Deep learning of transition probability densities for stochastic asset models with applications in option pricing

Su, H ORCID: https://orcid.org/0000-0002-7448-2730, Tretyakov, MV and Newton, DP, 2023. Deep learning of transition probability densities for stochastic asset models with applications in option pricing. Management Science. ISSN 0025-1909 (Forthcoming)

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Abstract

Transition probability density functions (TPDFs) are fundamental to computational finance, including option pricing and hedging. Advancing recent work in deep learning, we develop novel neural TPDF generators through solving backward Kolmogorov equations in parametric space for cumulative probability functions. The generators are ultra-fast, very accurate and can be trained for any asset model described by stochastic differential equations. These are “single solve”, so they do not require retraining when parameters of the stochastic model are changed (e.g. recalibration of volatility). Once trained, the neural TDPF generators can be transferred to less powerful computers where they can be used for e.g. option pricing at speeds as fast as if the TPDF were known in a closed form. We illustrate the computational efficiency of the proposed neural approximations of TPDFs by inserting them into numerical option pricing methods. We demonstrate a wide range of applications including the Black-Scholes-Merton model, the standard Heston model, the SABR model, and jump-diffusion models. These numerical experiments confirm the ultra-fast speed and high accuracy of the developed neural TPDF generators.

Item Type:	Journal article
Publication Title:	Management Science
Creators:	Su, H., Tretyakov, M.V. and Newton, D.P.
Publisher:	INFORMS
Date:	9 October 2023
ISSN:	0025-1909
Identifiers:	Number Type 1850466 Other
Divisions:	Schools > Nottingham Business School
Record created by:	Laura Ward
Date Added:	15 Jan 2024 15:35
Last Modified:	15 Jan 2024 15:35
URI:	https://irep.ntu.ac.uk/id/eprint/50696

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