We propose a deep Recurrent neural network (RNN) framework for computing
prices and deltas of American options in high dimensions. Our proposed
framework uses two deep RNNs, where one network learns the price and the other
learns the delta of the option for each timestep. Our proposed framework yields
prices and deltas for the entire spacetime, not only at a given point (e.g. t =
0). The computational cost of the proposed approach is linear in time, which
improves on the quadratic time seen for feedforward networks that price
American options. The computational memory cost of our method is constant in
memory, which is an improvement over the linear memory costs seen in
feedforward networks. Our numerical simulations demonstrate these
contributions, and show that the proposed deep RNN framework is computationally
more efficient than traditional feedforward neural network frameworks in time
and memory.