Pricing and hedging derivative securities with neural networks: Bayesian regularization, early stopping, and bagging.

We study the effectiveness of cross validation, Bayesian regularization, early stopping, and bagging to mitigate overfitting and improving generalization for pricing and hedging derivative securities with daily S&P 500 index daily call options from January 1988 to December 1993. Our results indicate that Bayesian regularization can generate significantly smaller pricing and delta-hedging errors than the baseline neural-network (NN) model and the Black-Scholes model for some years. While early stopping does not affect the pricing errors, it significantly reduces the hedging error (HE) in four of the six years we investigated. Although computationally most demanding, bagging seems to provide the most accurate pricing and delta hedging. Furthermore, the standard deviation of the MSPE of bagging is far less than that of the baseline model in all six years, and the standard deviation of the average HE of bagging is far less than that of the baseline model in five out of six years. We conclude that they be used at least in cases when no appropriate hints are available.