Hedging With Linear Regressions and Neural Networks

Abstract

We study neural networks as nonparametric estimation tools for the hedging of options. To this end, we design a network, named HedgeNet, that directly outputs a hedging strategy. This network is trained to minimize the hedging error instead of the pricing error. Applied to end-of-day and tick prices of S&P 500 and Euro Stoxx 50 options, the network is able to reduce the mean squared hedging error of the Black-Scholes benchmark significantly. However, a similar benefit arises by simple linear regressions that incorporate the leverage effect.

Keywords:

• Benchmarking
• Black–Scholes
• Hedging error
• Information leakage
• Leverage effect
• Statistical hedging

Acknowledgments

We thank Matthias Büchner, Agostino Capponi, Philipp Dörsek, Aleš Černý, Jean-Pierre Fouque, Camilo Garcia, Lukas Gonon, Harald Oberhauser, Philipp Illeditsch, Antoine Jacquier, Johannes Muhle-Karbe, Peter Spoida, Josef Teichmann, and James Wolter for helpful discussions on the subject matter of this article. We are grateful to Deutsche Börse, in particular, Peter Spoida, for providing us with Euro Stoxx 50 options and futures tick data. We are indebted to two anonymous referees and an associate editor for several very insightful comments that improved the article.