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Control variates for variance reduction in indirect inference: interest rate models in continuous time

  • Calzolari, Giorgio
  • Di Iorio, Francesca
  • Fiorentini, Gabriele

Simulation estimators, such as indirect inference or simulated maximum likelihood, are successfully employed for estimating stochastic differential equations. They adjust for the bias (inconsistency) caused by discretization of the underlying stochastic process, which is in continuous time. The price to be paid is an increased variance of the estimated parameters. There is, in fact, an additional component of the variance, which depends on the stochastic simulation involved in the estimation procedure. To reduce this udesirable effect one should enlarge the number of simulations (or the length of each simulation) and thus the computation cost. Alternatively, this paper shows how variance reduction can be achieved, at virtually no additional computation cost, by use of control variates. The Ornstein-Uhlenbeck equation, used by Vasicek to model the short term interest rate in continuous time, and the so called square root equation, used by Cox, Ingersoll and Ross, are explicitly considered and experimented with. Monte Carlo experiments show that, for some parameters of interest, a global efficiency gain about 35%-45% over the simplest indirect estimator is obtained at about the same computation cost.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23160.

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Date of creation: Nov 1996
Date of revision: Nov 1996
Handle: RePEc:pra:mprapa:23160
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  1. Bianchi, Carlo & Cleur, Eugene M, 1996. "Indirect Estimation of Stochastic Differential Equation Models: Some Computational Experiments," Computational Economics, Society for Computational Economics, vol. 9(3), pages 257-74, August.
  2. Gallant, A. Ronald & Tauchen, George, 1997. "Estimation Of Continuous-Time Models For Stock Returns And Interest Rates," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 135-168, January.
  3. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  4. 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.
  5. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  6. Calzolari, Giorgio & Sterbenz, Frederic P, 1986. "Control Variates to Estimate the Reduced Form Variances in Econometric Models," Econometrica, Econometric Society, vol. 54(6), pages 1483-90, November.
  7. Bianchi, C. & Cesari, R. & Panattoni, L., 1994. "Alternative Estimators of the Cox, ingersoll and Ross Model of the Term Structure of Interest Rates: A Monte Carlo Comparison," Papers 236, Banca Italia - Servizio di Studi.
  8. BROZE, Laurence & SCAILLET, Olivier & ZAKOIANÂ , Jean-Michel, 1993. "Testing for Continuous-Time Models of the Short-Term Interest Rate," CORE Discussion Papers 1993031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  9. Broze, Laurence & Scaillet, Olivier & Zako an, Jean-Michel, 1998. "Quasi-Indirect Inference For Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 14(02), pages 161-186, April.
  10. Hendry, David F. & Harrison, Robin W., 1974. "Monte Carlo methodology and the small sample behaviour of ordinary and two-stage least squares," Journal of Econometrics, Elsevier, vol. 2(2), pages 151-174, July.
  11. Calzolari, Giorgio, 1979. "Antithetic variates to estimate the simulation bias in non-linear models," Economics Letters, Elsevier, vol. 4(4), pages 323-328.
  12. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  13. Brennan, Michael J. & Schwartz, Eduardo S., 1979. "A continuous time approach to the pricing of bonds," Journal of Banking & Finance, Elsevier, vol. 3(2), pages 133-155, July.
  14. Michael J. Brennan and Eduardo S. Schwartz., 1979. "A Continuous-Time Approach to the Pricing of Bonds," Research Program in Finance Working Papers 85, University of California at Berkeley.
  15. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier.
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