Numerical Solution of Passport Option Pricing Problem with Polynomial Neural Networks
Paper proposes a single-layer polynomial neural network with extreme learning machine for solving passport option pricing PDEs and estimating Greeks.
What it examines
Using a single-layer feedforward polynomial neural network with Laguerre, Hermite, and Legendre activation functions, this study tackles the nonlinear backward PDE for passport option pricing. Uniform training points and an extreme learning machine optimize the network to accurately compute both option values and key Greeks.
What it concludes
The results confirm that polynomial neural networks reliably solve complex nonlinear PDEs in option pricing while efficiently computing values and Greeks. This method can be applied in financial risk management, derivative pricing, and trading, with future research exploring alternative polynomial bases and deeper network architectures.
Evidence objects
Innovative research introduces a single layer polynomial neural network employing Laguerre, Hermite, and Legendre activations with an extreme learning machine algorithm to solve nonlinear backward pricing PDE and compute Greeks.
key_findings bullet 1 · key_findings · validation V0
The study converts a complex passport option pricing problem into a practical numerical framework by integrating polynomial activations and advanced learning techniques, revealing unexpected convergence speed and solution precision improvements.
key_findings bullet 2 · key_findings · validation V0
While demonstrating robust numerical performance and accurate Greek estimation, the research acknowledges critical limitations in model scalability and broader applicability to diverse financial derivatives, urging further exploration in computational finance.
key_findings bullet 3 · key_findings · validation V0
Addressing a challenging derivative modeling problem, the paper numerically solves the passport option pricing $\text{PDE}$ using a specialized neural network enhanced with polynomial activation functions (Laguerre, Hermite, Legendre) and the extreme learning machine technique. This innovative integration efficiently approximates option prices and $\text{Greeks}$, offering a compelling yet moderately original contribution.
key_findings bullet 4 · key_findings · validation V0
Raw abstract and provenance
- … We propose a method for solving the PDEs involved in passport option pricing given in Eq. (1) using a single-layer neural network known as the Polynomial Neural …
Source row: 1452 · abstract type: snippet