{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T16:40:05Z","timestamp":1774888805063,"version":"3.50.1"},"reference-count":54,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,7,2]],"date-time":"2020-07-02T00:00:00Z","timestamp":1593648000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"FCT\/MCTES (Portuguese Science Foundation)","award":["CEMAPRE\/REM-UIDB\/05069\/2020"],"award-info":[{"award-number":["CEMAPRE\/REM-UIDB\/05069\/2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Risks"],"abstract":"<jats:p>In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models\u2014a simple one and a more complex one\u2014and 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\u2014Procter 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).<\/jats:p>","DOI":"10.3390\/risks8030073","type":"journal-article","created":{"date-parts":[[2020,7,3]],"date-time":"2020-07-03T06:51:20Z","timestamp":1593759080000},"page":"73","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Neural Network Pricing of American Put Options"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3294-3962","authenticated-orcid":false,"given":"Raquel M.","family":"Gaspar","sequence":"first","affiliation":[{"name":"ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal"},{"name":"CEMAPRE\/REM Research Center, Rua do Quelhas 6, 1200-078 Lisbon, Portugal"}]},{"given":"Sara D.","family":"Lopes","sequence":"additional","affiliation":[{"name":"ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal"},{"name":"CEMAPRE\/REM Research Center, Rua do Quelhas 6, 1200-078 Lisbon, Portugal"}]},{"given":"Bernardo","family":"Sequeira","sequence":"additional","affiliation":[{"name":"ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,7,2]]},"reference":[{"key":"ref_1","unstructured":"Abadi, Mart\u00edn, Barham, Paul, Chen, Jianmin, Chen, Zhifeng, Davis, Andy, Dean, Jeffrey, Devin, Matthieu, Ghemawat, Sanjay, Irving, Geoffrey, and Isard, Michael (, January November). 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