Volatility, Jumps and Predictability of Returns: a Sequential Analysis
In this article we propose a Monte Carlo algorithm for sequential parameter learning for a stochastic volatility model with leverage, nonconstant conditional mean and jumps. We are interested in estimating the time invariant parameters and the nonobservable dynamics involved in the model. Our simple but effective idea relies on the auxiliary particle filter algorithm mixed together with the Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm. A numerical comparison with a full MCMC procedure is also provided. We also extend our methodology to superposition models in which volatility is obtained by a linear combination of independent processes.
(This abstract was borrowed from another version of this item.)
|Date of creation:||May 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: +39 051 209 8019 and 2600
Fax: +39 051 209 8040 and 2664
Web page: http://www.dse.unibo.it
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ghysels, E. & Harvey, A. & Renault, E., 1996.
Cahiers de recherche
9613, Universite de Montreal, Departement de sciences economiques.
- Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
- Eric Ghysels & Andrew Harvey & Éric Renault, 1995. "Stochastic Volatility," CIRANO Working Papers 95s-49, CIRANO.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003.
"Alternative models for stock price dynamics,"
Journal of Econometrics,
Elsevier, vol. 116(1-2), pages 225-257.
- Chernov, Mikhail & Gallant, A. Ronald & Ghysels, Eric & Tauchen, George, 2002. "Alternative Models for Stock Price Dynamic," Working Papers 02-03, Duke University, Department of Economics.
- Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
- Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
- Merton, Robert C., 1971.
"Optimum consumption and portfolio rules in a continuous-time model,"
Journal of Economic Theory,
Elsevier, vol. 3(4), pages 373-413, December.
- R. C. Merton, 1970. "Optimum Consumption and Portfolio Rules in a Continuous-time Model," Working papers 58, Massachusetts Institute of Technology (MIT), Department of Economics.
- Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
- Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998.
"Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 65(3), pages 361-93, July.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Tom Doan, . "KSCPOSTDRAW: RATS procedure to draw from posterior density needed in stochastic volatility model," Statistical Software Components RTS00101, Boston College Department of Economics.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
- Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 20(1), pages 69-87, January.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997.
"Empirical Performance of Alternative Option Pricing Models,"
Yale School of Management Working Papers
ysm65, Yale School of Management.
- Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
- Charles Quanwei Cao & Gurdip S. Bakshi & Zhiwu Chen, 1997. "Empirical Performance of Alternative Option Pricing Models," Yale School of Management Working Papers ysm54, Yale School of Management.
- Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, vol. 70(1), pages 223-262, January.
- Liu, Jun & Longstaff, Francis & Pan, Jun, 2001.
"Dynamic Asset Allocation with Event Risk,"
University of California at Los Angeles, Anderson Graduate School of Management
qt9fm6t5nb, Anderson Graduate School of Management, UCLA.
- Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
- Davide Raggi, 2005. "Adaptive MCMC methods for inference on affine stochastic volatility models with jumps," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 235-250, 07.
- Siem Jan Koopman & Eugenie Hol Uspensky, 2002. "The stochastic volatility in mean model: empirical evidence from international stock markets," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(6), pages 667-689.
- Gallant, A. Ronald & Tauchen, George, 1996.
"Which Moments to Match?,"
Cambridge University Press, vol. 12(04), pages 657-681, October.
- Brandt, Michael W. & Santa-Clara, Pedro, 2002. "Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets," Journal of Financial Economics, Elsevier, vol. 63(2), pages 161-210, February.
- Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
When requesting a correction, please mention this item's handle: RePEc:bol:bodewp:636. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Luca Miselli)
If references are entirely missing, you can add them using this form.