Asset Pricing under uncertainty

TL;DR

This paper investigates how parameter uncertainty affects asset pricing and hedging in stochastic diffusion models, using Dirichlet forms to analyze sensitivities and explain bid-ask spreads and implied volatility smiles.

Contribution

It introduces a novel application of Dirichlet forms to quantify sensitivities and justify bid-ask spreads in option pricing under parameter uncertainty.

Findings

Sensitivity analysis can justify bid-ask spreads.

Closed-form sensitivities are obtainable for certain SDEs.

The framework produces implied volatility surfaces consistent with data.

Abstract

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.