Parameter Recovery for the Vasicek Model Using Kolmogorov-Arnold Networks: A Synthetic Study with Zero-Coupon Pricing Implications

Abstract

When governments, corporations, municipalities, or other public institutions require medium- or long-term funding, they frequently issue bonds to investors. This paper studies parameter calibration for the Vasicek short-rate model and the pricing implications of recovered parameters for zero-coupon bonds. The theory is stated under the risk-neutral measure, while the physical-torisk- neutral mapping is summarized explicitly to avoid ambiguity in the pricing drift. A splinebased Kolmogorov-Arnold Network (KAN) is compared with exact maximum likelihood estimation (EMLE), Euler-Maruyama maximum likelihood estimation (EMMLE), a quadratic-variationinitialized two-stage likelihood baseline (QV-2S), and a multilayer perceptron (MLP). The training corpus contains 1.2 million independent synthetic Vasicek paths, and the common out-of-sample test set contains 10,000 additional paths. KAN obtains the lowest overall root mean squared error (RMSE) for the long-run mean, volatility, and mean-reversion speed, although its advantage over the MLP is small. Downstream results are metric-dependent: KAN achieves the lowest aggregate zero-coupon price RMSE, whereas the MLP achieves a slightly lower aggregate yield RMSE. Paired path-level bootstrap intervals confirm KAN’s price-RMSE advantage over all comparators, but also confirm the MLP’s small yield-RMSE advantage over KAN. The findings therefore support supervised amortized parameter recovery in this in-distribution synthetic design, but do not establish that KAN uniformly dominates either likelihood estimation or a conventional neural network.