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Uniform Ergodicity and Exponential α-Mixing for Continuous Time Stochastic Volatility Model
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 Title & Authors
Uniform Ergodicity and Exponential α-Mixing for Continuous Time Stochastic Volatility Model
Lee, O.;
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A continuous time stochastic volatility model for financial assets suggested by Barndorff-Nielsen and Shephard (2001) is considered, where the volatility process is modelled as an Ornstein-Uhlenbeck type process driven by a general Lvy process and the price process is then obtained by using an independent Brownian motion as the driving noise. The uniform ergodicity of the volatility process and exponential -mixing properties of the log price processes of given continuous time stochastic volatility models are obtained.
Continuous time stochastic volatility model;Ornstein-Uhlenbeck type process;stationarity;uniform ergodicity;-mixing;
 Cited by
Barndorff-Nielsen, O. and Shephard, N. (2001). Non-Gaussian Ornstein-Uhlenbeck based models and some of their uses in financial economics, Journal of Royal Statistical Society. B 63, 167–241. crossref(new window)

Doukhan, P. (1994). Mixing: Properties and Examples, Lecture note in Statistics 85, Springer-Verlag, New York.

Down, D., Meyn, S. P. and Tweedie, R. L. (1995). Exponential and uniform ergodicity of Markov processes, The Annals of Probability, 23, 1671–1691.

Fasen, V. (2009). Extremes of continuous time processes, In Anderson, T.G., Davis, R.A., Kreiss, J.P. and Mikosch, T.(Eds.) Handbook of Financial Time Series, Springer, 653–667.

Haug, S. and Czado, C. (2007). An exponential continuous time GARCH process, Journal of Applied Probability, 44, 960–976.

Haug, S., Kluppelberg, A., Lindner, A. and Zapp, M. (2007). Method of moment estimation in the COGARCH(1,1) model, The Econometrics Journal, 10, 320–341.

Kluppelberg, C., Lindner, A. and Maller, R. (2006). Continuous time volatility modelling: COGARCH versus Ornstein-Uhlenbeck Models. In Kabanov, Y. Lispter, R. and Stoyanov, J (Eds.) Stochastic Calculus to Mathematical Finance. The Shiryaev Fostschrift, Springer, Berlin, 393–419.

Kusuoka, S. and Yoshida, N. (2000). Malliavin calculus, geometric mixing, and expansion of diffusion functionals, Probability Theory and Related Fields, 116, 457–484. crossref(new window)

Masuda, H. (2004). On multidimensional Ornstein-Uhlenbeck processes driven by a general Levy process, Bernoulli, 10, 97–120.

Meyn, S. P. and Tweedie, R. L. (1993). Stability of Markovian processes III: Foster-Lyapunov criteria for continuous time processes, Advances in Applied Probability, 25, 518–548.

Nelson, D. B. (1990). ARCH models as diffusion approximations, Journal of Econometrics, 45, 7–38.

Protter, P. E. (2005). Stochastic Integration and Differential Equations, 2nd Ed. Springer.

Sato, K. (1999). Levy Processes and Infinitely Divisible Distributions, Cambridge University press, Cambridge.

Sato, K. and Yamazato, M. (1984). Operator-self-decomposable distributions as limit distributions of processes of Ornstein-Uhlenbeck type, Stochastic Processes and their Applications, 17, 73–100. crossref(new window)