We introduce an algorithm for the pricing of finite expiry American options driven by L\'evy processes. The idea is to tweak Carr's `Canadisation' method, cf. Carr [9] (see also Bouchard et al [5]), in such a way that the adjusted algorithm is viable for any L\'evy process whose law at an...

Recent models of the insurance risk process use a Lévy process to generalise the traditional Cramér–Lundberg compound Poisson model. This paper is concerned with the behaviour of the distributions of the overshoot and undershoots of a high level, for a Lévy process which drifts to −∞...

This paper proves that the log-spot in the Heston model has a density and gives an expression of this density as an infinite convolution of Bessel type densities. Such properties are deduced from a factorization of the characteristic function, mainly obtained through an analysis of the complex...

Let {X1(t)}0<=t<=1 and {X2(t)}0<=t<=1 be two independent continuous centered Gaussian processes with covariance functions R1 and R2. We show that if the covariance functions are of finite p-variation and q-variation respectively and such that p-1+q-1>1, then the Lévy area can be defined as a double Wiener-Itô integral with respect to an isonormal Gaussian process induced by X1 and X2. Moreover, some properties of the characteristic function of that generalised Lévy area are studied.

We look at the problem of pricing CoCo bonds where the underlying risky asset dynamics are given by a smile conform model, more precisely an exponential Lévy process incorporating jumps and heavy tails. A core mathematical quantity that is needed in closed form in order to produce an exact...

We provide an alternative method for analysis of multifractal properties of time series. The new approach takes into account the behaviour of the whole multifractal profile of the generalized Hurst exponent $h(q)$ for all moment orders $q$, not limited only to the edge values of $h(q)$...

We construct explicitly a bridge process whose distribution, in its own filtration, is the same as the difference of two independent Poisson processes with the same intensity and its time 1 value satisfies a specific constraint. This construction allows us to show the existence of...