The impact of uncertainties on the pricing of contingent claims

TL;DR

This paper investigates how parameter uncertainties influence the pricing of contingent claims using Dirichlet Forms methods, demonstrating the model's ability to produce realistic bid-ask spreads and implied volatility surfaces.

Contribution

It introduces a novel application of Dirichlet Forms techniques to quantify sensitivities of SDEs to parameter perturbations in option pricing models.

Findings

Model reproduces bid-ask spreads.

Sensitivities have closed-form expressions in certain models.

Framework aligns with observed implied volatility smiles.

Abstract

We study the effect of parameters uncertainties on a stochastic diffusion model, in particular the impact on the pricing of contingent claims, thanks to Dirichlet Forms methods. We apply recent techniques, developed by Bouleau, to hedging procedures in order to compute the sensitivities of SDE trajectories with respect to parameter perturbations. We show that this model can reproduce a bid-ask spread. We also prove that, if the stochastic differential equation admits a closed form representation, also the sensitivities have closed form representations. We exhibit the case of log-normal diffusion and we show that this framework foresees a smiled implied volatility surface coherent with historical data.