Pricing and Hedging American-Style Options withDeep Learning: Algorithmic implementation

Sammanfattning: This thesis aims at evaluating and implementing Longstaff & Schwarz approach for approximating the value of American options. American options are generally hard to value, exercised at any time up to its expiration and moreover, there is no closed- form solution for an American option’s price. The proposed algorithm permits to estimate, starting from the data, a candidate optimal stopping strategy, lower and upper bounds for the value of the option and confidence intervals for these estimates. The computed lower and upper bounds are used to estimate a point for the value of the option. Finally, we have generated a set of realizations of a geometric Brownian motion (GBM) to simulate the price of an asset and the Deep Learning method used for training Neural Networks for the determination of optimal stopping strategy is presented. We tackled the question of precision and to estimate complexity of the algorithms based on these criteria.