Kernel based physics-informed machine learning for approximating CEV model under nonlinear volatility regimes in real-world financial environments

Artificial intelligence is increasingly being used to address complex modelling challenges in financial markets, especially for problems involving nonlinear dynamics. In this work, a novel Physics-Informed Least Squares Support Vector Machine framework has been applied to approximate the solution of the Constant Elasticity of Variance model, which is widely used for pricing European call options with state-dependent volatility. The method integrates the model's structure directly into the learning process, producing a smooth, mesh-free approximation of the option pricing surface. Multiple kernel functions are studied to evaluate the model's ability to capture different volatility regimes induced by the elasticity parameter. Extensive kernel wise comparisons, error analysis, and visualization are performed. The results are benchmarked against analytical solutions and further validated using real-world market data. A sensitivity analysis on financial and algorithmic parameters is also conducted to assess the method's robustness. This work demonstrates that physics-informed learning combined with kernel-based AI techniques offers a reliable and efficient approach for solving nonlinear problems in quantitative finance.