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On The Calculation Of Risk Measures Using Least-Squares Monte Carlo

Author

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  • GIUSEPPE BENEDETTI

    (Fastval (FIS), 42 Rue Notre Dame des Victoires, 75002 Paris, France)

Abstract

The paper establishes a convergence result for the Least-Squares Monte Carlo method, applied to the estimation of risk measures (such as VaR) depending on the distribution of the future value of some derivative contract (or portfolio). We extend previous results in the literature by focusing on the specific case where the distribution of the underlying factors is known. In particular, we are able to remove the requirement of bounded conditional variance which is usually not satisfied by common financial models and payoffs at the cost of using a weaker notion of convergence. Our main result shows the convergence of the empirical distribution function when the number of simulations n and of basis variables m are jointly sent to infinity under certain conditions on the payoff and the basis. With a suitable choice of basis functions, we finally prove that convergence can be ensured when (m2ln m)/n → 0.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:20:y:2017:i:03:n:s0219024917500200
    DOI: 10.1142/S0219024917500200
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    References listed on IDEAS

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    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. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    3. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2015. "Risk Estimation via Regression," Operations Research, INFORMS, vol. 63(5), pages 1077-1097, October.
    4. 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.
    5. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    6. 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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    Cited by:

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    3. 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.

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