Numerical Solution of Passport Option Pricing Problem with Polynomial Neural Networks

Satyadev Badireddi (), Saurabh Bansal () and Srinivasan Natesan ()
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Satyadev Badireddi: Indian Institute of Technology Guwahati, Department of Mathematics
Saurabh Bansal: Indian Institute of Technology Guwahati, Department of Mathematics
Srinivasan Natesan: Indian Institute of Technology Guwahati, Department of Mathematics

Computational Economics, 2025, vol. 66, issue 6, No 9, 4695-4726

Abstract: Abstract In this article, we proposed a single layer feedforward polynomial neural network for numerically solving the passport option pricing problem. The passport option can be valued by solving a nonlinear backward pricing PDE and it is difficult to find analytical solution of this PDE. Laguerre, Hermite and Legendre polynomials are employed separately as the hidden layer neuron’s activation function. The training points are uniformly chosen within the domain, the passport option PDE with the final condition and boundary conditions are defined as a penalty function. Network connection weights are optimized by means of the extreme learning machine technique. The proposed neural network approximates not only the passport option value but also some of its important Greeks (Delta, Gamma and Theta) without requiring any additional effort. Finally, exhaustive numerical experiments are carried out to verify the efficiency of the proposed technique.

Keywords: Option pricing; Passport options; Nonlinear PDE; Polynomial neural network; Numerical solution; Extreme learning machine algorithm; Greeks (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10614-025-10849-9

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