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Risk Estimation via Regression

Author

Listed:
  • Mark Broadie

    (Graduate School of Business, Columbia University, New York, New York 10027)

  • Yiping Du

    (Industrial Engineering and Operations Research, Columbia University, New York, New York 10027)

  • Ciamac C. Moallemi

    (Graduate School of Business, Columbia University, New York, New York 10027)

Abstract

We introduce a regression-based nested Monte Carlo simulation method for the estimation of financial risk. An outer simulation level is used to generate financial risk factors and an inner simulation level is used to price securities and compute portfolio losses given risk factor outcomes. The mean squared error (MSE) of standard nested simulation converges at the rate k −2/3 , where k measures computational effort. The proposed regression method combines information from different risk factor realizations to provide a better estimate of the portfolio loss function. The MSE of the regression method converges at the rate k −1 until reaching an asymptotic bias level which depends on the magnitude of the regression error. Numerical results consistent with our theoretical analysis are provided and numerical comparisons with other methods are also given.

Suggested Citation

  • Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    • Handle: RePEc:inm:oropre:v:63:y:2015:i:5:p:1077-1097
    DOI: 10.1287/opre.2015.1419
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    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 B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    3. Hai Lan & Barry L. Nelson & Jeremy Staum, 2010. "A Confidence Interval Procedure for Expected Shortfall Risk Measurement via Two-Level Simulation," Operations Research, INFORMS, vol. 58(5), pages 1481-1490, October.
    4. Jun Pan & Darrell Duffie, 2001. "Analytical value-at-risk with jumps and credit risk," Finance and Stochastics, Springer, vol. 5(2), pages 155-180.
    5. Mark Britten-Jones & Stephen M. Schaefer, 1999. "Non-Linear Value-at-Risk," Review of Finance, European Finance Association, vol. 2(2), pages 161-187.
    6. Yunpeng Sun & Daniel W. Apley & Jeremy Staum, 2011. "Efficient Nested Simulation for Estimating the Variance of a Conditional Expectation," Operations Research, INFORMS, vol. 59(4), pages 998-1007, August.
    7. Cho H. Hui, 1997. "Time‐dependent barrier option values," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(6), pages 667-688, September.
    8. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    9. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    10. 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.
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