  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. We examine the case of
log-normal diffusion and we show that this framework leads to a smiled implied
volatility surface coherent with historical data.
