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Estimating affine multifactor term structure models using closed-form likelihood expansions

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  • Aït-Sahalia, Yacine
  • Kimmel, Robert L.

Abstract

We develop and implement a technique for closed-form maximum likelihood estimation (MLE) of multifactor affine yield models. We derive closed-form approximations to likelihoods for nine Dai and Singleton (2000) affine models. Simulations show our technique very accurately approximates true (but infeasible) MLE. Using US Treasury data, we estimate nine affine yield models with different market price of risk specifications. MLE allows non-nested model comparison using likelihood ratio tests; the preferred model depends on the market price of risk. Estimation with simulated and real data suggests our technique is much closer to true MLE than Euler and quasi-maximum likelihood (QML) methods.

Suggested Citation

  • Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    • Handle: RePEc:eee:jfinec:v:98:y:2010:i:1:p:113-144
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    1. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 390-455.
    2. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-658.
    3. 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.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. 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.
    7. 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.
    8. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    9. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
    10. 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, February.
    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.
    12. 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.
    13. Jefferson Duarte, 2004. "Evaluating an Alternative Risk Preference in Affine Term Structure Models," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 379-404.
    14. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    15. Samuel Thompson, 2008. "Identifying Term Structure Volatility from the LIBOR-Swap Curve," Review of Financial Studies, Society for Financial Studies, vol. 21(2), pages 819-854, April.
    16. 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.
    17. 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(1), pages 115-130, March.
    18. Yacine Aït-Sahalia, 2001. "Transition Densities For Interest Rate And Other Nonlinear Diffusions," World Scientific Book Chapters, in: Marco Avellaneda (ed.), Quantitative Analysis In Financial Markets Collected Papers of the New York University Mathematical Finance Seminar(Volume II), chapter 1, pages 1-34, World Scientific Publishing Co. Pte. Ltd..
    19. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    20. 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, February.
    21. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc.
    22. Georg Mosburger & Paul Schneider, 2005. "Modelling International Bond Markets with Affine Term Structure Models," Finance 0509003, University Library of Munich, Germany.
    23. 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.
    24. McCulloch, J Huston, 1975. "The Tax-Adjusted Yield Curve," Journal of Finance, American Finance Association, vol. 30(3), pages 811-830, June.
    25. Egorov, Alexei V. & Li, Haitao & Ng, David, 2011. "A tale of two yield curves: Modeling the joint term structure of dollar and euro interest rates," Journal of Econometrics, Elsevier, vol. 162(1), pages 55-70, May.
    26. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    27. 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.
    28. Chacko, George & Viceira, Luis M., 2003. "Spectral GMM estimation of continuous-time processes," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 259-292.
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    More about this item

    Keywords

    Term structure Multifactor Interest rates Affine Closed-form maximum-likelihood;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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