A link between complete models with stochastic volatility and ARCH models

Finance and Stochastics

Volumn 8, Issue 1, 2004, Pages 111-131

  Jeantheau, Thierry ^a  

^a UFR des Sciences et Technologie   (France)

Author keywords

ARCH models; Asymptotic theory; Diffusion approximation; Markov chain; Stochastic volatility

Indexed keywords

EID: 24144476242     PISSN: 09492984     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00780-003-0103-6     Document Type: Review

References (25)

1. Attali, J. G.: Méthodes de stabilité pour des chaines de Markov non fellériennes. Thèse de l'université de Paris I, 1999
2. Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Pol. Econ. 87, 637-659 (1973)
3. Bollerslev, T. P.: Generalized autoregressive conditional heteroskedasticity. J. Econ. 31, 307-327 (1986)
4. Bollerslev, T. P., Chou, R. Y., Kroner, K. F.: ARCH modeling in finance: A review of the theory and empirical evidence. J. Econ. 52, 5-59 (1992)
5. Bougerol, P., Picard, N.: Stationarity of GARCH processes and of some nonnegative time series. J. Econ. 52, 115-127 (1992)
6. Comte, F., Lieberman, O.: Asymptotic theory for Multivariate GARCH processes. J. Multiv. Anal. (forthcoming)
7. Corradi, V.: Reconsidering the continuous time limit of the GARCH(1,1) process. J. Econ. 96, 145-153 (2000)
8. Droesbeke, J.-J., Fichet, B., Tassi P.: Modelisation ARCH: Théorie statistique et applications dans le domaine de la finance. Ellipses-Edition Marketing 1994
9. Duflo, M.: Random iterative models (Applications of Mathematics, stochastic modelling and applied probability). Berlin Heidelberg New York: Springer 1997
10. Engle, R. F.: Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987-1008 (1982)
11. Genon-Catalot V., Jeantheau, T., Larédo, C.: Stochastic volatility models as hidden Markov models and statistical applications. Bernoulli 6 (6), 1051-1079 (2000)
12. Genon-Catalot V., Jeantheau, T., Larédo, C.: Consistency of conditional likelihood estimators for stochastic volatility models. Scand. J. Stat. (forthcoming)
13. Hobson, D.G., Rogers, L.C.G.: Complete models with stochastic volatility. Math. Finance 8, 27-48 (1998)
14. Hull, J., White, A.: The pricing of options on assets with stochastic volatilities. J. Finance 42, 281-300 (1987)
15. Jeantheau, T.: Strong consistency of estimators for multivariate ARCH model. Econ. Theory 14, 70-86 (1998)
16. Kallsen, J., Taqqu, M. S.: Option pricing in ARCH type models. Math. Finance 8, 13-26 (1998)
17. Ling, S., McAleer, M.: Stationarity and the existence of moments of a family of GARCH processes. J. Econ. (forthcoming)
18. Meyn, S. P., Tweedie, R. L.: Markov chains and stochastic stability. Berlin Heidelberg New York: Springer 1993
19. Nelson, D.: Stationarity and persistence in the GARCH (1,1) model. Econ. Theory 6, 318-334 (1990a)
20. Nelson, D.: ARCH models as diffusion approximations. J. Econ. 45, 7-38 (1990b)
21. Pfanzagl, J.: On the measurability and consistency of minimum contrast estimates. Metrika 14, 249-272 (1969)
22. Scott, L. O.: Option pricing when the variance changes randomly: theory, estimation and an application. J. Financial Quant. Anal. 22, 419-438 (1987)
23. Talay, D.: Approximation of the invariant probability measure of stochastic Hamiltonian dissipative systems with non globally Lipschitz coefficients. Preprint INRIA, 2000
24. Tweedie, R.L.: Sufficient conditions for ergodicity and recurence of Markov chains on a general state space. Stochast. Proc. Their Applications 3, 385-403 (1975)
25. Tweedie, R. L.: Invariant measure for Markov chains with no irreducibility assumptions. J. Appl. Prob. 25A, 275-285 (1988)