CAT Bond Pricing with Kolmogorov--Arnold Networks

We study the approximation of CAT bond prices under a compound Poisson loss model with lognormal severities using Kolmogorov--Arnold Networks (KANs). Building on a baseline-plus-residual learning pipeline, we train a KAN on the deviation from a closed-form lognormal baseline price and extract an interpretable symbolic pricing formula. The extracted formula achieves an average relative pricing error of 0.483% on a fully disjoint holdout sample of 90,000 simulated prices. In contrast to purely empirical modelling, we also analyse structural properties of the true CAT bond pricing map, including monotonicity with respect to the catastrophe arrival intensity lambda, the initial short rate r0, and the trigger threshold D. We derive sufficient conditions on KAN edge functions that guarantee these monotonicities are preserved by the learned model, and formulate a monotonicity-constrained training objective with a convergence guarantee. Our results suggest that symbolic KAN surrogates provide a practical compromise between accuracy, computational speed, and interpretability for CAT bond valuation.