Abstract
We evaluate, through Monte Carlo experiments, the econometric performance of six alternative estimators of the basic parameters of the Cox—Ingersoll—Ross single-factor diffusion model of the term structure of interest rates. Different generating schemes are compared and the unobservability of the state-variable is taken into account. The effects of approximating interest rates, increasing frequency data and starting values are analyzed. A Monte Carlo evaluation of the effects on bond prices of biased parameter estimates is provided.
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References
L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley, New York, 1974.
G. Bamberg and K. Spremann (eds.), Risk and Capital, Lecture Notes in Economics and Mathematical Systems 227 (1984), Springer, Berlin.
G. Banon, Nonparametric identification for diffusion processes, SIAM Journal of Control and Optimization 16, 3 (1978), 380–395.
E. Barone and R. Cesari, Rischio e rendimento dei titoli a tasso fisso e a tasso variabile in un modello stocastico univariato, Temi di discussione, vol. 73, Banca d’Italia, 1986.
E. Barone and D. Cuoco, La Valutazione delle Obbligazioni e delle Opzioni su Obbligazioni, Quaderni di Ricerca N. 10, LUISS, Roma, 1991.
E. Barone, D. Cuoco, and E. Zautzik, La struttura dei rendimenti per scadenza secondo il modello di Cox, Ingersoll e Ross: una verifica empirica, Temi di discussione, vol. 128, Banca d’Italia, 1989.
Y. Bar-Shalom, On the asymptotic properties of the maximum-likelihood estimate obtained from dependent observations, Journal of the Royal Statistical Society, series B 33, 1 (1971), 72–77.
B. R. Bhat, On the method of maximum-likelihood for dependent observations, Journal of the Royal Statistical Society, series B 36, 1 (1974), 48–53.
F. Black and M. Scholes, The pricing of options and corporate liabilities, Journal of Political Economy 781, 3 (1973), 637–654.
M. J. Brennan and E. S. Schwartz, A continuous-time approach to the pricing of bonds, Journal of Banking and Finance 3 (1979), 133–155.
M. J. Brennan and E. S. Schwartz, An equilibrium model of bond pricing and a test of market efficiency, Journal of Financial and Quantitative Analysis 17, 3 (1982), 301–329.
R. H. Brown and S. M. Schaefer, The term structure of real interest rates and the Cox, Ingersoll 6 Ross model, London Business School, mimeo, 1988.
S. J. Brown and P. H. Dybvig, The empirical implications of the Cox, Ingersoll, Ross theory of the term structure of interest rates, Journal of Finance 41, 3 (1986), 617–630.
K. C. Chan, G. A. Karolyi, F. A. Longstaff, and A. B. Sanders, An empirical comparison of alternative models of the short-term interest rate,Journal of Finance 47, 3 (1992), 12091227.
J. C. Cox, J. E. Ingersoll, and S. A. Ross, Duration and the measurement of basis risk, Journal of Business 52, 1 (1979), 51–61.
J. C. Cox, J. E. Ingersoll, and S. A. Ross, A reexamination of traditional hypotheses about the term structure of interest rates, Journal of Finance 36, 4 (1981), 769–799.
J. C. Cox, J. E. Ingersoll, and S. A. Ross, An intertemporal general equilibrium model of asset prices, Econometrica 53, 2 (1985), 363–384.
J. C. Cox, J. E. Ingersoll, and S. A. Ross, A theory of the term structure of interest rates, Econometrica 53, 2 (1985), 385–407.
M. De Felice and F. Moriconi, La teoria dell’immunizzazione finanziaria. Modelli e strategie, Il Mulino, Bologna, 1991.
S. Dobson, R. Sutch, and D. Vanderford, An evaluation of alternative empirical models of the term structure of interest rates, Journal of Finance 31 (1976), 1035–1065.
L. U. Dothan, On the term structure of interest rates, Journal of Financial Economics 6 (1978), 59–69.
P. D. Feigin, Maximum-likelihood estimation for continuous-time stochastic processes, Advances in Applied Probability 8 (1976), 712–736.
W. Feller, Two singular diffusion problems, Annals of Mathematics 54, 1 (1951), 173–182.
E. O. Fischer and J. Zechner, Diffusion process specifications for interest rates, Bamberg and Spremann (ads.), 1984, pp. 64–73.
I. Fisher, The Theory of Interest, Macmillan, London, 1930.
E. Fournie and D. Talay, Application de la statistique des diffusions à un modèle de taux d’intérêt,Inria, mimeo (1992) (to appear in Finance).
A. Friedman, Stochastic Differential Equations and Applications, vol. 1, Academic Press, New York, 1975.
B. M. Friedman and F. H. Hahn (eds.), Handbook of Monetary Economics, North-Holland, 2 voll., Amsterdam, 1990.
M. R. Gibbons and K. Ramaswamy, The terra structure of interest rates: empirical evidence, The Wharton School, mimeo, 1986.
L. P. Hansen, Large sample properties of generalized method of moments estimators, Econometrica 50, 4 (1982), 1029–1054.
J. M. Harrison and D. M. Kreps, Martingale and arbitrage in multiperiod securities markets, Journal of Economic Theory 20 (1979), 381–408.
J. M. Harrison and S. R. Pliska, Martingales and stochastic integrals in the theory of continuous trading, Stochastic Processes and their Applications 11 (1981), 215–260.
J. R. Hicks, Value and Capital, Oxford University Press, Oxford, 1939 and 1946.
N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam, 1981.
S. Karlin and J. McGregor, Classical diffusion processes and total positivity, Journal of Mathematical Analysis and Applications 1 (1960), 163–183.
S. Karlin and H. M. Taylor, A Second Course in Stochastic Processes, Academic Press, San Diego, 1981.
P. E. Kloeden and E. Platen, Numerical Solutions of Stochastic Differential Equations, Springer, Berlin, 1992.
H. Korezlioglu, G. Mazziotto and J. Szpirglas (eds.), Filtering and Control of Random Processes, Lecture Notes in Control and Information Sciences, 61, Springer, Berlin, 1984.
A. Yu Kutoyants, Estimation of the trend parameter of a diffusion process in the smooth case, transl. by Durri-Hamdani, Theory of Probability and its Applications 23, 3 (1978), 399–405.
A. Le Breton, On continuous and discrete sampling for parameter estimation in diffusion type processes, Mathematical Programming Study 5 (1976), 124–144.
R. S. Liptser and A. N. Shiryayev, Statistics of Random Processes, I, II, transl. (1978), Springer, Berlin, 1974.
A. W. Lo, Statistical tests of contingent claims asset-pricing models: a new methodology, Journal of Financial Economics 17 (1986), 143–174.
A. W. Lo, Maximum-likelihood estimation of generalized Itô processes with discretely sampled data, Econometric Theory 4 (1988), 231–247.
T. A. Marsh and E. R. Rosenfeld, Stochastic processes for interest rates and equilibrium bond prices, Journal of Finance 38, 2 (1983), 635–646.
G. Maruyama, Continuous Markov processes and stochastic equations, Rendiconti del Circolo Matematico di Palermo 4 (1955), 48–90.
R. Masera, The term structure of interest rates. An expectations model tested on post-war Italian data, Oxford University Press, Oxford, 1972.
I. W. McKeague, Estimation for diffusion processes under misspecified models, Journal of Applied Probability 21 (1984), 511–520.
E. J. McShane, Unified Integration, Academic Press, New York, 1983.
G. N. Milstein, Approximate integration of stochastic differential equations, Theory of Probability and its Applications 19 (1974), 557–562.
F. Modigliani and R. Sutch, Innovations in interest rate policy, American Economic Review 56, 2 (1966), 178–197.
W. K. Newey and K. D. West, A simple, positive semi-definite, heteroskedasticity and auto-correlation consistent covariance matrix, Econometrica 55, 3 (1987), 703–708.
E. Platen and W. Wagner, On a Taylor formula for a class of Itô processes, Probability and Mathematical Statistics 3 (1982), 37–51.
P. M. Robinson, Estimation of a time series model from unequally spaced data, Stochastic Processes and their Applications 6 (1977), 9–24.
J. D. Sargan, Some discrete approximations to continuous time stochastic models, Journal of the Royal Statistical Society, Series B 36 (1974), 74–90.
R. J. Shiller, The term structure of interest rates, in Friedman and Hahn (eds.), Ch. 13, 1990.
A. N. Shiryayev, Martingales: recent developments, results, and applications, International Statistical Review 49 (1981), 199–233.
D. Talay, Efficient numerical schemes for the approximation of expectations of functionals of stochastic differential equations, in Korezlioglu, Mazziotto, and Szpirglas (eds.), 1984, pp. 294–313.
D. Talay, Simulation and numerical analysis of stochastic differential systems: a review, Inria, Report 1313, mimeo, 1990.
O. A. Vasicek, An equilibrium characterization of the term structure, Journal of Financial Economics 5 (1977), 177–188.
E. Wong and B. Hajek, Stochastic Processes in Engineering Systems, Springer, New York, 1985.
A.M. Yaglom, An Introduction to the Theory of Stationary Random Functions,y 19521, translated from Russian and edited by R. A. Silverman, Dover, New York, 1962.
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Bianchi, C., Cesari, R., Panattoni, L. (1995). Alternative Estimators of a Diffusion Model of the Term Structure of Interest Rates. A Monte Carlo Comparison. In: Bolthausen, E., Dozzi, M., Russo, F. (eds) Seminar on Stochastic Analysis, Random Fields and Applications. Progress in Probability, vol 36. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7026-9_20
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DOI: https://doi.org/10.1007/978-3-0348-7026-9_20
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