We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of Black-Scholes model (BSM). Even in the case of BSM, our approach is simpler as we essentially use only the Ito's formula and do not need more advanced results such as those of Bessel proces...

The conventional control variate method proposed by Kemna and Vorst (1990) to evaluate Asian options under the Black-Scholes model can be interpreted as a particular selection of linear martingale controls. We generalize the constant control parameter into a control process to gain more reduction on variance. By means of an option price approximation, we construct a martingale control variate m...

Hatem Ben-Ameur • Michèle Breton • Pierre L’Ecuyer GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7 GERAD and Département des Méthodes Quantitatives de Gestion, École des H.E.C., 3000 Chemin de la Côte Sainte-Catherine, Montréal, Canada H3T 2A7 GERAD and Département d’Informatique et de Recherche Opé...

The influence of the analytical properties of the Black-Scholes PDE formulation for American and Asian options on the quality of the numerical solution is discussed. It appears that numerical methods for PDEs are quite robust even when the mathematical formulation is not well posed.

This is the second part of our survey on exponential functionals of Brownian motion. We focus on the applications of the results about the distributions of the exponential functionals, which have been discussed in the first part. Pricing formula for call options for the Asian options, explicit expressions for the heat kernels on hyperbolic spaces, diffusion processes in random environments and ...

In this article, we give a brief informal introduction to Malliavin Calculus for newcomers. We apply these ideas to the simulation of Greeks in Finance. First to European-type options where formulas can be computed explicitly and therefore can serve as testing ground. Later we study the case of Asian options where close formulas are not available, and we also open the view for including more ex...

In a recent article, Barraquand and Pudet (1996) state that the lattice based Forward Shooting Grid (FSG) method is convergent for Asian options if either nearest lattice point or linear interpolation is used. Moreover, this result is claimed to be independent of any relationship between the grid quantization parameter (for the spacing of the nodal averages) and the timestep size. However, a mo...

We construct a sequence of functions that uniformly converge (on compact sets) to the price of Asian option, which is written on a stock whose dynamics follows a jump diffusion, exponentially fast. Each of the element in this sequence solves a parabolic partial differential equation (not an integro-differential equation). As a result we obtain a fast numerical approximation scheme whose accurac...