1900). He modelled stocks as a Brownian motion with drift. However, the …

The book offers an accessible reference for researchers in the probability, statistics and
special functions communities. It gives a variety of interdisciplinary relations between the two …

The only normal martingales which posses the chaotic representation property and the weaker
predictable representation property and which are at the same time also Lévy processes, …

The role of characteristic functions in finance has been strongly amplified by the development
of the general option pricing formula by Carr and Madan. As these functions are defined …

… Finally, we mention the Meixner model (see Grigelionis 1999; Schoutens 2001). All these
models give a much better fit to the data and lead to an improvement with respect to the Black-…

We show that several advanced equity option models incorporating stochastic volatility can
be calibrated very nicely to a realistic option surface. More specifically, we focus on the …

We study an unusual connection between orthogonal polynomials and martingales. We
prove that all classical orthogonal polynomials from the Meixner class, when evaluated at a …

We discuss a Lévy multivariate model for financial assets which incorporates jumps, skewness,
kurtosis and stochastic volatility. We use it to describe the behaviour of a series of stocks …

In the Black-Scholes option price model Brownian motion and the underlying Normal distribution
play a fundamental role. Empirical evidence however shows that the normal distribution …

In this paper, we show how we can deploy machine learning techniques in the context of
traditional quant problems. We illustrate that for many classical problems, we can arrive at …