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.

A risk-neutral valuation framework is developed for pricing and hedging in-play football bets based on modelling scores by independent Poisson processes with constant intensities. The Fundamental Theorems of Asset Pricing are extended to this set up which enables us to derive novel...

In this note we apply the recently established Wiener-Hopf Monte Carlo (WHMC) simulation technique for Levy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have...

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...

Recent work by Nualart and Schoutens (2000), where a kind of chaotic property for Lévy processes has been proved, has enabled us to develop a Malliavin calculus for Lévy processes. For simple Lévy processes some useful formulas for computing Malliavin derivatives are deduced. Applications for...

A suitable canonical Lévy process is constructed in order to study a Malliavin calculus based on a chaotic representation property of Lévy processes proved by Itô using multiple two-parameter integrals. In this setup, the two-parameter derivative Dt,x is studied, depending on whether x=0 or...

Let M be a continuous two-parameter L4-martingale, vanishing on the axes, and f a 1-function. In Itô's formula for f(M2) a new martingale M is involved. This martingale can be interpreted formally as the stochastic integral [integral operator][not partial differential]1M[not partial...