nach oben

Review of Quantitative Finance and Accounting

Erschienen in:

01.11.2009 | Original Research

Forecasting time-varying covariance with a range-based dynamic conditional correlation model

Erschienen in: Review of Quantitative Finance and Accounting | Ausgabe 4/2009

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

This paper proposes a range-based dynamic conditional correlation (DCC) model combined by the return-based DCC model and the conditional autoregressive range (CARR) model. The substantial gain in efficiency of volatility estimation can boost the accuracy for estimating time-varying covariances. As to the empirical study, we use the S&P 500 stock index and the 10-year treasury bond futures to examine both in-sample and out-of-sample results for six models, including MA100, EWMA_, CCC_, BEKK, return-based DCC, and range-based DCC. Of all the models considered, the range-based DCC model is largely supported in estimating and forecasting the covariance matrices.

Vorheriger Artikel Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter

Nächster Artikel Effects of takeover protection on earnings overstatements: evidence from restating firms

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

The k-dimensional VECH model is written as \( {\text{vech}}\left({H_{t}} \right) = A + B\,{\text{vech}}\left({\xi_{t - 1} \xi_{t - 1}^{'}} \right) + C\,{\text{vech}}\left({H_{t - 1}} \right) \), where H _t is the conditional covariance matrix at time t and vech(H _t) is the vector that stacks all the elements of the covariance matrix.

It is a general parameterization that involves the minimum number of parameters while imposing no cross equation restrictions and ensuring positive definiteness for any parameter value.

Other econometric methods for estimating the time-varying correlation are proposed by Tsay (2002) and by Tse and Tsui (2002).

Shu and Zhang (2006) provide relative performance of different range-based volatility estimators, and find that the range estimators all perform very well when an asset price follows a continuous geometric Brownian motion.

Fernandes et al. (2005) utilize the formula Cov(X,Y) = [V(X + Y) − V(X) − V(Y)]/2 to propose a kind of multivariate CARR model. However, this method limits the multivariate CARR model to a bivariate case only.

The MEM model is designed to fit a non-negative series, like duration or realized volatility.

The RiskMetrics database uses the exponentially-weighted moving average model with λ = 0.94 for updating daily volatility estimates. J.P. Morgan found that, across variant market variables, this value of λ results in forecasts of the volatility that come closest to the realized volatility. Following J.P. Morgan’s suggestion, the variable λ equals 0.94 for the time being in the later empirical discussion.

The estimate of λ is 0.94 approximately for the returns that we adopted in this study.

It is also intuitively clear that the out-of-sample forecasts for the covariance are all constant in the EWMA model.

The coffee data is obtained from Datastream.

Naïve here is the short hedge with selling one unit futures.

Alizadeh S, Brandt M, Diebold F (2002) Range-based estimation of stochastic volatility models. J Finance 57(3):1047–1091. doi:10.1111/1540-6261.00454 CrossRef

Andersen T, Bollerslev T, Diebold F, Ebens H (2001) The distribution of realized stock return volatility. J Financ Econ 61(1):43–76. doi:10.1016/S0304-405X(01)00055-1 CrossRef

Bollerslev T (1990) Modeling the coherence in short-run nominal exchange rates: a multivariate generalized ARCH model. Rev Econ Stat 72(3):498–505. doi:10.2307/2109358 CrossRef

Bollerslev T, Engle R, Wooldridge JM (1988) A capital asset pricing model with time varying covariances. J Polit Econ 96(1):116–131. doi:10.1086/261527 CrossRef

Bollerslev T, Chou RY, Kroner K (1992) ARCH modeling in finance: a review of the theory and empirical evidence. J Econom 52(1–2):5–59. doi:10.1016/0304-4076(92)90064-X CrossRef

Brandt M, Jones C (2006) Volatility forecasting with range-based EGARCH models. J Bus Econ Stat 24(4):470–486. doi:10.1198/073500106000000206 CrossRef

Cappiello L, Engle R, Sheppard K (2006) Asymmetric dynamics in the correlations of global equity and bond returns. J Financ Econometrics 4(4):537–572. doi:10.1093/jjfinec/nbl005 CrossRef

Chou RY (2005) Forecasting financial volatilities with extreme values: the conditional autoregressive range (CARR) model. J Money Credit Bank 37(3):561–582. doi:10.1353/mcb.2005.0027 CrossRef

Chou RY (2006) Modeling the asymmetry of stock movements using price ranges. Adv Econometrics 20(Part A):231–258CrossRef

Engle R (2002a) Dynamic conditional correlation: a simple class of multivariate GARCH models. J Bus Econ Stat 20(3):339–350. doi:10.1198/073500102288618487 CrossRef

Engle R (2002b) New frontiers for ARCH models. J Appl Econ 17(5):425–446. doi:10.1002/jae.683 CrossRef

Engle R (2004) Risk and volatility: econometric models and financial practice. Am Econ Rev 94(3):405–420. doi:10.1257/0002828041464597 CrossRef

Engle R, Kroner K (1995) Multivariate simultaneous GARCH. Econometric Theory 11(1):122–150CrossRef

Engle R, Manganelli S (2004) CAViaR: conditional autoregressive value at risk by regression quantiles. J Bus Econ Stat 22(4):367–381. doi:10.1198/073500104000000370 CrossRef

Engle R, Sheppard K (2001) ‘Theoretical and empirical properties of dynamic conditional correlation multivariate GARCH’, Working Paper. University of California, San Diego

Ferland R, Lalancette S (2006) Dynamics of realized volatilities and correlations: an empirical study. J Bank Finance 30(7):2109–2130. doi:10.1016/j.jbankfin.2005.05.020 CrossRef

Fernades M, Mota B, Rocha G (2005) A multivariate conditional autoregressive range model. Econ Lett 86(3):435–440. doi:10.1016/j.econlet.2004.09.005 CrossRef

French KR, Schwert GW, Stambaugh RF (1987) Expected stock returns and volatility. J Financ Econ 19(1):3–29. doi:10.1016/0304-405X(87)90026-2 CrossRef

Gallant R, Hsu C, Tauchen G (1999) Using daily range data to calibrate volatility diffusions and extracting integrated volatility. Rev Econ Stat 81(4):617–631. doi:10.1162/003465399558481 CrossRef

Garman M, Klass M (1980) On the estimation of security price volatilities from historical data. J Bus 53(1):67–78. doi:10.1086/296072 CrossRef

Hafner CM, Franses PH (2003) A generalized dynamic conditional correlation model for many asset returns, Working Paper. Erasmus University Rotterdam

Kunitomo N (1992) Improving the Parkinson method of estimating security price volatilities. J Bus 65(2):295–302. doi:10.1086/296570 CrossRef

Martens M, van Dijk D (2007) Measuring volatility with the realized range. J Econom 138(1):181–207. doi:10.1016/j.jeconom.2006.05.019 CrossRef

Parkinson M (1980) The extreme value method for estimating the variance of the rate of return. J Bus 53(1):61–65. doi:10.1086/296071 CrossRef

Rogers LCG, Satchell SE (1991) Estimating variance from high, low and closing prices. Ann Appl Probab 1(4):504–512. doi:10.1214/aoap/1177005835 CrossRef

Shu JH, Zhang JE (2006) Testing range estimators of historical volatility. J Futures Mark 26(3):297–313. doi:10.1002/fut.20197 CrossRef

Taylor N (2004) Trading intensity, volatility, and arbitrage activity. J Bank Finance 28(5):1137–1162. doi:10.1016/S0378-4266(03)00116-X CrossRef

Tsay RS (2002) Analysis of financial time series. Wiley, New YorkCrossRef

Tse YK, Tsui AKC (2002) A multivariate GARCH model with time-varying correlations. J Bus Econ Stat 20(3):351–362. doi:10.1198/073500102288618496 CrossRef

White H (1994) Estimation, inference and specification analysis. Cambridge University Press, Cambridge

Wiggins J (1991) Empirical tests of the bias and efficiency of the extreme-value variance estimator for common stocks. J Bus 64(3):417–432. doi:10.1086/296544 CrossRef

Yang D, Zhang Q (2000) Drift independent volatility estimation based on high, low, open, and close prices. J Bus 73(3):477–491. doi:10.1086/209650 CrossRef

Titel: Forecasting time-varying covariance with a range-based dynamic conditional correlation model
Publikationsdatum: 01.11.2009
Erschienen in: Review of Quantitative Finance and Accounting / Ausgabe 4/2009
Print ISSN: 0924-865X
Elektronische ISSN: 1573-7179
DOI: https://doi.org/10.1007/s11156-009-0113-3

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 4/2009

Effects of takeover protection on earnings overstatements: evidence from restating firms

The effect of earnings quality and country-level institutions on the value relevance of earnings

Oil prices and transport sector returns: an international analysis

Estimating continuous-time stochastic volatility models of the short-term interest rate: a comparison of the generalized method of moments and the Kalman filter