A New Method for Option Pricing Based on Cardinal Hermite Interpolant Multiwavelets and the Characteristic Function

ABSTRACT This paper introduces a novel and efficient numerical method for pricing European options. Our approach leverages the characteristic function framework and approximates the risk‐neutral density of the underlying asset price process using a series expansion in cardinal Hermite interpolant multiwavelets. We first detail the construction and key properties of these multiwavelets, including their interpolation capabilities and suitability for function approximation on bounded intervals. A primary challenge in collocation methods is their inherent sensitivity to the selection of collocation points. To address this, we formulate the pricing problem as a rectangular system of linear equations, which is then solved robustly using a least squares technique, thereby enhancing the method's stability and accuracy. We provide a rigorous theoretical analysis of the proposed scheme, establishing its convergence and deriving the associated order of convergence. The analytical findings are strongly supported by extensive numerical experiments. These results not only validate the theoretical convergence rates but also demonstrate the high computational efficiency and accuracy of our method compared to established benchmarks.