The Compound BSDE Method: A Fully Forward Method for Option Pricing and Optimal Stopping Problems in Finance

Battle Count: 78

Highly relevant for quantitative finance practitioners dealing with exotic derivatives pricing, particularly Bermudan and compound options in high dimensions. The fully forward nature of the method makes it computationally efficient and scalable. Directly applicable to derivatives desk pricing, risk management, and hedging of complex structured products. The method provides both prices and Greeks (deltas) simultaneously. However, it is primarily a pricing/valuation tool rather than a trading signal generator, and practical deployment would require integration with existing trading infrastructure and consideration of model risk.

Moderate to high complexity. Requires understanding of BSDE theory, stochastic calculus, and deep learning. The neural network architecture is relatively simple (fully connected, 2 hidden layers), but the simultaneous training of M coupled BSDEs with compounding conditions adds complexity. Implementation requires careful handling of time discretization, Brownian increments, and the joint loss functional. The code is available on GitHub, reducing implementation burden. Key challenges include: ensuring Lipschitz conditions are met, tuning hyperparameters for different problem sizes, handling high-dimensional state spaces, and achieving stable convergence for large M.

The paper provides a GitHub repository with code for numerical experiments, specifies all hyperparameters (network architecture: 2 hidden layers with 10+d1 neurons, tanh activations, Adam optimizer, learning rate 0.01 with exponential decay, batch size 5000), uses standard PyTorch 2.4, and provides analytical reference solutions for validation. The mathematical formulation is complete with all assumptions stated explicitly. Minor deduction for the reliance on specific hardware (MacBook Pro M1) and the need for careful tuning of Lipschitz constants.