Markov chain Monte Carlo methods for stochastic volatility models

Journal of Econometrics

Volumn 108, Issue 2, 2002, Pages 281-316

  Chib, Siddhartha ^a   Nardari, Federico ^b   Shephard, Neil ^c  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^b ARIZONA STATE UNIVERSITY   (United States)

^c NUFFIELD COLLEGE   (United Kingdom)

Author keywords

Bayes factor; Marginal likelihood; Markov chain Monte Carlo; Mixture models; Particle filters; Simulation based inference; Stochastic volatility

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; DEGREES OF FREEDOM (MECHANICS); MATHEMATICAL MODELS; MONTE CARLO METHODS;

BAYES FACTOR; MARGINAL LIKELIHOOD; MIXTURE MODELS; PARTICLE FILTERS; SIMULATION BASED INFERENCE; STOCHASTIC VOLATILITY;

MARKOV PROCESSES;

EID: 0011716069     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4076(01)00137-3     Document Type: Article

References (55)

1. Albert J., Chib S. Bayes inference via Gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. Journal of Business and Economic Statistics. 11:1993;1-15.
2. Andersen T.G., Lund J. Estimating continuous-time stochastic volatility models of the short term interest rate. Journal of Econometrics. 77(2):1997;343-377.
3. Andersen, T.G., Benzoni, L., Lund, J., 2002. An empirical investigation of continuous-time equity return models. Journal of Finance, forthcoming.
4. Aguilar O., West M. Bayesian dynamic factor models and variance matrix discounting for portfolio allocation. Journal of Business and Economic Statistics. 18:2000;338-357.
5. Ball C., Torous W. On jumps in common stock prices and their impact on call option pricing. Journal of Finance. 40:1985;155-173.
6. Barndorff-Nielsen O.E., Shephard N. Non-Gaussian OU processes and some of their uses in financial economics (with discussion). Journal of the Royal Statistical Society, Series B. 63:2001;167-241.
7. Barndorff-Nielsen, O.E., Shephard, N., 2001b. Econometric analysis of realised volatility and its use in estimating stochastic volatility models, to appear. Journal of the Royal Statistical Society Series B, 64.
8. Barndorff-Nielsen, O.E., Shephard, N., 2002. Lévy based dynamic models for financial economics. Unpublished book manuscript.
9. Bates D.S. Jumps and stochastic volatility: exchange rate processes implicit in Deutsche mark options. The Review of Financial Studies. 9:1996;69-107.
10. Berzuini C., Best N.G., Gilks W.R., Larizza C. Dynamic conditional independence models and Markov chain Monte Carlo methods. Journal of the American Statistical Association. 92:1997;1403-1412.
11. Chernov, M., Gallant, A.R., Ghysels, E., Tauchen, G., 2000. A new class of stochastic volatility models with jumps. Theory and estimation. Working Paper, Columbia University.
12. Chib S. Marginal likelihood from the Gibbs output. Journal of the American Statistical Association. 90:1995;1313-1321.
13. Chib S. Calculating posterior distributions and modal estimates in markov mixture models. Journal of Econometrics. 75:1996;79-97.
14. Chib S., Greenberg E. Bayes inference for regression models with ARMA. (p,q) errors Journal of Econometrics. 64:1994;183-206.
15. Chib S., Greenberg E. Understanding the Metropolis-Hastings algorithm. American Statistician. 49:1995;327-335.
16. Chib S., Greenberg E. Markov chain Monte Carlo simulation methods in Econometrics. Econometric Theory. 12:1996;409-431.
17. Chib S., Jeliazkov I. Marginal likelihood from the Metropolis Hastings output. Journal of the American Statistical Association. 96:2001;270-281.
18. Chib, S., Nardari, F., Shephard, N., 1999. Analysis of high dimensional multivariate stochastic volatility models. Unpublished paper, John M. Olin School of Business, Washington University, St. Louis. Revised June 2001.
19. Danielsson J. Stochastic volatility in asset prices: estimation with simulated maximum likelihood. Journal of Econometrics. 61:1994;375-400.
20. de Jong P., Shephard N. The simulation smoother for time series models. Biometrika. 82:1995;339-350.
21. Diebold F.X., Gunther T., Tay A. Evaluating density forecasts, with applications to financial risk management. International Economic Review. 39:1997;863-883.
22. Doucet, A., deFreitas, N., Gordon, N., 2001. Sequential Monte Carlo Methods in Practice. Springer-Verlag, New York.
23. Duffie D., Pan J., Singleton K. Transform analysis and asset pricing for affine jump-diffusions. Econometrica. 68:2000;1343-1376.
24. Eberlein E. Application of generalized hyperbolic Lévy motion to finance. Barndorff-Nielsen O.E., Mikosch T., Resnick S. Lévy Processes - Theory and Applications. 2001;319-337 Birkhauser, Boston.
25. Eberlein, E., Prause, K., 2002. The generalized hyperbolic model: financial derivatives and risk measures. In: Mathematical Finance - Bachelier Congress 2000. Springer Verlag, forthcoming.
26. Eberlein, E., Kallsen, J., Kristen, J., 2001. Risk management based on stochastic volatility. FDM Preprint 72, University of Freiburg.
27. Elerian O., Chib S., Shephard N. Likelihood inference for discretely observed non-linear diffusions. Econometrica. 69:2001;959-994.
28. Eraker B. MCMC analysis of diffusion models with applications to finance. Journal of Business and Economic Statistics. 19:2001;177-191.
29. Eraker, B., Johannes, M., Polson, N., 2002. The impact of jumps in volatility and returns. Journal of Finance, forthcoming.
30. Gallant A.R., Tauchen G. Reprojection partially observed systems with applications to interest rate diffusions. Journal of the American Statistical Association. 93:1998;10-24.
31. Gallant, A.R., Hsu, C., Tauchen, G., 1998. Calibrating volatility diffusions and extracting integrated volatility. Unpublished paper, Duke University.
32. Gerlach R., Carter C.K., Kohn R. Diagnostics for time series analysis. Journal of Time Series Analysis. 21:1999;309-330.
33. Geweke J. Evaluating the accuracy of sampling-based approaches to the calculation of moments (with discussion). Bernardo J.M., Berger J.O., Dawid A.P., Smith A.F.M. Bayesian Statistics, Vol. 4. 1992;169-193 Oxford University Press, Oxford.
34. Ghysels E., Harvey A.C., Renault E. Stochastic volatility. Rao C.R., Maddala G.S. Statistical Methods in Finance. 1996;119-191 North-Holland, Amsterdam.
35. Gordon N.J., Salmond D.J., Smith A.F.M. A novel approach to non-linear and non-Gaussian Bayesian state estimation. IEE-Proceedings F. 140:1993;107-113.
36. Harvey A.C., Ruiz E., Shephard N. Multivariate stochastic variance models. Review of Economic Studies. 61:1994;247-264.
37. Isard, M., Blake, A., 1996. Contour tracking by stochastic propagation of conditional density. Proceedings of the European Conference on Computer Vision, Cambridge, Vol. 1, pp. 343-356.
38. Jacquier E., Polson N.G., Rossi P.E. Bayesian analysis of stochastic volatility models (with discussion). Journal of Business and Economic Statistics. 12:1994;371-417.
39. Jacquier, E., Polson, N.G., Rossi, P.E., 1999. Models and prior distributions for multivariate stochastic volatility. Draft paper, Chicago School of Business (first version circulated 1994).
40. Jeffreys, H., 1961. Theory of Probability, 3rd ed. Oxford, Clarendon Press.
41. Kim S., Shephard N., Chib S. Stochastic volatility: likelihood inference and comparison with ARCH models. Review of Economic Studies. 65:1998;361-393.
42. Kitagawa G. Monte Carlo filter and smoother for Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics. 5:1996;1-25.
43. Mahieu R., Schotman P. An empirical application of stochastic volatility models. Journal of Applied Econometrics. 16:1998;333-359.
44. Merton R.C. Option pricing when underlying stock returns are discontinuous. Journal of Financial Economics. 3:1976;125-144.
45. Nardari, F., 1999. Comparing stochastic volatility models of the short term interest rate: a Bayesian approach. Manuscript, Arizona State University, Tempe, AZ, USA.
46. Pitt M., Shephard N. Filtering via simulation: auxiliary particle filter. Journal of the American Statistical Association. 94:1999;590-599.
47. Pitt M., Shephard N. Time varying covariances: a factor stochastic volatility approach (with discussion). Bernardo J., Berger J.O., Dawid A.P., Smith A.F.M. Bayesian Statistics, Vol. 6. 1999;547-570 Oxford University Press, Oxford.
48. Prause, K., 1999. The generalised hyperbolic models: estimation, financial derivatives and risk measurement. Unpublished Ph.D. Thesis, Mathematics Faculty, Freiburg University.
49. Sandmann G., Koopman S.J. Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics. 87:1998;271-301.
50. Shephard N. Partial non-Gaussian state space. Biometrika. 81:1994;115-131.
51. Shephard N. Statistical aspects of ARCH and stochastic volatility. Cox D.R., Hinkley D.V., Barndorff-Nielson O.E. Time Series Models with Econometric, Finance and Other Applications. 1996;1-67 Chapman & Hall, London.
52. Shephard N. Discussion of Durbin and Koopman. (2000) Journal of the Royal Statistical Society, Series B. 62:2000;30-32.
53. So M.K.P., Lam K., Lee W.K. A stochastic volatility model with Markov switching. Journal of Business and Economic Statistics. 16:1998;244-253.
54. Taylor S.J. Modelling stochastic volatility. Mathematical Finance. 4:1994;183-204.
55. Wong, C.K., 2000. Estimation of latent factor models by simulation methods. Unpublished D. Phil. Thesis, Department of Economics, Oxford University.