Arbitrage Opportunities and their Implications to Derivative Hedging

TL;DR

This paper investigates how random arbitrage opportunities affect derivative hedging, extending existing pricing theories to include arbitrage risk and providing adaptable hedging confidence intervals.

Contribution

It extends asymptotic pricing theory to incorporate arbitrage risk in derivative hedging, offering practical hedging bands independent of arbitrage statistical details.

Findings

Hedging confidence intervals can be adapted to arbitrage risk levels.

Hedging bands are independent of arbitrage statistical characteristics.

The approach provides practical tools for arbitrage-aware derivative hedging.

Abstract

We explore the role that random arbitrage opportunities play in hedging financial derivatives. We extend the asymptotic pricing theory presented by Fedotov and Panayides [Stochastic arbitrage return and its implication for option pricing, Physica A 345 (2005), 207-217] for the case of hedging a derivative when arbitrage opportunities are present in the market. We restrict ourselves to finding hedging confidence intervals that can be adapted to the amount of arbitrage risk an investor will permit to be exposed to. The resulting hedging bands are independent of the detailed statistical characteristics of the arbitrage opportunities.