Multivariate Jacobi process with application to smooth transitions

Journal of Econometrics

Volumn 131, Issue 1-2, 2006, Pages 475-505

  Gourieroux, Christian ^a   Jasiak, Joann ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b YORK UNIVERSITY   (Canada)

Author keywords

Contingency table; Credit risk; Jacobi process; Regime switching; Stochastic volatility

Indexed keywords

DISCRETE TIME CONTROL SYSTEMS; MATHEMATICAL MODELS; PROBABILITY DISTRIBUTIONS;

CONTINGENCY TABLE; CREDIT RISK; JACOBI PROCESS; REGIME SWITCHING; STOCHASTIC VOLATILITY;

RANDOM PROCESSES;

EID: 33644532586     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2005.01.014     Document Type: Conference Paper

References (55)

1. Albanese, C., Chen, O., 2005. Credit banking models in a discrete time framework. Contemporary Mathematics, forthcoming.
2. A. Ang, and G. Bekaert Regimes switches in interest rates Journal of Business and Economic Statistics 20 2002 163 182
3. A. Ang, and G. Bekaert Short rate nonlinearities and regime switches Journal of Economic Dynamic and Control 26 2002 1243 1274
4. J. Ashford, and R. Sowden Multivariate probit analysis Biometrics 26 1970 535 546
5. C. Ball, and A. Roma Stochastic volatility option pricing Journal of Financial and Qualitative Analysis 29 1994 589 607
6. R. Bansal, and H. Zhou Term structure of interest rates with regime shifts The Journal of Finance 57 2002 1997 2042
7. D. Bates Jumps and stochastic volatility exchange rate processes implicit in Deutsche mark options The Review of Financial Studies 9 1996 69 107
8. F. Black, and M. Scholes The Pricing of options and corporate liabilities Journal of Political Economy 81 1973 637 654
9. Cagetti, M., Hansen, L., Sargent, T., Williams, N., 2000. Robustness and pricing with uncertain growth. Working paper, University of Chicago.
10. J. Cai A Markov model of switching regime ARCH Journal of Business and Economic Statistics 12 1994 309 316
11. D. Chapman, and N. Pearson Is the short rate drift actually nonlinear? Journal of Finance 55 2000 355 388
12. Cox, J., Ingersoll, J., Ross, S., 1985. A theory of the term structure of interest rates. Econometrica 53, 385-408.
13. Q. Dai, and K. Singleton Term structure dynamics in theory and reality Review of Financial Studies 16 2003 635 678
14. Dai, Q., Singleton, K., Yang, W., 2003. Are regime shifts priced in US treasury markets? DP Stanford University.
15. A. David Fluctuating confidence in stock markets implications for returns and volatility Journal of Financial and Quantitative Analysis 32 1997 457 462
16. F. Diebold, J. Lee, and G. Weinbuch Regime switching with time varying transition probabilities C. Hargreaves Nonstationary Time Series Analysis and Cointegration 1994 Oxford University Press Oxford
17. D. Duffie, and R. Kan A yield factor model of interest rates Mathematical Finance 6 1996 379 406
18. R. Engle, and J. Hamilton Long swings in the dollar are they in the data and do markets know it? American Economic Review 89 1990 689 713
19. Feng, D., Gourieroux, C., Jasiak, J., 2004. The ordered qualitative model for credit rating transitions. DP CREF 04-05, HEC Montreal.
20. D. Fudenberg, and C. Harris Evolutionary dynamics with aggregate shocks Journal of Economic Theory 57 1992 420 441
21. Gagliardini, P., Gourieroux, C., 2003. Spread term structure and default correlation. DP CREF 03-02, HEC Montreal.
22. Gagliardini, P., Gourieroux, C., 2005a. Migration correlation and efficient estimation. Journal of Banking and Finance, forthcoming.
23. Gagliardini, P., Gourieroux, C., 2005b. Stochastic migration models with applications to corporate risk. Journal of Financial Econometrics, forthcoming.
24. I. Gihman, and A.V. Skorohod Stochastic Differential Equations 1972 Springer Berlin
25. C. Gourieroux, and J. Jasiak Financial Econometrics 2001 Princeton University Press Princeton
26. C. Granger, and R. Joyeux An introduction to long memory time series models and fractional differencing Journal of Time Series Analysis 1 1980 15 29
27. S. Gray Modelling the conditional distribution of interest rates as a regime switching process Journal of Financial Economics 42 1996 27 62
28. J. Hamilton A new approach to the economic analysis of nonstationary time series and the business cycle Econometrica 57 1989 357 384
29. J. Hamilton Analysis of time series subject to changes in regime Journal of Econometrics 45 1990 39 70
30. J. Hamilton, and R. Susmel Autoregressive conditional heteroscedasticity and changes in regime Journal of Econometrics 64 1994 307 333
31. S. Heston A closed form solution for options with stochastic volatility with applications to bond and foreign currency options Review of Financial Studies 6 1993 327 393
32. J. Hull, and A. White The pricing of options on assets with stochastic volatilities Journal of Finance 42 1987 281 300
33. R. Jarrow, and F. Yu Counterparty risk and the pricing of defaultable securities Journal of Finance 56 2001 1756 1799
34. R. Jarrow, D. Lando, and S. Turnbull A Markov model for the term structure of credit risk spreads Review of Financial Studies 10 1997 481 523
35. Johnson, N., Kotz, S., Balakrishnan, N., 1995. Continuous Univariate Distributions, second ed., vol. 2. Wiley, New York.
36. P. Jorion On jump processes in the foreign exchange and stock markets Review of Financial Studies 1 1988 427 445
37. I. Karatzas, and S. Shreve Brownian Motion and Stochastic Calculus second ed. 1991 Springer Berlin
38. S. Karlin, and H. Taylor A Second Course in Stochastic Processes 1981 Academic Press New York
39. M. Kessler, and H. Sorensen Estimating equation based on eigenfunctions for a discretely observed diffusion process Bernoulli 5 1999 299 314
40. N. Krylov Controlled Diffusion Processes 1980 Springer New York
41. C. Lamoureux, and W. Lastrapes Persistence in variance, structural change and the GARCH model Journal of Business and Economic Statistics 8 1990 225 234
42. H. Lancaster The structure of bivariate distributions Annals of Mathematics and Statistics 29 1958 716 736
43. Larsen, K., Sorensen, H., 2003. Diffusion models for exchange rates in a target zone. University of Copenhagen D.P.
44. Mason, S., Bhattacharya, S., 1981. Risky debt, jump processes and safety covenants. Journal of Financial Economics.
45. D. McFadden Quantal choice analysis; a survey Annals of Economics and Social Measurement 5 1976 369 390
46. R. Merton On the pricing of corporate debt the risk structure of interest rates Journal of Finance 29 1974 449 470
47. R. Merton Option pricing when the underlying stock returns are discontinuous Journal of Financial Economics 3 1976 125 144
48. J. Pan The jump risk premia implicit in options evidence from an integrated time series study Journal of Financial Economics 63 2002 3 50
49. T. Terasvirta Specification, estimation and evaluation of smooth transition autoregressive models Journal of the American Statistical Association 89 1994 208 218
50. T. Terasvirta, and H. Anderson Characterizing nonlinearities in business cycles using smooth transition autoregressive models Journal of Applied Econometrics 7 1992 119 136
51. A. Timmermann Moments of Markov switching models Journal of Econometrics 96 2000 75 112
52. Valery, P., 2004. Estimation of the Jacobi process. University of Montreal, D.P.
53. O. Vasicek An equilibrium characterization of the term structure Journal of Financial Economics 5 1977 177 188
54. E. Wong The construction of a class of stationary Markoff process R. Bellman Sixteenth Symposium in Applied Mathematics - Stochastic Processes in Mathematical Physics and Engineering 1964 American Mathematical Society Providence, RI 264 276
55. Wu, S., Zeng, Y., 2003. A general equilibrium model of the term structure of interest rates under regime-switching risk. D.P. University of Kansas.