Discrete-Time Quadratic Hedging of Barrier Options in Exponential L\'{e}vy Model

TL;DR

This paper investigates the effectiveness of discrete-time quadratic hedging strategies for barrier options within a calibrated exponential Lévy model, highlighting the significant influence of hedging errors on pricing accuracy.

Contribution

It introduces a realistic discrete-time hedging approach for barrier options in Lévy models and quantifies the dominant effect of hedging errors on prices.

Findings

Hedging errors significantly impact option prices.

Hedging errors are several times more influential than other biases.

The model reflects leptokurtic features of equity returns.

Abstract

We examine optimal quadratic hedging of barrier options in a discretely sampled exponential L\'{e}vy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing biases studied in the literature.