Hedging with Small Uncertainty Aversion

TL;DR

This paper develops a framework for pricing and hedging derivatives under small volatility uncertainty by penalizing less plausible models, resulting in explicit formulas linked to the security's cash gamma.

Contribution

It introduces a novel approach that incorporates small uncertainty aversion into derivative pricing, providing explicit formulas based on model penalization.

Findings

Explicit pricing formulas derived for small uncertainty aversion.

Hedging strategies expressed in terms of cash gamma.

Framework accounts for model plausibility via penalization.

Abstract

We study the pricing and hedging of derivative securities with uncertainty about the volatility of the underlying asset. Rather than taking all models from a prespecified class equally seriously, we penalise less plausible ones based on their "distance" to a reference local volatility model. In the limit for small uncertainty aversion, this leads to explicit formulas for prices and hedging strategies in terms of the security's cash gamma.