Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan

Journal of Econometrics

Volumn 141, Issue 2, 2007, Pages 1245-1280

  Yu, Jialin ^a  

^a Howard Hughes Medical Institute   (United States)

Author keywords

Chinese Yuan; Currency realignment; Discrete sampling; Jump diffusion; Maximum likelihood estimation

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC ANALYSIS; DATA STRUCTURES; FINANCE; PROBABILITY; RISK ANALYSIS;

CURRENCY REALIGNMENT; DISCRETE SAMPLING; JUMP DIFFUSION; MAXIMUM LIKELIHOOD ESTIMATOR;

ECONOMIC ANALYSIS;

EID: 34848848418     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2007.02.003     Document Type: Article

References (56)

1. Ai{dotless}̈t-Sahalia Y. Nonparametric pricing of interest rate derivative securities. Econometrica 64 (1996) 527-560
2. Ai{dotless}̈t-Sahalia Y. Maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach. Econometrica 70 (2002) 223-262
3. Ai{dotless}̈t-Sahalia, Y., 2006. Closed-form likelihood expansions for multivariate diffusions. Working paper.
4. Ai{dotless}̈t-Sahalia Y., and Kimmel R. Maximum likelihood estimation of stochastic volatility models. Journal of Financial Economics 83 (2007) 413-452
5. Ai{dotless}̈t-Sahalia Y., and Yu J. Saddlepoint approximations for continuous-time Markov processes. Journal of Econometrics 134 (2006) 507-551
6. Ai{dotless}̈t-Sahalia Y., Mykland P., and Zhang L. How often to sample a continuous-time process in the presence of market microstructure noise. Review of Financial Studies 18 (2005) 351-416
7. Andersen T., Benzoni L., and Lund J. An empirical investigation of continuous-time equity return models. Journal of Finance 57 (2002) 1239-1284
8. Andersen, T., Bollerslev, T., Diebold, F., 2006. Roughing it up: including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics, forthcoming.
9. Bakshi G., and Ju N. A refinement to Ai{dotless}̈t-sahalia's (2002) "maximum likelihood estimation of discretely sampled diffusions: a closed-form approximation approach". Journal of Business 78 (2005) 2037-2052
10. Bakshi G., Ju N., and Ou-Yang H. Estimation of continuous-time models with an application to equity volatility. Journal of Financial Economics 82 (2006) 227-249
11. Bandi F., and Nguyen T. On the functional estimation of jump-diffusion models. Journal of Econometrics 116 (2003) 293-328
12. Bandi F., and Phillips P. Fully nonparametric estimation of scalar diffusion models. Econometrica 71 (2003) 241-284
13. Bandi, F., Russell, J., 2006. Volatility. In: Handbook of Financial Engineering. Elsevier, Amsterdam, forthcoming.
14. Barndorff-Nielsen O.E., and Shephard N. Non-Gaussian ornstein-uhlenbeck-based models and some of their uses in financial economics. Journal of the Royal Statistical Society Series B 63 (2001) 167-241
15. Barndorff-Nielsen O.E., and Shephard N. Power and bipower variation with stochastic volatility and jumps. Journal of Financial Econometrics 2 (2004) 1-48
16. Bates D. Jumps and stochastic volatility: exchange rate processes implicit in deutsche mark options. Review of Financial Studies 9 (1996) 69-107
17. Bichteler K., Gravereaux J.-B., and Jacod J. Malliavin Calculus for Processes with Jumps (1987), Gordon and Breach Science Publishers, London
18. 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
19. Brémaud P. Point Processes and Queues, Martingale Dynamics (1981), Springer, Berlin
20. Carr P., Geman H., Madan D., and Yor M. Stochastic volatility for lévy processes. Mathematical Finance 13 (2003) 345-382
21. Carrasco, M., Chernov, M., Florens, J.-P., Ghysels, E., 2007. Efficient estimation of general dynamic models with a continuum of moment conditions. Journal of Econometrics, in press, doi:10.1016/j.jeconom.2006.07.013.
22. Carrier G.F., and Pearson C.E. Partial differential equations. 2nd ed. (1988), Academic Press, New York
23. Duffee G. Term premia and interest rate forecasts in affine models. Journal of Finance 57 (2002) 405-443
24. Duffie D., and Glynn P. Estimation of continuous-time Markov processes sampled at random time intervals. Econometrica 72 (2004) 1773-1808
25. Duffie D., and Singleton K. Credit Risk (2003), Princeton University Press, Princeton, NJ
26. Duffie D., Pan J., and Singleton K. Transform analysis and asset pricing for affine jump diffusions. Econometrica 68 (2000) 1343-1376
27. Elerian O., Chib S., and Shephard N. Likelihood inference for discretely observed nonlinear diffusions. Econometrica 69 (2001) 959-993
28. Eraker B., Johannes M., and Polson N. The impact of jumps in volatility and returns. Journal of Finance 58 (2003) 1269-1300
29. Gallant A.R., and Tauchen G. Which moments to match?. Econometric Theory 12 (1996) 657-681
30. Gouriéroux, C., Monfort, A., Renault, E., 1993. Indirect inference. Journal of Applied Econometrics, S85-S118.
31. Hansen L.P., and Scheinkman J. Back to the future: generating moment implications for continuous-time Markov processes. Econometrica 63 (1995) 767-804
32. Has'minskii{dotless}̌ R.Z. Stochastic Stability of Differential Equations (1980), Sijthoff & Noordhoff
33. Hoffman K. Analysis in Euclidean Space (1975), Prentice-Hall, Englewood Cliffs, NJ
34. Huang Y. Selling China (2003), Cambridge University Press, Cambridge
35. Huang X., and Tauchen G. The relative contribution of jumps to total price variance. Journal of Financial Econometrics 3 (2005) 456-499
36. Jeganathan P. Some aspects of asymptotic theory with applications to time series models. Econometric Theory 11 (1995) 818-887
37. Jensen B., and Poulsen R. Transition densities of diffusion processes: numerical comparison of approximation techniques. Journal of Derivatives 9 (2002) 18-32
38. Johannes M. The statistical and economic role of jumps in continuous-time interest rate models. Journal of Finance 59 (2004) 227-260
39. Kessler M., and Sørensen M. Estimating equations based on eigenfunctions for a discretely observed diffusion process. Bernoulli 5 (1999) 299-314
40. Kristensen, D., 2004. Estimation in two classes of semiparametric diffusion models. Working paper.
41. Ledoit, O., Santa-Clara, P., Yan, S., 2002. Relative pricing of options with stochastic volatility. Working paper.
42. Liu J., Longstaff F.A., and Pan J. Dynamic asset allocation with event risk. Journal of Finance 58 (2003) 231-259
43. Merton R. Continuous-Time Finance (1992), Blackwell Publishers, London
44. Pan J. The jump-risk premia implicit in options: evidence from an integrated time-series study. Journal of Financial Economics 63 (2002) 3-50
45. Pedersen A. A new approach to maximum-likelihood estimation for stochastic differential equations based on discrete observations. Scandinavian Journal of Statistics 22 (1995) 55-71
46. Piazzesi M. Bond yields and the federal reserve. Journal of Political Economy 113 (2005) 311-344
47. Protter P. Stochastic Integration and Differential Equations (1990), Springer, Berlin
48. Revuz D., and Yor M. Continuous Martingales and Brownian Motion. third ed. (1999), Springer, Berlin
49. Robinson P.M. The stochastic difference between econometric statistics. Econometrica 56 (1988) 531-548
50. Rudin W. Principles of Mathematical Analysis. third ed. (1976), McGraw-Hill, New York
51. Schaumburg, E., 2001. Maximum likelihood estimation of lévy type SDEs. Ph.D. Thesis, Princeton University.
52. Singleton K. Estimation of affine asset pricing models using the empirical characteristic function. Journal of Econometrics 102 (2001) 111-141
53. Stokey N., Lucas R., and Prescott E. Recursive Methods in Economic Dynamics (1996), Harvard University Press
54. Sundaresan S. Continuous-time methods in finance: a review and an assessment. Journal of Finance 55 (2000) 1477-1900
55. Varadhan S.R.S. On the behavior of the fundamental solution of the heat equation with variable coefficients. Communications on Pure and Applied Mathematics 20 (1967) 431-455
56. White H. Maximum likelihood estimation of misspecified models. Econometrica 50 (1982) 1-26