European option pricing under a generalized fractional Brownian motion Heston exponential Hull-White model with transaction costs by the Deep Galerkin Method

European option pricing under a generalized fractional Brownian motion Heston exponential Hull-White model with transaction costs by the Deep Galerkin Method | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article European option pricing under a generalized fractional Brownian motion Heston exponential Hull-White model with transaction costs by the Deep Galerkin Method Mahsa Motameni, Farshid Mehrdoust, Ali Reza Najafi This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3937872/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 03 Feb, 2025 Read the published version in Soft Computing → Version 1 posted 5 You are reading this latest preprint version Abstract We propose a new financial model called the generalized fractional Brownian motion Heston exponential Hull-White model, which has stochastic volatility and interest rate, long memory, and heavy tail distribution. Based on the market price of the volatility and delta hedging strategies, we propose a partial differential equation (PDE) to obtain the European option price. To do this, portfolio changes contain long one position of the European call option and shares of the underlying assets (stock, zero coupon bond, volatility), where we use the mentioned model to obtain the price. Due to transaction costs, the resulting equation is a fully nonlinear PDE, which we use the Deep Galerkin Method (DGM) to solve it. Also, we present the proof of the convergence of the method to this class of equations, which includes two parts: the convergence of the loss function to zero and the convergence of the neural network to the exact solution of the equation. We finally present numerical results to show the model and method’s effectiveness. European option pricing Fractional Brownian motion Deep Galerkin Method Convergence Full Text Cite Share Download PDF Status: Published Journal Publication published 03 Feb, 2025 Read the published version in Soft Computing → Version 1 posted Reviewers agreed at journal 08 Mar, 2024 Reviewers invited by journal 07 Mar, 2024 Editor invited by journal 14 Feb, 2024 Editor assigned by journal 13 Feb, 2024 First submitted to journal 11 Feb, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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