Stochastic volatility models as hidden Markov models and statistical applications

Bernoulli

Volumn 6, Issue 6, 2000, Pages 1051-1079

  Genon Catalot, Valentine ^a   Jeantheau, Thierry ^b   Larédo, Catherine ^a  

^a UFR des Sciences et Technologie   (France)

^b CEMAGREF   (France)

Author keywords

Diffusion processes; Discrete time observations; Hidden markov models; Mixing; Parametric inference; Stochastic volatility

Indexed keywords

EID: 0003215606     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318471     Document Type: Article

References (32)

1. Barndorff-Nielsen, O.E. and Shephard, N. (1998) Aggregation and model construction for volatility models. Centre for Analytical Finance, University of Aarhus, Working Paper Series No. 10.
2. Bhattacharya, R.N. (1982) On the functional limit theorem and tliS law of iterated logarithm for Markov processes. Z. Wahrscheinlichkeitstheorie Venv. Geb., 60, 185-201.
3. Bibby, B. and Sorensen, M. (1995) Martingale estimation functions for discretely observed diffusion processes. Bernoulli, 1, 17-39.
4. Bickel, P.J. and Ritov, Y. (1996) Inference in hidden Markov models I: Local asymptotic normality in the stationary case. Bernoulli, 2, 199-228.
5. Bradley, R.C. (1986) Basic properties of strong mixing conditions. In E. Eberlein and M.S. Taqqu (eds), Dependence in Probability and Statistics, A Survey of Recent Results, pp. 165-192, Boston: Birkhauser.
6. Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A theory of term structure of interest rates. Econometrica, 53, 385-407.
7. Doukhan, P. (1994) Mixing: Properties and Examples, Lecture Notes in Statist. 85. Berlin: Springer-Verlag.
8. Drost, EC. and Werker, B. (1996) Closing the GARCH gap: Continuous time GARCH modelling. J. Econometrics, 74, 31-57.
9. Ethier, S.N. and Kurtz, T.G. (1986) Markov Processes. New York: Wiley.
10. Genon-Catalot, V, Jeantheau, T. and Larédo, C. (1998) Limit theorems for discretely observed stochastic volatility models. Bernoulli, 4, 283-303.
11. Genon-Catalot, V, Jeantheau, T. and Larédo, C. (1999) Parameter estimation for discretely observed stochastic volatility models. Bernoulli, 5, 855-872.
12. Ghysels, E., Harvey, A. and Renault, E. (1996) Stochastic volatility. In O.S. Maddala and C.R. Rao (eds), Handbook of Statistics 14: Statistical Methods in Finance, pp. 119-192. Amsterdam: North-Holland.
13. Hall, P. and Heyde, C.C. (1980) Martingale Limit Theory and its Application. New York: Academic Press.
14. Hansen, L.P. and Scheinkman, J.A. (1995) Back to the future: generating moment implication for continuous-time Markov processes. Econometrica, 63, 767-804.
15. Hansen, L.P., Scheinkman, J.A. and Touzi, N. (1998) Spectral methods for identifying scalar ; diffusions. J. Econometrics, 86(1), 1-32. 1
16. Heston, S.L. (1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options. Rev. Financial Stud., 6, 327-343.
17. Hull, J. and White, A. (1987) The pricing of options on assets with stochastic volatilities. J. Finance, 42, 281-300.
18. Jensen, J.L. and Petersen, N.V (1998) Asymptotic normality of the maximum likelihood estimator in state space models. Research Reports of University of Aarhus, No. 392.
19. Kent, J. (1978) Time-reversible diffusions. Adv. Appl. Probab., 10, 819-835.
20. Kessler, M. (1996) Simple and explicit estimating functions for a discretely observed diffusion process. Scand. J. Statist., 27(1), 65-82
21. Klaassen, C.A.J. (1985) On a inequality of ChernofT. Ann. Probab., 13, 966-974.
22. Krengel, U. (1985) Ergodic Theorems. Berlin: de Gruyter.
23. Ledoux, M. (1999) Concentration of measure and logarithmic Sobolev inequalities. In J. Azéma, M. Emery, M. Ledoux and M. Yor (eds), Séminaire de Probabilités XXXIII, Lecture Notes in Math. 1709, pp. 120-216. Berlin: Springer-Verlag.
24. Leroux, B.G. (1992) Maximum likelihood estimation for hidden Markov models. Stochastic Process. Appl, 40, 127-143.
25. Lindgren, G. (1978) Markov regime models for mixed distributions and switching regressions. Scand. J. Statist., 5, 81-91.
26. Lindvall, T. (1983) On coupling of diffusion processes. J. Appl. Probab., 20, 82-93.
27. Nagel, P. (ed.) (1986) One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184. Berlin: Springer-Verlag
28. Nelson, D.D. (1990) ARCH models as diffusion approximations. J. Econometrics, 45, 7-38.
29. Orey, S. (1971) Limit Theorems for Markov Chain Transition Probabilities. London: Van Nostrand.
30. Rogers, L.C.G. and Williams, D. (1987) Diffusions, Markov processes and Martingales. Vol. 2: Ito calculus. New York: Wiley.
31. Veretennikov, A.Y. (1988) Bounds for the mixing rate in the theory of stochastic differential equations. TJieory Probab. Appl, 32, 273-281.
32. Veretennikov, A.Y. (1997) On polynomial mixing bounds for stochastic differential equations. Stochastic Process. Appl, 70, 115-127.