# Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions

@article{Chen2019DeepNN, title={Deep neural network framework based on backward stochastic differential equations for pricing and hedging American options in high dimensions}, author={Yangang Chen and Justin W. L. Wan}, journal={Quantitative Finance}, year={2019}, volume={21}, pages={45 - 67} }

We propose a deep neural network framework for computing prices and deltas of American options in high dimensions. The architecture of the framework is a sequence of neural networks, where each network learns the difference of the price functions between adjacent timesteps. We introduce the least squares residual of the associated backward stochastic differential equation as the loss function. Our proposed framework yields prices and deltas for the entire spacetime, not only at a given point (e…

## 37 Citations

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