Stochastic Volatility: Univariate and Multivariate Extensions
Discrete time stochastic volatility models (hereafter SVOL) are noticeably more difficult to estimate than the successful ARCH family of models. In this paper we demonstrate efficient estimation and prediction for a number of univariate and multivariate SVOL models. Namely, we model fat-tailed and skewed conditional distributions, correlated errors distributions (leverage effect), and two multivariate models, a stochastic factor-structure model and a stochastic discount dynamic model. These extensions to the basic model are needed if one wants, for example, to compare SVOL models with ARCH-style models or to implement option pricing and portfolio selection under stochastic volatility. We specify the models as a hierarchy of conditional probability distributions: Pr(data | volatilities), Pr(volatilities | parameters) and Pr(parameters). This conceptually simple methodology provides a natural environment for the construction of stochastic volatility models that depart from standard distributional assumptions. Given a model and the data, inference and prediction are based on the joint posterior distribution of the volatilities and the parameters that we simulate via Markov chain Monte Carlo (MCMC) methods. Our approach also provides a sensitivity analysis for parameter inference and an outlier diagnostic. We estimate the model for several financial time series and find that the extensions considered are indeed needed. For the SVOL model we find strong evidence of non-normal conditional distributions for stock returns and exchange rates. We also find evidence of correlated errors for stock returns.
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|Date of creation:||01 Mar 1999|
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- 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.
- Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005.
CFS Working Paper Series
2005/08, Center for Financial Studies (CFS).
- Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," NBER Working Papers 11188, National Bureau of Economic Research, Inc.
- Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993.
"On the relation between the expected value and the volatility of the nominal excess return on stocks,"
157, Federal Reserve Bank of Minneapolis.
- Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
- Friedman, Moshe & Harris, Lawrence, 1998. "A Maximum Likelihood Approach for Non-Gaussian Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 284-91, July.
- Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De.
- 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.
- Geweke, John, 1994.
"Priors for Macroeconomic Time Series and Their Application,"
Cambridge University Press, vol. 10(3-4), pages 609-632, August.
- John Geweke, 1992. "Priors for macroeconomic time series and their application," Discussion Paper / Institute for Empirical Macroeconomics 64, Federal Reserve Bank of Minneapolis.
- John Geweke & Guofu Zhou, 1995.
"Measuring the pricing error of the arbitrage pricing theory,"
189, Federal Reserve Bank of Minneapolis.
- Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-87.
- John Geweke & Guofu Zhou, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," CEMA Working Papers 276, China Economics and Management Academy, Central University of Finance and Economics.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996.
"Stochastic Volatility: Likelihood Inference And Comparison With Arch Models,"
- 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.
- 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.
- Sangjoon Kim & Neil Shephard, 1994. "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers 3., Economics Group, Nuffield College, University of Oxford.
- Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994.
"Multivariate Stochastic Variance Models,"
Review of Economic Studies,
Wiley Blackwell, vol. 61(2), pages 247-64, April.
- Tom Doan, . "RATS programs to estimate multivariate stochastic volatility models," Statistical Software Components RTZ00093, Boston College Department of Economics.
- Ghysels, E. & Harvey, A. & Renault, E., 1995.
95.400, Toulouse - GREMAQ.
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- 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).
- Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
- repec:cup:etheor:v:10:y:1994:i:3-4:p:609-32 is not listed on IDEAS
- John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
- Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
- Ronald Mahieu & Peter Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
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