Robust hedging of double touch barrier options

TL;DR

This paper develops model-free bounds and hedging strategies for digital double touch barrier options, demonstrating their effectiveness over traditional methods especially under market frictions and model uncertainties.

Contribution

It introduces tight bounds and hedging strategies for double touch barrier options using minimal assumptions and Skorokhod embedding techniques, advancing model-free pricing methods.

Findings

Derived tight bounds on option prices.

Constructed hedging strategies outperform standard methods.

Applicable under weak assumptions about the underlying process.

Abstract

We consider model-free pricing of digital options, which pay out if the underlying asset has crossed both upper and lower barriers. We make only weak assumptions about the underlying process (typically continuity), but assume that the initial prices of call options with the same maturity and all strikes are known. Under such circumstances, we are able to give upper and lower bounds on the arbitrage-free prices of the relevant options, and further, using techniques from the theory of Skorokhod embeddings, to show that these bounds are tight. Additionally, martingale inequalities are derived, which provide the trading strategies with which we are able to realise any potential arbitrages. We show that, depending of the risk aversion of the investor, the resulting hedging strategies can outperform significantly the standard delta/vega-hedging in presence of market frictions and/or model misspecification.