Estimating Correlated Jumps and Stochastic Volatilities
AbstractWe formulate a bivariate stochastic volatility jump-diffusion model with correlated jumps and volatilities. An MCMC Metropolis-Hastings sampling algorithm is proposed to estimate the model’s parameters and latent state variables (jumps and stochastic volatilities) given observed returns. The methodology is successfully tested on several artificially generated bivariate time series and then on the two most important Czech domestic financial market time series of the FX (CZK/EUR) and stock (PX index) returns. Four bivariate models with and without jumps and/or stochastic volatility are compared using the deviance information criterion (DIC) confirming importance of incorporation of jumps and stochastic volatility into the model.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies in its series Working Papers IES with number 2011/35.
Length: 31 pages
Date of creation: Nov 2011
Date of revision: Nov 2011
jump-diffusion; stochastic volatility; MCMC; Value at Risk; Monte Carlo;
Other versions of this item:
- Jiří Witzany, 2013. "Estimating Correlated Jumps and Stochastic Volatilities," Prague Economic Papers, University of Economics, Prague, vol. 2013(2), pages 251-283.
- C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
- G1 - Financial Economics - - General Financial Markets
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-11-28 (All new papers)
- NEP-ECM-2011-11-28 (Econometrics)
- NEP-ETS-2011-11-28 (Econometric Time Series)
- NEP-MST-2011-11-28 (Market Microstructure)
- NEP-ORE-2011-11-28 (Operations Research)
- NEP-RMG-2011-11-28 (Risk Management)
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.:
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994.
"Bayesian Analysis of Stochastic Volatility Models,"
Journal of Business & Economic Statistics,
American Statistical Association, vol. 12(4), pages 371-89, October.
- Tom Doan, . "RATS programs to replicate Jacquier, Polson, Rossi (1994) stochastic volatility," Statistical Software Components RTZ00105, Boston College Department of Economics.
- Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
- David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika van der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639.
- Jun Yu & Renate Meyer, 2004.
"Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison,"
23-2004, Singapore Management University, School of Economics.
- Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
- Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
- Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
- Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, 06.
- Jacquier, Eric & Johannes, Michael & Polson, Nicholas, 2007. "MCMC maximum likelihood for latent state models," Journal of Econometrics, Elsevier, vol. 137(2), pages 615-640, April.
- 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.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Lenka Herrmannova).
If references are entirely missing, you can add them using this form.