Calzolari, Giorgio and Di Iorio, Francesca and Fiorentini, Gabriele (1996): Control variates for variance reduction in indirect inference: interest rate models in continuous time.
There is a more recent version of this item available. 

PDF
MPRA_paper_23160.pdf Download (880kB)  Preview 
Abstract
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 OrnsteinUhlenbeck 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.
Item Type:  MPRA Paper 

Original Title:  Control variates for variance reduction in indirect inference: interest rate models in continuous time 
Language:  English 
Keywords:  Monte Carlo; variance reduction techniques; control variates; indirect inference; discretization; shortterm interest rate; stochastic equation 
Subjects:  C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C51  Model Construction and Estimation 
Item ID:  23160 
Depositing User:  Giorgio Calzolari 
Date Deposited:  10. Jun 2010 04:26 
Last Modified:  31. Dec 2015 00:29 
References:  Arnold, L. (1975): Stochastic Differential Equations New York, John Wiley and Sons. Bianchi, C., R. Cesari and L. Panattoni (1995): Alternative Estimators of the Cox, Ingersoll and Ross Model of the term Structure of Interest Rates. Roma, Banca d'Italia, Temi di Discussione N.326. Bianchi, C. and E. M. Cleur (1996, forthcomning): Indirect Estimation of Stochastic Differential Equation Models: Some Computational Experiment, Computational Statistics. Brennan, M.J. and E.S. Schwartz (1979): A Continuous Time Approach to the Pricing of Bonds, Journal of Banking and Finance, 3, 135155. Broze, L., O. Scaillet and J.M. Zakoian (1994): Quasi Indirect Inference for Diffusion Processes. Paris: Crest, document de travail No.9511. Broze, L., O. Scaillet and J.M. Zakoian (1995): Testing for Continuous Time Models of the ShortTerm Interest Rate Journal of Empirical Finance, 2, 199223. Calzolari, G. (1979): Antithetic Variates to Estimate the Simulation Bias in NonLinear Models, Economics Letters 4, 323328. Calzolari, G., and F. P. Sterbenz (1986): Control Variates to Estimate the Reduced Form Variances in Econometric Models, Econometrica 54, 14831490. Chan K.C., G.A. Karolyi, F.A. Longstaff and A.B. Sanders (1992): An empirical Comparison of Alternative Models of the ShortTerm Interest Rate, The Journal of Finance, vol. 47, n. 3, 12091227. Cleur E. (1995): A Comparison of Alternative Discrete Approximations to the Cox Ingersoll Ross model, mimeo, University of Pisa. Cox, J.C., J. Ingersoll and S.A. Ross (1985): A Theory of Term Structure of Interest Rates, Econometrica, vol. 53, n.2, 385408. Di Iorio, F. (1996): Metodo Generalizzato dei Momenti e Modelli Markoviani per la Valutazione delle Attivita' Finanziarie, PhD Thesis, Dipartimento di Statistica, Universita' di Firenze. Gallant, R. and G. Tauchen (1992): Which Moment to Match? mimeo, Duke University. Gallant, R. and G. Tauchen (1995): Estimation of Continuos Time Models for Stock Returns and Interest Rates, mimeo, Duke University. Geweke, J. (1996): Simulation and Numerical Integration. Federal Reserve Bank of Minneapolis, Working Paper N.526. Gourieroux, C., A. Monfort and E. Renault (1993): Indirect Inference, Journal of Applied Econometrics, vol. 8, 85118. Hendry, D. F. (1984): Monte Carlo Experimentation in Econometrics, in Handbook of Econometrics, ed. by Z. Griliches and M. D. Intriligator. Amsterdam: NorthHolland Publishing Company, Vol. II, 937976. Hendry, D. F. and R. W. Harrison (1974): Monte Carlo Methodology and the Small Sample Behaviour of Ordinary and TwoStage Least Squares, Journal of Econometrics 2, 151174. Ikeda, N. and S. Watanabe (1989): Stochastic Differential Equations and Diffusion Processes North Holland, Amsterdam. Kahn, H. (1956): Use of Different Monte Carlo Sampling Techniques, in Symposium on Monte Carlo Methods, ed. by H. A. Meyer. New York: John Wiley, 146190. Kloeden, P.E. and E. Platen (1992): Numerical Solution of Stochastic Differential Equations, SpringerVerlag, Berlin. Mikhail, W. M. (1975): A Comparative Monte Carlo Study of the Properties of Econometric Estimators, Journal of the American Statistical Association 70, 94104. Moy, W. A. (1971): Variance Reduction, in Computer Simulation Experiments with Models of Economic Systems, ed. by T. H. Naylor. New York: John Wiley \& Sons, Inc., 269289. Newton, N. J. (1994): Variance Reduction for Simulated Diffusions, SIAM J. Appl. Math 54, 17801805. Pastorello, S., E. Renault and N. Touzi (1994): Statistical Inference for Random Variance Option Pricing. Universita' di Padova, Dipartimento di Scienze Economiche, Quaderno No. 31. Rao, C. R. (1973): Linear Statistical Inference and its Applications. New York: John Wiley \& Sons. Richard, J. F. (1996): Simulation Techniques, in The Econometrics of Panel Data, ed. by Laszlo Matya and Patrick Sevestre. Dordrecht: Kluver Academic Publishers, 613638. Simon, G. (1976): Computer Simulation Swindles, with Applications to Estimates of Location and Dispersion, Applied Statistics, Journal of the Royal Statistical Society, series C 25, 266274. Smith, A. (1993): Estimating Nonlinear TimeSeries Models Using Simulated Vector Autoregressions, Journal of Applied Econometrics, vol. 8 6384 Sterbenz, F. P., and G. Calzolari (1990): Alternative Specifications of the Error Process in the Stochastic Simulation of Econometric Models, Journal of Applied Econometrics 5, 137150. Vasicek, O.A. (1977): An Equilibrium Characterization of the Term Structure, Journal of Financial Economics, vol. 5, n. 2, 17788. White, H. (1982): Maximum Likelihood Estimation of Misspecified Models, Econometrica 50, 125. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/23160 
Available Versions of this Item
 Control variates for variance reduction in indirect inference: interest rate models in continuous time. (deposited 10. Jun 2010 04:26) [Currently Displayed]