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We propose a deep neural network framework for computing prices and deltas ofAmerican options in high dimensions. The architecture of the framework is asequence of neural networks, where each network learns the difference of theprice functions between adjacent timesteps. We introduce the least squaresresidual of the associated backward stochastic differential equation as theloss function. Our proposed framework yields prices and deltas on the entirespacetime, not only at a given point. The computational cost of the proposedapproach is quadratic in dimension, which addresses the curse of dimensionalityissue that state-of-the-art approaches suffer. Our numerical simulationsdemonstrate these contributions, and show that the proposed neural networkframework outperforms state-of-the-art approaches in high dimensions.

Deep Neural Network Framework Based on Backward Stochastic Differential Equations for Pricing and Hedging American Options in High Dimensions