Abstract
In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models—a simple one and a more complex one—and we discuss the performance of two NN models with the Least-Squares Monte Carlo (LSM) method. This study relies on American put option market prices, for four large U.S. companies—Procter and Gamble Company (PG), Coca-Cola Company (KO), General Motors (GM), and Bank of America Corp (BAC). Our dataset is composed of all options traded within the period December 2018 until March 2019. Although on average, both NN models perform better than LSM, the simpler model (NN Model 1) performs quite close to LSM. Moreover, the second NN model substantially outperforms the other models, having an RMSE ca. 40% lower than the presented by LSM. The lower RMSE is consistent across all companies, strike levels, and maturities. In summary, all methods present a good accuracy; however, after calibration, NNs produce better results in terms of both execution time and Root Mean Squared Error (RMSE).
Highlights
This study compares two different methods to price American put options
We compare our Neural Networks (NNs) models’ results with those of the Least-Squares Monte Carlo (LSM) method, using the Root Mean Squared Error (RMSE) as the comparison measure for error, as well as the execution time for the comparison of the time spent by each method to price the options
Even if we took the total fitting time into account, dividing it by the number of options in the test set, we got 0.07 s per option for NN Model 2, less than 20% of the time when compared to LSM, and 0.03 s for NN Model 1
Summary
This study compares two different methods to price American put options. European style options can only be exercised at a pre-defined fixed date, the maturity. Instead, can be exercised at any moment until maturity, leading to an optimal stopping time problem. The case of American put options is hard to solve, and there are no closed-form solutions. This problem was first studied by Brennan and Schwartz (1977), and it has been recurrent in the literature ever since. Important references on this matter are Bunch and Johnson (2000); Carr et al
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