Pricing under uncertainty

English

Séminaire Probabilités & Statistique

29/09/2011 - 14:00 Simone Scotti (Université de Paris 7 / LPMA) Salle 1 - Tour IRMA

We study the effect of parameter uncertainty on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, using methods from the  theory of Dirichlet forms. We apply these techniques to hedging procedures in order to compute  the sensitivity  of SDE trajectories with respect to parameter perturbations. We show that this analysis can justify endogenously the presence of a bid-ask spread on the option prices. We also prove that if the stochastic differential equation admits a closed form representation then the sensitivities have closed form representations.
The same technique can be applied to a large class of physical and economical problems.