Solving highdimensional optimal stopping problems using deep learning
Abstract
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to highdimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets. Highdimensional optimal stopping problems are, however, notoriously difficult to solve due to the wellknown curse of dimensionality. In this work, we propose an algorithm for solving such problems, which is based on deep learning and computes, in the context of early exercise option pricing, both approximations of an optimal exercise strategy and the price of the considered option. The proposed algorithm can also be applied to optimal stopping problems that arise in other areas where the underlying stochastic process can be efficiently simulated. We present numerical results for a large number of example problems, which include the pricing of many highdimensional American and Bermudan options, such as Bermudan maxcall options in up to 5000 dimensions. Most of the obtained results are compared to reference values computed by exploiting the specific problem design or, where available, to reference values from the literature. These numerical results suggest that the proposed algorithm is highly effective in the case of many underlyings, in terms of both accuracy and speed.
 Publication:

arXiv eprints
 Pub Date:
 August 2019
 arXiv:
 arXiv:1908.01602
 Bibcode:
 2019arXiv190801602B
 Keywords:

 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Computer Science  Machine Learning;
 Mathematics  Probability;
 Quantitative Finance  Computational Finance;
 68T07;
 60G40;
 65C05;
 91G60
 EPrint:
 54 pages, 1 figure