Deep learning-based least squares forward-backward stochastic differential equation solver for high-dimensional derivative pricing. Issue 8 (3rd August 2021)

• Record Type: Journal Article
• Authors: Liang, Jian; Xu, Zhe; Li, Peter
• Is Part Of: Quantitative finance. Volume 21:Issue 8(2021)
• Page Start: 1309
• Page End: 1323
• Publication Date: 2021-08-03
• Subjects: Forward-backward stochastic differential equation (FBSDE) -- Deep neural network (DNN) -- Least square regression (LSQ) -- Bermudan option -- Callable yield note (CYN) -- High-dimensional derivative pricing; C45 -- C63; Finance -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Investments -- Mathematics -- Periodicals; Economics -- Periodicals; Finances -- Modèles mathématiques -- Périodiques; 332.015118
• DOI: 10.1080/14697688.2021.1881149
• Languages: English
• ISSNs: 1469-7688

Abstract

Abstract : We propose a new forward-backward stochastic differential equation solver for high-dimensional derivative pricing problems by combining a deep learning solver with a least squares regression technique widely used in the least squares Monte Carlo method for the valuation of American options. Our numerical experiments demonstrate the accuracy of our least squares backward deep neural network solver and its capability to produce accurate prices for complex early exercisable 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 accurate means for pricing high-dimensional derivatives with early exercise features.