Statistical hedging with neural networks

This thesis investigates the problem of statistical hedging with artificial neural networks (ANNs). The statistical hedging is a data-driven approach that derives hedging strategy from data and hence does not rely on making assumptions of the underlying asset. Consider an investor who sells an option and wishes to hedge it with some amount of underlying asset. ANNs can be used to determine this number by minimising the discrete hedging error. In the first chapter, we provide a comprehensive literature review of papers on the topic of using ANNs for option pricing and hedging, as well as other related ones. Based on our research experience and summary of papers, we provide several advices that we believe are critical in using ANNs for option pricing and hedging problem. In particular, we point out an existing information leakage issue in the literature when preparing data. This review is invaluable for future researchers who are wish to work in this topic. In the second chapter, we consider the hedging problem in the single period case. The ANN is designed to output a hedging ratio directly, instead of first learning to prices. The experiments are taken on simulated Black-Scholes (BS), Heston, end-of-day S&P 500, and tick Euro Stoxx 50 datasets. The results show the ANN can significantly outperform the BS benchmark, but is only comparable to linear regressions on sensitivities. Hence, we illustrate that the edge of the two statistical hedging methods arises mainly from the existence of the leverage effect. Moreover, the information leakage found in the literature is reproduced. It’s shown that a wrong in- and out-of-sample split can overestimate the performance of statistical hedging methods. This leakage can be further exploited by tagging independent variables. Building on the previous chapter, sensitivity analysis are given in the third chapter. They concern data cleaning on the two historical datasets, different simulation parameters of the two simulated datasets, and data preparations. In particular, we show that the statistical hedging methods can also exploit drift and convexity apart from the leverage effect. In the last chapter, our model is extended to multiple periods on the Black-Scholes data. The replicating portfolio is rebalanced with a fixed frequency over the option’s life. We show again the ANN and linear regression methods outperform the BS benchmark, and their performance are comparable