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

Area of Science:

• Quantitative Finance
• Computational Finance
• Machine Learning in Finance

Background:

• Overfitting and poor generalization are significant challenges in derivative pricing and hedging.
• Traditional models like Black-Scholes may not capture complex market dynamics.
• Neural networks (NNs) offer flexibility but require careful regularization.

Purpose of the Study:

• To evaluate the effectiveness of cross-validation, Bayesian regularization, early stopping, and bagging in mitigating overfitting.
• To improve the generalization performance of models for pricing and hedging derivative securities.
• To compare these techniques against a baseline neural network and the Black-Scholes model.

Main Methods:

• Application of four regularization techniques: cross-validation, Bayesian regularization, early stopping, and bagging.
• Utilizing daily S&P 500 index daily call options data from January 1988 to December 1993.
• Measuring pricing errors and delta-hedging errors (HE) against baseline and Black-Scholes models.

Main Results:

• Bayesian regularization yielded significantly smaller pricing and delta-hedging errors than baseline NN and Black-Scholes models in certain years.
• Early stopping reduced hedging error in four of six years, with no impact on pricing errors.
• Bagging, despite higher computational cost, provided the most accurate pricing and delta hedging, with substantially lower MSPE and HE standard deviations.

Conclusions:

• Bayesian regularization and bagging are effective strategies for improving derivative pricing and hedging accuracy.
• These advanced techniques offer superior generalization compared to baseline models, especially when model specifications are uncertain.
• The findings suggest incorporating these methods in practice for more robust financial modeling.