Error Propagation in Dynamic Programming: From Stochastic Control to Option Pricing

Battle Count: 84

Highly relevant to quantitative trading and derivatives pricing. The paper directly addresses American/Bermudan option pricing, a core problem in quantitative finance. The KRR-DP algorithm provides provable convergence guarantees for value function estimation, which is critical for risk management and hedging. The method scales to high-dimensional settings (tested up to d=20) and offers competitive accuracy with significantly reduced computation time compared to GPR-Tree (e.g., 11s vs 49609s for d=20). However, it is primarily a pricing/valuation tool rather than a direct trading signal generator.

Moderate complexity. The algorithm requires: (1) Monte Carlo simulation of GBM paths, (2) backward induction loop with Bellman operator evaluation, (3) KRR regression at each time step using FALKON, (4) proper hyperparameter tuning (regularization lambda, kernel bandwidth). The use of FALKON simplifies the kernel computation, but the nested structure (MC within regression within backward recursion) adds implementation complexity. The clipped estimator and source condition assumptions require careful handling. No complete open-source implementation of the full pipeline is provided.

The paper references the FALKON algorithm from a public GitHub repository (https://github.com/FalkonML/falkon). Simulation parameters are described (T=9, X0=100, K=100, r=0.05, sigma=0.2, rho=0.2, lambda=10^-6, RBF lengthscale grid {40,80}). However, no dedicated code repository for the full KRR-DP pipeline is provided. Benchmarks are replicated from Goudenege et al. (2020). Hardware specifications are given (NVIDIA T4 GPU, 16GB, Intel Xeon CPU, 12GB RAM).