IDEAS home Printed from https://ideas.repec.org/a/gam/jrisks/v8y2020i3p73-d379508.html
   My bibliography  Save this article

Neural Network Pricing of American Put Options

Author

Listed:
  • Raquel M. Gaspar

    (ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal
    CEMAPRE/REM Research Center, Rua do Quelhas 6, 1200-078 Lisbon, Portugal)

  • Sara D. Lopes

    (ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal
    CEMAPRE/REM Research Center, Rua do Quelhas 6, 1200-078 Lisbon, Portugal)

  • Bernardo Sequeira

    (ISEG, Universidade de Lisboa, Rua do Quelhas 6, 1200-078 Lisbon, Portugal)

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).

Suggested Citation

  • Raquel M. Gaspar & Sara D. Lopes & Bernardo Sequeira, 2020. "Neural Network Pricing of American Put Options," Risks, MDPI, vol. 8(3), pages 1-24, July.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:73-:d:379508
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-9091/8/3/73/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-9091/8/3/73/
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Xinfu Chen & John Chadam & Lishang Jiang & Weian Zheng, 2008. "Convexity Of The Exercise Boundary Of The American Put Option On A Zero Dividend Asset," Mathematical Finance, Wiley Blackwell, vol. 18(1), pages 185-197, January.
    3. Michael Kohler, 2008. "A regression-based smoothing spline Monte Carlo algorithm for pricing American options in discrete time," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 92(2), pages 153-178, May.
    4. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-889, July.
    5. David Kelly & Jamsheed Shorish, 1994. "Valuing and Hedging American Put Options Using Neural Networks," GSIA Working Papers 8, Carnegie Mellon University, Tepper School of Business.
    6. Laura Brown & Saeed Moshiri, 2004. "Unemployment variation over the business cycles: a comparison of forecasting models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(7), pages 497-511.
    7. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115.
    8. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 229-242.
    9. M. Ali Choudhary & Adnan Haider, 2012. "Neural network models for inflation forecasting: an appraisal," Applied Economics, Taylor & Francis Journals, vol. 44(20), pages 2631-2635, July.
    10. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    11. Cremers, Martijn & Weinbaum, David, 2010. "Deviations from Put-Call Parity and Stock Return Predictability," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 335-367, April.
    12. Shuaiqiang Liu & Cornelis W. Oosterlee & Sander M. Bohte, 2019. "Pricing Options and Computing Implied Volatilities using Neural Networks," Risks, MDPI, vol. 7(1), pages 1-22, February.
    13. Parkinson, Michael, 1977. "Option Pricing: The American Put," The Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January.
    14. Yao, Jingtao & Li, Yili & Tan, Chew Lim, 2000. "Option price forecasting using neural networks," Omega, Elsevier, vol. 28(4), pages 455-466, August.
    15. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-462, May.
    16. Jinsha Zhao, 2018. "American Option Valuation Methods," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 10(5), pages 1-13, May.
    17. Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 75-94.
    18. Kim, In Joon, 1990. "The Analytic Valuation of American Options," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 547-572.
    19. Barty Kengy & Girardeau Pierre & Strugarek Cyrille & Roy Jean-Sébastien, 2008. "Application of kernel-based stochastic gradient algorithms to option pricing," Monte Carlo Methods and Applications, De Gruyter, vol. 14(2), pages 99-127, January.
    20. Huisu Jang & Jaewook Lee, 2019. "Generative Bayesian neural network model for risk-neutral pricing of American index options," Quantitative Finance, Taylor & Francis Journals, vol. 19(4), pages 587-603, April.
    21. David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October.
    22. Peter Carr & Robert Jarrow & Ravi Myneni, 2008. "Alternative Characterizations Of American Put Options," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 5, pages 85-103, World Scientific Publishing Co. Pte. Ltd..
    23. Philip Protter & Emmanuelle Clément & Damien Lamberton, 2002. "An analysis of a least squares regression method for American option pricing," Finance and Stochastics, Springer, vol. 6(4), pages 449-471.
    24. Nikola Gradojevic & Ramazan Gencay & Dragan Kukolj, 2009. "Option Pricing with Modular Neural Networks," Working Paper series 32_09, Rimini Centre for Economic Analysis.
    25. Tkacz, Greg, 2001. "Neural network forecasting of Canadian GDP growth," International Journal of Forecasting, Elsevier, vol. 17(1), pages 57-69.
    26. Rotundo, G., 2004. "Neural networks for large financial crashes forecast," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 77-80.
    27. L. C. G. Rogers, 2002. "Monte Carlo valuation of American options," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 271-286, July.
    28. Rachel Kuske & Joseph Keller, 1998. "Optimal exercise boundary for an American put option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 5(2), pages 107-116.
    29. Zaiyong Tang & Paul A. Fishwick, 1993. "Feedforward Neural Nets as Models for Time Series Forecasting," INFORMS Journal on Computing, INFORMS, vol. 5(4), pages 374-385, November.
    30. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yanhui Shen, 2023. "American Option Pricing using Self-Attention GRU and Shapley Value Interpretation," Papers 2310.12500, arXiv.org.
    2. S'andor Kuns'agi-M'at'e & G'abor F'ath & Istv'an Csabai & G'abor Moln'ar-S'aska, 2022. "Deep Weighted Monte Carlo: A hybrid option pricing framework using neural networks," Papers 2208.14038, arXiv.org, revised Dec 2022.
    3. Antal Ratku & Dirk Neumann, 2022. "Derivatives of feed-forward neural networks and their application in real-time market risk management," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(3), pages 947-965, September.
    4. Riccardo Aiolfi & Nicola Moreni & Marco Bianchetti & Marco Scaringi & Filippo Fogliani, 2021. "Learning Bermudans," Papers 2105.00655, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Minqiang Li, 2010. "A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes," Review of Derivatives Research, Springer, vol. 13(2), pages 177-217, July.
    2. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    3. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    4. Yanhui Shen, 2023. "American Option Pricing using Self-Attention GRU and Shapley Value Interpretation," Papers 2310.12500, arXiv.org.
    5. In oon Kim & Bong-Gyu Jang & Kyeong Tae Kim, 2013. "A simple iterative method for the valuation of American options," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 885-895, May.
    6. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November.
    7. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May.
    8. Minqiang Li, 2010. "Analytical approximations for the critical stock prices of American options: a performance comparison," Review of Derivatives Research, Springer, vol. 13(1), pages 75-99, April.
    9. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
    10. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    11. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    12. Zhongkai Liu & Tao Pang, 2016. "An efficient grid lattice algorithm for pricing American-style options," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 5(1), pages 36-55.
    13. Chockalingam, Arun & Muthuraman, Kumar, 2015. "An approximate moving boundary method for American option pricing," European Journal of Operational Research, Elsevier, vol. 240(2), pages 431-438.
    14. Song-Ping Zhu & Xin-Jiang He & XiaoPing Lu, 2018. "A new integral equation formulation for American put options," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 483-490, March.
    15. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    16. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
    17. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
    18. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    19. Doobae Jun & Hyejin Ku, 2013. "Valuation of American partial barrier options," Review of Derivatives Research, Springer, vol. 16(2), pages 167-191, July.
    20. Muthuraman, Kumar, 2008. "A moving boundary approach to American option pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 32(11), pages 3520-3537, November.

    More about this item

    Keywords

    machine learning; neural networks; American put options; least-squares Monte Carlo;
    All these keywords.

    JEL classification:

    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:73-:d:379508. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.