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

Author

Listed:
  • Hyeong-Ohk Bae

    (Ajou University)

  • Seunggu Kang

    (Korea Asset Pricing & Korea Ratings)

  • Muhyun Lee

    (Samsung Securities)

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.

Suggested Citation

  • Hyeong-Ohk Bae & Seunggu Kang & Muhyun Lee, 2024. "Option Pricing and Local Volatility Surface by Physics-Informed Neural Network," Computational Economics, Springer;Society for Computational Economics, vol. 64(5), pages 3143-3159, November.
    • Handle: RePEc:kap:compec:v:64:y:2024:i:5:d:10.1007_s10614-024-10551-2
    DOI: 10.1007/s10614-024-10551-2
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    More about this item

    Keywords

    Option pricing; Local volatility; Artificial neural network; Black–Scholes equation (BSE); Physics-informed neural network (PINN); Constant elasticity of variance (CEV);
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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