A regularization approach to continuous learning with an application to financial derivatives pricing

Area of Science:

• Computational finance
• Machine learning for finance
• Neural network training

Background:

• Modeling time-varying nonlinear relationships is crucial in finance.
• Traditional methods struggle with dynamic financial data.
• Neural networks offer potential but require robust training for evolving patterns.

Purpose of the Study:

• To develop and evaluate a novel approach for training neural networks with time-varying relationships.
• To apply this method to the problem of financial derivatives pricing.
• To improve the accuracy and robustness of neural network models in dynamic financial markets.

Main Methods:

• Regularization techniques, specifically adding a variation penalty to the mean squared error criterion.
• Iterative Extended Kalman Filter (IEKF) as a learning rule, derived from a Bayesian perspective.
• Development of a specialized neural network architecture incorporating no-arbitrage pricing restrictions.

Main Results:

• The regularized neural network trained with IEKF demonstrated superior performance compared to benchmark models.
• Experiments with German stock index options data validated the effectiveness of the proposed method.
• The novel neural network architecture significantly enhanced pricing accuracy by adhering to no-arbitrage principles.

Conclusions:

• The IEKF-trained regularized neural network is a powerful tool for financial derivatives pricing with time-varying dynamics.
• Incorporating no-arbitrage constraints into neural network design further boosts performance.
• This approach offers a significant advancement in applying machine learning to complex financial modeling.