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Accurate Yield Curve Scenarios Generation using Functional Gradient Descent

Author

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  • Fabio Trojani
  • Francesco Audrino

Abstract

We propose a multivariate nonparametric technique for generating reliable historical yield curve scenarios and confidence intervals. The approach is based on a Functional Gradient Descent (FGD) estimation of the conditional mean vector and volatility matrix of a multivariate interest rate series. It is computationally feasible in large dimensions and it can account for non-linearities in the dependence of interest rates at all available maturities. Based on FGD we apply filtered historical simulation to compute reliable out-of-sample yield curve scenarios and confidence intervals. We back-test our methodology on daily USD bond data for forecasting horizons from 1 to 10 days. Based on several statistical performance measures we find significant evidence of a higher predictive power of our method when compared to scenarios generating techniques based on (i) factor analysis, (ii) a multivariate CCC-GARCH model, or (iii) an exponential smoothing volatility estimators as in the RiskMetrics approach

Suggested Citation

  • Fabio Trojani & Francesco Audrino, 2005. "Accurate Yield Curve Scenarios Generation using Functional Gradient Descent," Computing in Economics and Finance 2005 14, Society for Computational Economics.
  • Handle: RePEc:sce:scecf5:14
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    File URL: http://repec.org/sce2005/up.21584.1103185889.pdf
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    References listed on IDEAS

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    1. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
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    4. Farshid Jamshidian & Yu Zhu, 1996. "Scenario Simulation: Theory and methodology (*)," Finance and Stochastics, Springer, vol. 1(1), pages 43-67.
    5. Peter Christoffersen, 2004. "Backtesting Value-at-Risk: A Duration-Based Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 84-108.
    6. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    7. Francesco Audrino & Giovanni Barone-Adesi, 2005. "A multivariate FGD technique to improve VaR computation in equity markets," Computational Management Science, Springer, vol. 2(2), pages 87-106, March.
    8. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    9. Gourieroux,Christian, 2000. "Econometrics of Qualitative Dependent Variables," Cambridge Books, Cambridge University Press, number 9780521331494.
    10. Gourieroux,Christian, 2000. "Econometrics of Qualitative Dependent Variables," Cambridge Books, Cambridge University Press, number 9780521589857.
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    More about this item

    Keywords

    Conditional mean and volatility estimation; Filtered Historical Simulation; Functional Gradient Descent; Term structure; Multivariate CCC-GARCH models;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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