On model-independent pricing/hedging using shortfall risk and quantiles

TL;DR

This paper develops model-independent methods for pricing and hedging exotic options using shortfall risk and quantiles, extending duality results to a broader setting with given marginal distributions.

Contribution

It introduces new duality results for model-independent pricing and hedging using shortfall risk and quantiles, generalizing previous duality frameworks.

Findings

Minimum initial amount equals super-hedging price plus inverse utility at shortfall level

Quantile hedging is equivalent to super-hedging for knockout options

Results extend duality theory to model-independent setting with given marginals

Abstract

We consider the pricing and hedging of exotic options in a model-independent set-up using \emph{shortfall risk and quantiles}. We assume that the marginal distributions at certain times are given. This is tantamount to calibrating the model to call options with discrete set of maturities but a continuum of strikes. In the case of pricing with shortfall risk, we prove that the minimum initial amount is equal to the super-hedging price plus the inverse of the utility at the given shortfall level. In the second result, we show that the quantile hedging problem is equivalent to super-hedging problems for knockout options. These results generalize the duality results of [5,6] to the model independent setting of [1].