Stochastic volatility with leverage: Fast and efficient likelihood inference

Journal of Econometrics

Volumn 140, Issue 2, 2007, Pages 425-449

  Omori, Yasuhiro ^a   Chib, Siddhartha ^b   Shephard, Neil ^c   Nakajima, Jouchi ^a  

^a UNIVERSITY OF TOKYO   (Japan)

^b WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^c NUFFIELD COLLEGE   (United Kingdom)

Author keywords

Leverage effect; Markov chain Monte Carlo; Mixture sampler; Stochastic volatility; Stock returns

Indexed keywords

APPROXIMATION THEORY; ERROR ANALYSIS; MARKOV PROCESSES; MATHEMATICAL MODELS; MONTE CARLO METHODS;

LEVERAGE EFFECT; MARKOV CHAIN MONTE CARLO; MIXTURE SAMPLERS; STOCHASTIC VOLATILITY; STOCK RETURNS;

BAYESIAN NETWORKS;

EID: 34547697278     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2006.07.008     Document Type: Article

References (47)

1. Barndorff-Nielsen O.E., and Shephard N. Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics (with discussion). Journal of the Royal Statistical Society, Series B 63 (2001) 167-241
2. Barndorff-Nielsen O.E., and Shephard N. Impact of jumps on returns and realised variances: econometric analysis of time-deformed Lévy processes. Journal of Econometrics 131 (2006) 217-252
3. Black, F., 1976. Studies of stock price volatility changes. Proceedings of the Business and Economic Statistics Section, American Statistical Association, pp. 177-181.
4. Carr P., and Wu L. Time-changed Lévy processes and option pricing. Journal of Financial Economics 71 (2004) 113-141
5. Carr P., Geman H., Madan D.B., and Yor M. Stochastic volatility for Lévy processes. Mathematical Finance 13 (2003) 345-382
6. Carter C.K., and Kohn R. On Gibbs sampling for state space models. Biometrika 81 (1994) 541-553
7. Chernov M., Gallant A.R., Ghysels E., and Tauchen G. Alternative models of stock price dynamics. Journal of Econometrics 116 (2003) 225-257
8. Chib S. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association 90 (1995) 1313-1321
9. Chib S. Markov chain Monte Carlo methods: computation and inference. In: Heckman J.J., and Leamer E. (Eds). Handbook of Econometrics vol. 5 (2001), North-Holland, Amsterdam 3569-3649
10. Chib S., and Greenberg E. Bayes inference for regression models with ARMA (p, q) errors. Journal of Econometrics 64 (1994) 183-206
11. Chib S., and Greenberg E. Understanding the Metropolis-Hastings algorithm. The American Statistician 49 (1995) 327-335
12. Chib S., and Jeliazkov I. Marginal likelihood from the Metropolis-Hastings output. Journal of the American Statistical Association 96 (2001) 270-281
13. Chib S., Nardari F., and Shephard N. Markov chain Monte Carlo methods for generalized stochastic volatility models. Journal of Econometrics 108 (2002) 281-316
14. Cont R., and Tankov P. Financial Modelling with Jump Processes (2004), Chapman & Hall, London
15. de Jong P., and Shephard N. The simulation smoother for time series models. Biometrika 82 (1995) 339-350
16. Diebold F.X., Gunther T.A., and Tay T.S. Evaluating density forecasts with applications to financial risk management. International Economic Review 39 (1998) 863-883
17. Doornik J.A. Ox: Object Oriented Matrix Programming, 3.0 (2001), Timberlake Consultants Press, London
18. Doucet, A., de Freitas, N., Gordon, N.J. (Eds.), 2001. Sequential Monte Carlo Methods in Practice. Springer, New York.
19. Durbin J., and Koopman S.J. Time Series Analysis by State Space Methods (2001), Oxford University Press, Oxford
20. Durbin J., and Koopman S.J. A simple and efficient simulation smoother for state space time series analysis. Biometrika 89 (2002) 603-616
21. Elerian O., Chib S., and Shephard N. Likelihood inference for discretely observed non-linear diffusions. Econometrica 69 (2001) 959-993
22. Engle R.F., and Lee G.G.J. A permanent and transitory component model of stock return volatility. In: Engle R.F., and White H. (Eds). Cointegration, Causality, and Forecasting. A Festschrift in Honour of Clive W.J. Granger (1999), Oxford University Press, Oxford 475-497
23. Eraker B. Markov chain Monte Carlo analysis of diffusion models with application to finance. Journal of Business and Economic Statistics 19 (2001) 177-191
24. Frühwirth-Schnatter S. Data augmentation and dynamic linear models. Journal of Time Series Analysis 15 (1994) 183-202
25. Geweke, J., 1992. Efficient simulation from the multivariate normal and student-t distributions subject to linear constraints. Computing Science and Statistics: Proceedings of the 23rd Symposium, pp. 571-578.
26. Ghysels E., Harvey A.C., and Renault E. Stochastic volatility. In: Rao C.R., and Maddala G.S. (Eds). Statistical Methods in Finance (1996), North-Holland, Amsterdam 119-191
27. Harvey A.C. Forecasting, Structural Time Series Models and the Kalman Filter (1989), Cambridge University Press, Cambridge
28. Harvey A.C., and Shephard N. The estimation of an asymmetric stochastic volatility model for asset returns. Journal of Business and Economic Statistics 14 (1996) 429-434
29. Harvey A.C., Ruiz E., and Shephard N. Multivariate stochastic variance models. Review of Economic Studies 61 (1994) 247-264
30. Jacquier E., Polson N.G., and Rossi P.E. Stochastic volatility models: univariate and multivariate extensions. Journal of Econometrics 122 (2004) 185-212
31. Kim S., Shephard N., and Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies 65 (1998) 361-393
32. Koopman S.J., Shephard N., and Doornik J.A. Statistical algorithms for models in state space using SsfPack 2.2. The Econometrics Journal 2 (1999) 107-166
33. Li, H., Wells, M., Yu, L., 2004. A MCMC analysis of time-changed Lévy processes of stock returns, unpublished paper. Johnson Graduate School of Management, Cornell University, Ithaca, U.S.A.
34. Mahieu R., and Schotman P. An empirical application of stochastic volatility models. Journal of Applied Econometrics 16 (1998) 333-359
35. Nelson, D.B., 1988. The time series behaviour of stock market volatility and returns, Unpublished Ph.D., MIT, Cambridge, MA.
36. Nelson D.B. Conditional heteroskedasticity in asset pricing: a new approach. Econometrica 59 (1991) 347-370
37. Pitt M.K., and Shephard N. Filtering via simulation: auxiliary particle filter. Journal of the American Statistical Association 94 (1999) 590-599
38. Primiceri G. Time varying structural vector autoregressions and monetary policy. Review of Economic Studies 72 (2005) 821-852
39. Roberts G.O., and Stramer O. On inference for nonlinear diffusion models using the Hastings-Metropolis algorithms. Biometrika 88 (2001) 603-621
40. Rosenblatt M. Remarks on a multivariate transformation. Annals of Mathematical Statistics 23 (1952) 470-472
41. Shephard N. Partial non-Gaussian state space. Biometrika 81 (1994) 115-131
42. Shephard N. Statistical aspects of ARCH and stochastic volatility. In: Cox D.R., Hinkley D.V., and Barndorff-Nielsen O.E. (Eds). Time Series Models in Econometrics, Finance and Other Fields (1996), Chapman & Hall, London 1-67
43. Shephard N. Stochastic Volatility: Selected Readings (2005), Oxford University Press, Oxford
44. Smith J.Q. Diagnostic checks of non-standard time series models. Journal of Forecasting 4 (1985) 283-291
45. Stroud J.R., Muller P., and Polson N.G. Nonlinear state-space models with state-dependent variances. Journal of the American Statistical Association 98 (2003) 377-386
46. West M., and Harrison J. Bayesian Forecasting and Dynamic Models. second ed. (1997), Springer, New York
47. Yu J. On leverage in a stochastic volatility model. Journal of Econometrics 127 (2005) 165-178