PRICE ROBUSTNESS TO MODEL RISK

Two types of price models with jumps are considered: either we describe small variations of price dynamics with a Poisson random measure with infinite activity, or with a Brownian motion.
We prove and discuss the robustness of prices of options written on the underlying dynamics above.
As for the computation of these prices itself, we introduce the conditional density method as an alternative to the other methods for the computation of the deltas already in use. This method can be successfully applied also to multi-factor type of models, popular in the modeling of spot prices in electricity markets.
We extend the work to a jump-diffusion framework where robustness of option prices is discussed and an extension of the Malliavin method is proposed for the computation of prices.
Various examples will be given for the different aspect treated.
The presentation is based on joint works with Fred E. Benth e Asma Khedher.