Deep Learning-Based Least Square Forward-Backward Stochastic Differential Equation Solver for High-Dimensional Derivative Pricing
22 Pages Posted: 11 Jun 2019 Last revised: 24 Jul 2019
Date Written: July 23, 2019
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the efficiency and accuracy of our least square backward deep neural network solver and its capability to provide accurate prices for complex early exercise derivatives such as callable yield notes. Our method can serve as a generic numerical solver for pricing derivatives across various asset groups, in particular, as an efficient means for pricing high-dimensional derivatives with early exercises features.
Keywords: partial differential equation (PDE), forward-backward stochastic differential equation (FBSDE), deep neural network (DNN), least square regression (LSQ), derivative pricing, Bermudan option, callable yield note (CYN), high-dimensional derivative pricing
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