×

Simulation-based Bayesian estimation of an affine term structure model. (English) Zbl 1429.62477

Summary: A Bayesian simulation-based method is developed for estimating a class of interest rate models known as affine term structure (ATS) models. The technique is based on a Markov chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time process using an approximate discrete time model. The technique is demonstrated using a single-factor term structure model that possesses closed-form solutions for the transition densities. Numerical application of the method is demonstrated using simulated data. The results show that increasing the degree of augmentation in the yield curve does, overall, produce estimates that more closely reflect those based on the use of the exact transition functions. However, the results also indicate that the benefits of increasing the degree of augmentation may, to some extent, be offset by the increased uncertainty in estimation associated with the introduction of additional highly correlated latent yields.

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62M05 Markov processes: estimation; hidden Markov models
62-08 Computational methods for problems pertaining to statistics
91G30 Interest rates, asset pricing, etc. (stochastic models)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Babbs, S.H.; Nowman, K.B., Kalman filtering of generalized vasicek term structure models, J. financial quantitative anal., 34, 115-130, (1999)
[2] Bolder, D.J., 2001. Affine term-structure models: theory and implementation. Working Paper 2001-15, Bank of Canada.
[3] Chen, R., Scott, L., 1995. Multifactor Cox-Ingersoll-Ross models of the term structure: estimates and tests from a Kalman filter model. Working Paper, University of Georgia.
[4] Chib, S.; Greenberg, E., Understanding the metropolis – hastings algorithm, Amer. statist., 49, 327-335, (1995)
[5] Chib, S.; Greenberg, E., Markov chain Monte Carlo simulation methods in econometrics, Econometric theory, 12, 409-431, (1996)
[6] Cox, J.C.; Ingersoll, J.E.; Ross, S.A., A theory of the term structure of interest rates, Econometrica, 53, 385-407, (1985) · Zbl 1274.91447
[7] Dai, Q.; Singleton, K.J., Specification analysis of affine term structure models, J. finance, LV, 1943-1978, (2000)
[8] Duffee, G.R., 2000. Term premia and interest rate forecasts in affine models. Working Paper, Haas School of Business, University of California.
[9] Duffee, G.R., Stanton, R.H., 2001. Estimation of dynamic term structure models. Working Paper, Haas School of Business University of California, Berkley.
[10] Elerian, O., 1999. Simulation estimation of continuous-time models with applications to finance. Ph.D., Nuffield College, University of Oxford, unpublished.
[11] Elerian, O.; Chib, S.; Shephard, N., Likelihood inference for discretely observed nonlinear diffusions, Econometrica, 69, 959-993, (2001) · Zbl 1017.62068
[12] Eraker, B., MCMC analysis of diffusion models with application to finance, J. bus. econom. statist., 19, 177-191, (2001)
[13] Frühwirth-Schnatter, S., Geyer, A.L.J., 1998. Bayesian estimation of econometric multifactor Cox Ingersoll Ross models of the term structure of interest rates via MCMC methods. Working Paper, Department of Statistics, Vienna University of Economics and Business Administration.
[14] Geyer, A., Pichler, S., 1996. A state space approach to estimate the term structure of interest rates: some empirical evidence. Working Paper, University of Economics, Vienna.
[15] Gilks, W.R.; Richardson, S.; Spiegelhalter, D.J., Markov chain Monte Carlo in practice, (1996), Chapman & Hall New York · Zbl 0832.00018
[16] Gourieroux, C.; Jasiak, J., Financial econometricsproblems, models and methods, (2001), Princeton University Press Princeton, NJ · Zbl 0968.91036
[17] Jegadeesh, N.; Pennacchi, G., The behaviour of interest rates implied by the term structure of eurodollar futures, J. money, credit, banking, 28, 426-446, (1996)
[18] Jones, C., 1998. Bayesian estimation of continuous-time finance models. Working Paper, Simon School of Business, University of Rochester, New York.
[19] Jones, C., Nonlinear Mean reversion in the short-term interest rate, Rev. finan. stud., 16, 793-843, (2003)
[20] Kim, S.; Shepherd, N.; Chib, S., Stochastic volatilitylikelihood inference and comparison with ARCH models, Rev. econom. stud., 65, 361-393, (1998) · Zbl 0910.90067
[21] Lamoureux, C.G.; Witte, M.D., Empirical analysis of the yield curvethe information in the data viewed through the window of Cox, ingersoll and ross, J. finance, LVII, 1479-1520, (2002)
[22] Litterman, R.; Scheinkman, J.A., Common factors affecting bond returns, J. fixed income, 1, 54-61, (1991)
[23] Maes, K., 2003. Modeling the term structure of interest rates: where do we stand? Working Paper, University of Amsterdam.
[24] Martin, V.L.; Pagan, A., Simulation-based estimation of some factor models in econometrics, () · Zbl 1184.62211
[25] Mikkelsen, P., 2002. MCMC based estimation of term structure models. Working Paper, Department of Finance, The Aarhus School of Business, Denmark.
[26] Pearson, N.D., Sun, T.S., 1989. A test of the Cox, Ingersoll and Ross model of the term structure of interest rates using the method of maximum likelihood. Working Paper, MIT, Cambridge, MA.
[27] Pedersen, A.R., A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations, Scand. J. statist., 22, 55-71, (1995) · Zbl 0827.62087
[28] Polson, N.G., Stroud, J.R., Müller, P., 2002. Affine state-dependent variance models. Technical Report, Institute of Statistics and Decision Sciences, Duke University.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.