Asymptotic properties of Monte Carlo estimators of diffusion processes

Journal of Econometrics

Volumn 134, Issue 1, 2006, Pages 1-68

  Detemple, Jérôme ^a,b   Garcia, René ^b,c,d   Rindisbacher, Marcel ^b,e  

^a BOSTON UNIVERSITY   (United States)

^b CIRANO   (Canada)

^c UNIVERSITÉ DE MONTRÉAL   (Canada)

^d Canada H3A 2T7   (Canada)

^e UNIVERSITY OF TORONTO   (Canada)

Author keywords

Diffusion processes; Doss transformation; Monte Carlo estimators; Simulation based estimation

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; COMPUTER SIMULATION; DIFFUSION; ERROR ANALYSIS; MATHEMATICAL TRANSFORMATIONS;

DIFFUSION PROCESSES; DOSS TRANSFORMATION; MONTE CARLO ESTIMATORS; SIMULATION-BASED ESTIMATION;

MONTE CARLO METHODS;

EID: 33746218657     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2005.06.028     Document Type: Article

References (63)

1. Ait-Sahalia, Y., 1996. Testing continuous-time models of the spot interest rate. Review of Financial Studies 9, 385-426.
2. Ait-Sahalia Y. Transition densities for interest rate and other nonlinear diffusions. Journal of Finance 54 (1999) 1361-1395
3. Ait-Sahalia Y. Maximum likelihood estimation of discretely observed diffusions: a closed form approximation approach. Econometrica 70 (2002) 223-262
4. Bally V., and Talay D. The law of the Euler scheme for stochastic differential equations (I): convergence rate of the distribution function. Probability Theory and Related Fields 104 (1996) 43-60
5. Bally V., and Talay D. The law of the Euler scheme for stochastic differential equations (II): convergence rate of the density. Monte Carlo Methods and its Applications 2 (1996) 93-128
6. Barberis N. Investing for the long run when returns are predictable. Journal of Finance 55 (2000) 225-264
7. Basawa, I.V., Scott, D.J., 1982. Asymptotic optimal inference for non-ergodic models. Lecture Notes in Statistics, vol. 17. Springer, New York.
8. Bawa V.S., Brown S.J., and Klein R.W. Estimation Risk and Optimal Portfolio Choice (1979), North-Holland, New York
9. Bibby B.M., and Sørensen M. Martingale estimating functions for discretely observed diffusion processes. Bernoulli 1 (1995) 17-39
10. Billingsley P. Convergence of Probability Measures (1968), Wiley, New York
11. Brandt M., and Santa-Clara P. Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets. Journal of Financial Economics 63 (2002) 161-210
12. Broze L., Scaillet O., and Zakoian J.-M. Quasi-indirect inference for diffusion processes. Econometric Theory 14 (1998) 161-186
13. Chamberlain G. Asymptotic efficiency in estimation with conditional moment restrictions. Journal of Econometrics 34 (1987) 305-334
14. Chamberlain G. Efficiency bounds for semiparametric regression. Econometrica 60 (1992) 567-596
15. Chan, K.C., Karolyi, A., Longstaff, F.A., Saunders, A., 1992. A comparison of alternative models of the short-term interest rates. Journal of Finance 47, 1209-1227.
16. Chib S., Elerian O., and Shephard N. Likelihood inference for discretely observed non-linear diffusions. Econometrica 69 (2001) 959-993
17. Dacunha-Castelle D., and Florens-Zmirou D. Estimation of the coefficients of a diffusion from discrete observations. Stochastics 19 (1986) 263-284
18. Detemple J.B., Garcia R., and Rindisbacher M. A Monte Carlo method for optimal portfolios. Journal of Finance 58 (2003) 401-446
19. Detemple, J.B., Garcia, R., Rindisbacher, M., 2005. Representation formulas for Malliavin derivatives of diffusion processes. Finance and Stochastics 9, 349-369.
20. Doss H. Liens entre équations différentielles stochastiques et ordinaires. Annales de l'Institut H. Poincaré 13 (1977) 99-125
21. Duffie D., and Glynn P. Efficient Monte Carlo simulation of security prices. Annals of Applied Probability 5 (1995) 897-905
22. Duffie D., and Protter P. From discrete to continuous finance: weak convergence of the financial gain process. Mathematical Finance 2 (1992) 1-15
23. Duffie D., and Singleton K. Simulated moments estimation of Markov models of asset prices. Econometrica 61 (1993) 929-952
24. Durham G.B., and Gallant A.R. Numerical techniques for maximum likelihood estimation of continuous-time diffusion processes. Journal of Business and Economic Statistics 20 (2002) 297-316
25. Eraker B. MCMC analysis of diffusion models with application to finance. Journal of Business and Economic Statistics 19 (2001) 177-191
26. Florens-Zmirou D. Approximate discrete-time schemes for statistics of diffusion processes. Statistics 20 (1989) 547-557
27. Florens-Zmirou D. On estimating the diffusion coefficient from discrete observations. Journal of Applied Probability 30 (1993) 790-804
28. Gaines J.G., and Lyons T.J. Variable step size control in the numerical solution of stochastic differential equations. SIAM Journal of Applied Mathematics 57 (1997) 1455-1484
29. Gallant A.R., and Tauchen G. Which moments to match?. Econometric Theory 12 (1996) 657-681
30. Gallant, A.R., Tauchen, G., 2002. Simulated score methods and indirect inference for continuous-time models. Handbook of Financial Econometrics, forthcoming.
31. Genon-Catalot V. Maximum contrast estimation for diffusion processes from discrete observations. Statistics 21 (1990) 99-116
32. Genon-Catalot V., and Jacod J. On the estimation of the diffusion coefficient for multidimensional diffusion processes. Annales de l'I.H.P., Probabilité et Statistiques 29 (1993) 119-151
33. Gouriéroux C., Montfort A., and Renault E. Indirect inference. Journal of Applied Econometrics 8 (1993) 85-118
34. Hansen, L., 1985. A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators. Journal of Econometrics 30, 203-238.
35. Hansen L.P., and Scheinkman J.A. Back to the future: generating moment implications for continuous-time Markov processes. Econometrica 63 (1995) 767-804
36. Hansen, L.P., Heaton, J.C., Ogaki, M., 1988. Efficiency bounds implied by multi-period conditional moment restrictions. Journal of the American Statistical Association 83, 863-871.
37. Heyde C.C. On best asymptotic confidence intervals for parameters of stochastic processes. Annals of Statistics 20 (1992) 603-607
38. Jacod J., and Protter P. Asymptotic error distributions for the Euler method for stochastic differential equations. Annals of Probability 26 (1998) 267-307
39. 1 de Skorohod. Probability Theory and Related Fields 81 (1989) 111-137
40. Kallenberg O. Foundations of Modern Probability Theory (1997), Springer, New York
41. Kessler M., and Sørensen M. Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli 5 2 (1999) 299-314
42. Kloeden P., and Platen E. Numerical Solution of Stochastic Differential Equations (1997), Springer, Berlin
43. Kurtz T.G., and Protter P. Wong-Zakai corrections, random evolutions and numerical schemes for SDE's. Stochastic Analysis (1991), Academic Press, New York 331-346
44. Kurtz T.G., and Protter P. Weak limit theorems of stochastic integrals and stochastic differential equations. Annals of Probability 19 (1991) 1035-1070
45. Kurtz, T.G., Protter, P., 1996. Weak convergence and stochastic integrals and differential equations, 1995 CIME School in Probability. Lecture Notes in Mathematics, vol. 1627. Springer, Berlin, pp. 1-41.
46. Lo A. Maximum likelihood estimation of generalized Ito processes with discretely-sampled data. Econometric Theory 4 (1988) 231-247
47. Meyn S.P., and Tweedie R.L. Markov Chains and Stochastic Stability. Communications and Control Engineering Series (1993), Springer, Berlin, New York
48. Milshtein G.N. Weak approximation of solutions of systems of stochastic differential equation. Theory of Probability and its Application 4 (1984) 750-768
49. Milshtein G.N. Numerical Integration of Stochastic Differential Equations (1995), Kluwer Academic Publishers, New York
50. Milshtein G.N., Schoenmakers J., and Spokoiny V. Transition density estimation for stochastic differential equations via forward-reverse representations. Bernoulli 10 (2004) 281-312
51. Müller, U.U., Wefelmeyer, W., 2002. Autoregression, estimating functions, and optimality criteria. In Advances in Statistics, Combinatorics and Related Areas, Selected Papers from the SCRA2001-FIM VIII Proceedings of the Wollongong Conference. World Scientific, Singapore.
52. Newey W.K. Semiparametric efficiency bounds. Journal of Applied Econometrics 5 (1990) 90-135
53. Nualart D. The Malliavin Calculus and Related Topics (1995), Springer, New York
54. Pedersen A.R. A new approach to maximum likelihood estimation for stochastic differential equations based on discrete observations. Scandinavian Journal of Statistics 22 (1995) 55-71
55. Pedersen A.R. Consistency and asymptotic normality of an approximate maximum likelihood estimator for discretely observed diffusion processes. Bernoulli 1 (1995) 257-279
56. Santa-Clara, P., 1995. Simulated likelihood estimation of diffusions with and application to the short term interest rate. Ph.D. Dissertation, INSEAD.
57. Smith, A.A., Jr. 1990. Three Essays on the Solution and estimation of dynamic macroeconomic models. Ph.D. Thesis, Duke University.
58. Talay, D., 1984. Efficient numerical schemes for the approximation of expectations of functionals of S.D.E. In: Korezioglu, H., Maziotto, G., Szpirglas, J. (Eds.), Filtering and Control of Random Processes, Lecture Notes in Control and Information Sciences, vol. 61, Springer, New York, pp. 294-313.
59. Talay D. Discrétisation d'une équation différentielle stochastique et calcul approché d'éspérance de fonctionelles de la solution. Mathematical Modelling and Numerical Analysis (1986) 141-179
60. Talay, D., 1996. Probabilistic numerical methods for partial differential equations: elements of analysis. CIME School in Probability, Lecture Notes in Mathematics, vol. 1627. Springer, Berlin, pp. 149-196.
61. Talay D., and Tubaro L. Expansion of the global error for numerical schemes solving stochastic differential equations. Stochastic Analysis and its Application 8 (1990) 483-509
62. Wefelmeyer W. Quasi-likelihood models and optimal inference. Annals of Statistics 24 (1996) 405-422
63. Wong E., and Zakai M. On the convergence of ordinary integrals to stochastic integrals. Annals of Mathematical Statistics 36 (1964) 1560-1564