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Refining the least squares Monte Carlo method by imposing structure

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  • Pascal L�tourneau
  • Lars Stentoft

Abstract

The least squares Monte Carlo method of Longstaff and Schwartz has become a standard numerical method for option pricing with many potential risk factors. An important choice in the method is the number of regressors to use and using too few or too many regressors leads to biased results. This is so particularly when considering multiple risk factors or when simulation is computationally expensive and hence relatively few paths can be used. In this paper we show that by imposing structure in the regression problem we can improve the method by reducing the bias. This holds across different maturities, for different categories of moneyness and for different types of option payoffs and often leads to significantly increased efficiency.

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  • Pascal L�tourneau & Lars Stentoft, 2014. "Refining the least squares Monte Carlo method by imposing structure," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 495-507, March.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:3:p:495-507
    DOI: 10.1080/14697688.2013.787543
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    Cited by:

    1. Pascal Létourneau & Lars Stentoft, 2019. "Bootstrapping the Early Exercise Boundary in the Least-Squares Monte Carlo Method," JRFM, MDPI, vol. 12(4), pages 1-21, December.
    2. Gabriel J Power & Charli D. Tandja M. & Josée Bastien & Philippe Grégoire, 2015. "Measuring infrastructure investment option value," Journal of Risk Finance, Emerald Group Publishing, vol. 16(1), pages 49-72, January.
    3. Stübinger, Johannes, 2018. "Statistical arbitrage with optimal causal paths on high-frequencydata of the S&P 500," FAU Discussion Papers in Economics 01/2018, Friedrich-Alexander University Erlangen-Nuremberg, Institute for Economics.
    4. Michael Ludkovski, 2015. "Kriging Metamodels and Experimental Design for Bermudan Option Pricing," Papers 1509.02179, arXiv.org, revised Oct 2016.
    5. Jeechul Woo & Chenru Liu & Jaehyuk Choi, 2024. "Leave‐one‐out least squares Monte Carlo algorithm for pricing Bermudan options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(8), pages 1404-1428, August.
    6. Ruimeng Hu, 2019. "Deep Learning for Ranking Response Surfaces with Applications to Optimal Stopping Problems," Papers 1901.03478, arXiv.org, revised Mar 2020.
    7. Fabozzi, Frank J. & Paletta, Tommaso & Tunaru, Radu, 2017. "An improved least squares Monte Carlo valuation method based on heteroscedasticity," European Journal of Operational Research, Elsevier, vol. 263(2), pages 698-706.
    8. Cortazar, Gonzalo & Naranjo, Lorenzo & Sainz, Felipe, 2021. "Optimal decision policy for real options under general Markovian dynamics," European Journal of Operational Research, Elsevier, vol. 288(2), pages 634-647.

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