Option Pricing and Local Volatility Surface by Physics-Informed Neural Network

Hyeong-Ohk Bae (), Seunggu Kang () and Muhyun Lee ()
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Hyeong-Ohk Bae: Ajou University
Seunggu Kang: Korea Asset Pricing & Korea Ratings
Muhyun Lee: Samsung Securities

Computational Economics, 2024, vol. 64, issue 5, No 20, 3143-3159

Abstract: Abstract We use an artificial neural network for finance in two directions: to estimate prices and Greeks based on the geometric Brownian motion and the constant elasticity of variance model for European options, and to construct a local volatility surface. To show the efficiency and successful usage of the network, we compare prices and Greeks obtained by a solution formula and by the artificial neural network when there is a solution formula is known. Then, we calculate Dupire’s equations to construct a local volatility surface by the network.

Keywords: Option pricing; Local volatility; Artificial neural network; Black–Scholes equation (BSE); Physics-informed neural network (PINN); Constant elasticity of variance (CEV); 68T07; 91G20 (search for similar items in EconPapers)
JEL-codes: C63 G13 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10614-024-10551-2

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