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Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions

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Author Info
Ait-Sahalia, Yacine (Princeton U)
Kimmel, Robert L. (Ohio State U)

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Abstract

We develop and implement a technique for maximum likelihood estimation in closed-form of multivariate affine yield models of the term structure of interest rates. We derive closed-form approximations to the likelihood functions for all nine of the Dai and Singleton (2000) canonical affine models with one, two, or three underlying factors. Monte Carlo simulations reveal that this technique very accurately approximates true maximum likelihood, which is, in general, infeasible for affine models. We also apply the method to a dataset consisting of synthetic US Treasury strips, and find parameter estimates for nine different affine yield models, each using two different market price of risk specifications. One advantage of maximum likelihood estimation is the ability to compare non-nested models using likelihood ratio tests. We find, using these tests, that the choice of preferred canonical model depends on the market price of risk specification. Comparison to other approximation methods, Euler and QML, on both simulated and real data suggest that our approximation technique is much closer to true MLE than alternative methods.

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Paper provided by Ohio State University, Charles A. Dice Center for Research in Financial Economics in its series Working Paper Series with number 2008-19.

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Date of creation: Oct 2008
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Handle: RePEc:ecl:ohidic:2008-19

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Cheridito, Patrick & Filipovic, Damir & Kimmel, Robert L., 2007. "Market price of risk specifications for affine models: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 83(1), pages 123-170, January. [Downloadable!] (restricted)
  2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November. [Downloadable!] (restricted)
  3. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, 02. [Downloadable!] (restricted)
  4. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March. [Downloadable!] (restricted)
    Other versions:
  5. Yacine Aït-Sahalia, 1999. "Transition Densities for Interest Rate and Other Nonlinear Diffusions," Journal of Finance, American Finance Association, vol. 54(4), pages 1361-1395, 08. [Downloadable!] (restricted)
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March. [Downloadable!] (restricted)
  7. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(3), pages 619-58. [Downloadable!] (restricted)
  8. Samuel Thompson, 2008. "Identifying Term Structure Volatility from the LIBOR-Swap Curve," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 21(2), pages 819-854, April. [Downloadable!] (restricted)
  9. Darrell Duffie & Lasse Heje Pedersen & Kenneth J. Singleton, 2003. "Modeling Sovereign Yield Spreads: A Case Study of Russian Debt," Journal of Finance, American Finance Association, vol. 58(1), pages 119-159, 02. [Downloadable!] (restricted)
  10. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May. [Downloadable!] (restricted)
  11. Ai[diaeresis]t-Sahalia, Yacine & Kimmel, Robert, 2007. "Maximum likelihood estimation of stochastic volatility models," Journal of Financial Economics, Elsevier, vol. 83(2), pages 413-452, February. [Downloadable!] (restricted)
  12. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  13. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 115-130, March. [Downloadable!]
  14. Georg Mosburger & Paul Schneider, 2005. "Modelling International Bond Markets with Affine Term Structure Models," Finance 0509003, EconWPA. [Downloadable!]
  15. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October. [Downloadable!] (restricted)
  16. Bakshi, Gurdip & Ju, Nengjiu & Ou-Yang, Hui, 2006. "Estimation of continuous-time models with an application to equity volatility dynamics," Journal of Financial Economics, Elsevier, vol. 82(1), pages 227-249, October. [Downloadable!] (restricted)
  17. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May. [Downloadable!] (restricted)
  18. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January. [Downloadable!] (restricted)
  19. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 17(2), pages 379-404. [Downloadable!] (restricted)
  20. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292. [Downloadable!] (restricted)
  21. Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Peter C.B. Phillips & Jun Yu, 2007. "Simulation-based Estimation of Contingent-claims Prices," Cowles Foundation Discussion Papers 1596, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Sergio Pastorello & Valentin Patilea & Éric Renault, 2003. "Iterative and Recursive Estimation in Structural Non-Adaptive Models," CIRANO Working Papers 2003s-08, CIRANO. [Downloadable!]
  3. Konstantijn Maes, 2004. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," Research series 200402, National Bank of Belgium. [Downloadable!]
    Other versions:
  4. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  5. Pierre Collin-Dufresne & Christopher S. Jones & Robert S. Goldstein, 2004. "Can Interest Rate Volatility be Extracted from the Cross Section of Bond Yields? An Investigation of Unspanned Stochastic Volatility," NBER Working Papers 10756, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  6. Patrick Cheridito & Damir Filipovic, 2004. "Market Price of Risk Specifications for Affine Models: Theory and Evidence," Econometric Society 2004 North American Winter Meetings 536, Econometric Society. [Downloadable!]
  7. Georg Mosburger & Paul Schneider, 2005. "Modelling International Bond Markets with Affine Term Structure Models," Finance 0509003, EconWPA. [Downloadable!]
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