Stochastic Volatility: Univariate and Multivariate Extensions
Discrete time stochastic volatility models (hereafter SVOL) are noticeably harder to estimate than the successful ARCH family of models. Recent advances in the literature now make it possible to produce efficient estimation and prediction for a basic univariate SVOL model. However, the basic model may be insufficient for numerous economics and finance applications. In this paper, we develop methods for finite sample inference, smoothing, and prediction for a number of univariate and multivariate SVOL models. Specifically, 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. We apply some of these extensions to financial series. We find (1) strong evidence of non-normal conditional distributions for stock returns and exchange rates, and (2) evidence of correlated errors for stock returns. These departures from the basic model affect the measured persistence and hence the prediction of volatility. This result as a policy implication on decisions and models such as asset allocation and option pricing which inputs are prediction of volatility. We specify the models as a hierarchy of conditional distributions: p(data | volatilities), p(volatilities | parameters) and p(parameters). Given a model and the data, inference and prediction are based on the joint posterior distribution of the volatilities and the parameters which we simulate via Markov chain Monte Carlo (hereafter MCMC) methods. This approach also provides a sensitivity analysis for parameter inference and an outlier diagnostic. The hierarchical framework is a natural environment for the construction of SVOL models departing from the standard distributional assumptions.
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- 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.
- Ghysels, E. & Harvey, A. & Renault, E., 1996.
Cahiers de recherche
9613, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
- 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, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
- 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.
- Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
- 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.
- 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.
- 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.
- 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.
- John F. Geweke & Guofu Zhou, 1995. "Measuring the pricing error of the arbitrage pricing theory," Staff Report 189, Federal Reserve Bank of Minneapolis.
- John F. Geweke, 1994. "Bayesian comparison of econometric models," Working Papers 532, Federal Reserve Bank of Minneapolis.
- John Geweke, 1992.
"Priors for macroeconomic time series and their application,"
Discussion Paper / Institute for Empirical Macroeconomics
64, Federal Reserve Bank of Minneapolis.
- Geweke, John, 1994. "Priors for Macroeconomic Time Series and Their Application," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 609-632, August.
- 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.
- Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
- 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.
- 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.
- Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265.
- repec:cup:etheor:v:10:y:1994:i:3-4:p:609-32 is not listed on IDEAS
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