IDEAS home Printed from https://ideas.repec.org/a/spr/finsto/v26y2022i3d10.1007_s00780-022-00478-7.html
   My bibliography  Save this article

A least-squares Monte Carlo approach to the estimation of enterprise risk

Author

Listed:
  • Hongjun Ha

    (Saint Joseph’s University)

  • Daniel Bauer

    (University of Wisconsin-Madison)

Abstract

The estimation of enterprise risk for financial institutions entails a re-evaluation of the company’s economic balance sheet at a future time for a (large) number of stochastic scenarios. The current paper discusses tackling this nested valuation problem based on least-squares Monte Carlo techniques familiar from American option pricing. We formalise the algorithm in an operator setting and discuss the choice of the regressors (“basis functions”). In particular, we show that the left singular functions of the corresponding conditional expectation operator present robust basis functions. Our numerical examples demonstrate that the algorithm can produce accurate results at relatively low computational costs.

Suggested Citation

  • Hongjun Ha & Daniel Bauer, 2022. "A least-squares Monte Carlo approach to the estimation of enterprise risk," Finance and Stochastics, Springer, vol. 26(3), pages 417-459, July.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00478-7
    DOI: 10.1007/s00780-022-00478-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00780-022-00478-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00780-022-00478-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    3. Carriere, Jacques F., 1996. "Valuation of the early-exercise price for options using simulations and nonparametric regression," Insurance: Mathematics and Economics, Elsevier, vol. 19(1), pages 19-30, December.
    4. M. Kaina & L. Rüschendorf, 2009. "On convex risk measures on L p -spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 475-495, July.
    5. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    6. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    7. Giuseppe Benedetti, 2017. "On The Calculation Of Risk Measures Using Least-Squares Monte Carlo," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-14, May.
    8. Anne-Sophie Krah & Zoran Nikolić & Ralf Korn, 2018. "A Least-Squares Monte Carlo Framework in Proxy Modeling of Life Insurance Companies," Risks, MDPI, vol. 6(2), pages 1-26, June.
    9. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    10. Carrasco, Marine & Florens, Jean-Pierre, 2011. "A Spectral Method For Deconvolving A Density," Econometric Theory, Cambridge University Press, vol. 27(3), pages 546-581, June.
    11. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    12. 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.
    13. Floryszczak, Anthony & Le Courtois, Olivier & Majri, Mohamed, 2016. "Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 15-26.
    14. Lars Stentoft, 2004. "Convergence of the Least Squares Monte Carlo Approach to American Option Valuation," Management Science, INFORMS, vol. 50(9), pages 1193-1203, September.
    15. Bauer, Daniel & Reuss, Andreas & Singer, Daniela, 2012. "On the Calculation of the Solvency Capital Requirement Based on Nested Simulations," ASTIN Bulletin, Cambridge University Press, vol. 42(2), pages 453-499, November.
    16. Mathieu Cambou & Damir Filipović, 2018. "Replicating portfolio approach to capital calculation," Finance and Stochastics, Springer, vol. 22(1), pages 181-203, January.
    17. 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.
    18. Anthony Floryszczak & Olivier Le Courtois & Mohamed Majri, 2016. "Inside the Solvency 2 Black Box : Net asset values and solvency capital requirements with a least-squares Monte-Carlo approach," Post-Print hal-02313445, HAL.
    19. L. Jeff Hong & Sandeep Juneja & Guangwu Liu, 2017. "Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement," Operations Research, INFORMS, vol. 65(3), pages 657-673, June.
    20. 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.
    21. Lars Stentoft, 2004. "Assessing the Least Squares Monte-Carlo Approach to American Option Valuation," Review of Derivatives Research, Springer, vol. 7(2), pages 129-168, August.
    Full references (including those not matched with items on IDEAS)

    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. Hainaut, Donatien & Akbaraly, Adnane, 2023. "Risk management with Local Least Squares Monte-Carlo," LIDAM Discussion Papers ISBA 2023003, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Patrick Cheridito & John Ery & Mario V. Wüthrich, 2020. "Assessing Asset-Liability Risk with Neural Networks," Risks, MDPI, vol. 8(1), pages 1-17, February.
    3. 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.
    4. Zhiyi Shen & Chengguo Weng, 2019. "A Backward Simulation Method for Stochastic Optimal Control Problems," Papers 1901.06715, arXiv.org.
    5. Patrick Cheridito & John Ery & Mario V. Wuthrich, 2021. "Assessing asset-liability risk with neural networks," Papers 2105.12432, arXiv.org.
    6. Floryszczak, Anthony & Le Courtois, Olivier & Majri, Mohamed, 2016. "Inside the Solvency 2 Black Box: Net Asset Values and Solvency Capital Requirements with a least-squares Monte-Carlo approach," Insurance: Mathematics and Economics, Elsevier, vol. 71(C), pages 15-26.
    7. Massimo Costabile & Fabio Viviano, 2020. "Testing the Least-Squares Monte Carlo Method for the Evaluation of Capital Requirements in Life Insurance," Risks, MDPI, vol. 8(2), pages 1-13, May.
    8. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    9. Nelson Areal & Artur Rodrigues & Manuel Armada, 2008. "On improving the least squares Monte Carlo option valuation method," Review of Derivatives Research, Springer, vol. 11(1), pages 119-151, March.
    10. Berridge, S.J. & Schumacher, J.M., 2002. "An Irregular Grid Approach for Pricing High Dimensional American Options," Discussion Paper 2002-99, Tilburg University, Center for Economic Research.
    11. Katarzyna Toporek, 2012. "Simple is better. Empirical comparison of American option valuation methods," Ekonomia journal, Faculty of Economic Sciences, University of Warsaw, vol. 29.
    12. Kun Zhang & Ben Mingbin Feng & Guangwu Liu & Shiyu Wang, 2022. "Sample Recycling for Nested Simulation with Application in Portfolio Risk Measurement," Papers 2203.15929, arXiv.org.
    13. Lars Stentoft, 2013. "American option pricing using simulation with an application to the GARCH model," Chapters, in: Adrian R. Bell & Chris Brooks & Marcel Prokopczuk (ed.), Handbook of Research Methods and Applications in Empirical Finance, chapter 5, pages 114-147, Edward Elgar Publishing.
    14. Alexander Boogert & Cyriel de Jong, 2007. "Gas Storage Valuation Using a Monte Carlo Method," Birkbeck Working Papers in Economics and Finance 0704, Birkbeck, Department of Economics, Mathematics & Statistics.
    15. Zhu, Lei & Zhang, ZhongXiang & Fan, Ying, 2015. "Overseas oil investment projects under uncertainty: How to make informed decisions?," Journal of Policy Modeling, Elsevier, vol. 37(5), pages 742-762.
    16. Lucio Fernandez‐Arjona & Damir Filipović, 2022. "A machine learning approach to portfolio pricing and risk management for high‐dimensional problems," Mathematical Finance, Wiley Blackwell, vol. 32(4), pages 982-1019, October.
    17. Chen Liu & Henry Schellhorn & Qidi Peng, 2019. "American Option Pricing With Regression: Convergence Analysis," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-31, December.
    18. Joseph Y. J. Chow & Hamid R. Sayarshad, 2016. "Reference Policies for Non-myopic Sequential Network Design and Timing Problems," Networks and Spatial Economics, Springer, vol. 16(4), pages 1183-1209, December.
    19. Maciej Klimek & Marcin Pitera, 2014. "The least squares method for option pricing revisited," Papers 1404.7438, arXiv.org, revised Nov 2015.
    20. Jin, Xing & Yang, Cheng-Yu, 2016. "Efficient estimation of lower and upper bounds for pricing higher-dimensional American arithmetic average options by approximating their payoff functions," International Review of Financial Analysis, Elsevier, vol. 44(C), pages 65-77.

    More about this item

    Keywords

    Risk management; Least-squares Monte Carlo; Basis functions;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

    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:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00478-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.