Efficient Calibration for Option Pricing via a Physics-Informed Chebyshev Kolmogorov-Arnold Network

Efficient calibration is essential for the practical application of option pricing models. The Fractional Stochastic Volatility Jump Diffusion (FVSJ) model proposed by Zhang and Yong [1] can reproduce several stylized features observed in option markets, including the volatility smile, volatility clustering, and long-memory effects. However, its multiple stochastic components make conventional calibration computationally expensive. This paper proposes a two-step calibration framework that combines a neural network with a differential evolution (DE) algorithm. In the first step, we construct a Physics-Informed Kolmogorov-Arnold Network (PCKAN) to approximate the FVSJ pricing map. Specifically, we replace the B-spline basis in KAN with second-kind Chebyshev polynomials and incorporate a Black-Scholes PDE residual as an additional penalty term in the training objective, aiming to improve global approximation and enhance numerical stability and interpretability. In the second step, the trained PCKAN is used as a fast surrogate pricer within the DE algorithm to accelerate parameter estimation. Empirical results show that the proposed method achieves calibration accuracy comparable to direct pricing while substantially reducing computational time.