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Asset Return Volatility and Correlation Measurement, Modeling and Forecasting General Issues Diebold, F.X. and Yilmaz, K. (2009), "Better to Give than to Receive: Predictive Directional Measurement of Volatility Spillovers," Manuscript, University of Pennsylvania. Using a generalized vector autoregressive framework in which forecast-error variance decompositions are invariant to variable ordering, we propose measures of both total and directional volatility spillovers. We use our methods to characterize daily volatility spillovers across U.S. stock, bond, foreign exchange and commodities markets, from January 1999 through October 2008. We show that despite significant volatility fluctuations in all markets during the sample, cross-market volatility spillovers were quite limited until the global financial crisis that began in 2007. As the crisis intensified, so too did volatility spillovers, with particularly important spillovers from the bond market to other markets. Diebold, F.X. and Yilmaz, K. (2010), "Equity Market Spillovers in the Americas," in R. Alfaro and D. Gray (eds.) Financial Satbility, Monetary Policy, and Central Banking. Santiago: Bank of Chile, in press. We provide an empirical analysis of return and volatility spillovers among five equity markets in the Americas: Argentina, Brazil, Chile, Mexico and the U.S. The results indicate that both return and volatility spillovers vary widely. Return spillovers, however, tend to evolve gradually, whereas volatility spillovers display clear bursts that often correspond closely to economic events.
Diebold, F.X. and Yilmaz, K. (2009), "Macroeconomic Volatility and Stock Market Volatility, Worldwide," in T. Bollerslev, J. Russell and M. Watson (eds.), Volatility and Time Series Econometrics: Essays in Honor of Robert F. Engle. Oxford: Oxford University Press, in press. We study a broad international cross section of stock markets, and we find a clear link between macroeconomic fundamentals and stock market volatilities, with volatile fundamentals translating into volatile stock markets. Diebold, F.X. and Yilmaz, K. (2009), "Measuring Financial Asset Return and Volatility Spillovers, With Application to Global Equity Markets," Economic Journal, 119, 158-171. We provide a simple and intuitive measure of interdependence of asset returns and/or volatilities. In particular, we formulate and examine precise and separate measures of return spillovers and volatility spillovers. Our framework facilitates study of both non-crisis and crisis episodes, including trends and bursts in spillovers, and both turn out to be empirically important. In particular, in an analysis of nineteen global equity markets from the early 1990s to the present, we find striking evidence of divergent behavior in the dynamics of return spillovers vs. volatility spillovers: Return spillovers display a gently increasing trend but no bursts, whereas volatility spillovers display no trend but clear bursts.
Andersen, T.G., Bollerslev, T. and Diebold, F.X. (2009), "Parametric and Nonparametric Volatility Measurement," in L.P. Hansen and Y. Ait-Sahalia (eds.), Handbook of Financial Econometrics. Amsterdam: North-Holland, in press. All the technical rigor you (or at least I) could ever want... Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and Diebold, F.X. (2006), "Practical Volatility and Correlation Modeling for Financial Market Risk Management," in M. Carey and R. Stulz (eds.), Risks of Financial Institutions, University of Chicago Press for NBER, 513-548. What academics have to offer market financial institution risk management practitioners. Improvements to current industry practice that are nevertheless parsimonious and easily estimated. Practical approaches to high-dimensional covariance matrix modeling, and pitfalls to avoid... Andersen, T.G., Bollerslev, T., Christoffersen, P.F., and Diebold, F.X. (2006), "Volatility and Correlation Forecasting," in G. Elliott, C.W.J. Granger, and A. Timmermann (eds.), Handbook of Economic Forecasting. Amsterdam: North-Holland, 778-878. We survey the most important theoretical developments and empirical insights to emerge from the burgeoning volatility and correlation literature, with a focus on forecasting applications in financial risk management, asset management, and asset pricing. Andersen, T.G., Bollerslev, T., Diebold, F.X. and Wu, J. (2005), “A Framework for Exploring the Macroeconomic Determinants of Systematic Risk,” American Economic Review, 95, 398-404. We selectively survey, unify and extend the literature on realized volatility of financial asset returns. Rather than focusing exclusively on characterizing the properties of realized volatility, we progress by examining economically interesting functions of realized volatility, namely realized betas for equity portfolios, relating them both to their underlying realized variance and covariance parts and to underlying macroeconomic fundamentals. Diebold, F.X. Hickman, A., Inoue, A. and Schuermann, T. (1998), "Converting 1-Day Volatility to h-Day Volatility: Scaling by Root-h is Worse than You Think," Wharton Financial Institutions Center, Working Paper 97-34. Published in condensed form as "Scale Models," Risk, 11, 104-107, 1998.
Realized Volatility Andersen, T.G., Bollerslev, T. and Diebold, F.X. (2009), "Parametric and Nonparametric Volatility Measurement," in L.P. Hansen and Y. Ait-Sahalia (eds.), Handbook of Financial Econometrics. Amsterdam: North-Holland, in press. All the technical rigor you (or at least I) could ever want... Diebold, F.X. and Strasser, G.H. (2008), "On the Correlation Structure of Microstructure Noise in Theory and Practice," Manuscript, Department of Economics, University of Pennsylvania. We bring some financial economics to bear on the financial econometrics of volatility estimation in the presence of market microstructure noise, using microstructure theory to derive the cross-correlation function between latent returns and market microstructure noise. The cross-correlation at zero displacement is typically negative, and cross-correlations at nonzero displacements are positive and decay geometrically. When market makers are very risk averse, the crosscorrelation pattern is inverted. The results may be useful for choosing among different market microstructure models and estimation of noise-robust measures of realized volatility. Diebold, F.X. (2006), "On Market Microstructure Noise and Realized Volatility," Journal of Business and Economic Statistics, 24, 181-183. Incorporating jumps, time-varying expected returns, and intrinsic market microstructure nonlinearities when correcting realized volatility for microstructure noise. The wide-ranging predictions of economic theory for the correlation between microstructure noise and latent price. Andersen, T.G., Bollerslev, T., Diebold, F.X. and Wu, J. (2006), "Realized Beta: Persistence and Predictability," in T. Fomby and D. Terrell (eds.) Advances in Econometrics: Econometric Analysis of Economic and Financial Time Series in Honor of R.F. Engle and C.W.J. Granger , Volume B, 1-40. (Appendix here.) We move beyond analysis of more statistical objects like realized variances and covariances to a key financial economic object: systematic risk as captured by realized beta. Realized betas turn out to be noticeably more stable than the underlying realized variance and covariances, due to nonlinear fractional cointegration between the realized variance and covariances. Andersen, T.G., Bollerslev, T. and Diebold, F.X. (2007), "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," Review of Economics and Statistics, 89, 701-720. Separating jump from non-jump movements in asset return volatility fluctuations. This is potentially of great value for volatility forecasting, because jump movements are likely very quickly mean reverting, whereas non-jump movements are not. Andersen, T., Bollerslev, T., Diebold, F.X. and Labys, P. (2003), "Modeling and Forecasting Realized Volatility," Econometrica, 71, 529-626. Andersen, T., Bollerslev, T., Diebold, F.X. and Ebens, H. (2001), "The Distribution of Realized Stock Return Volatility," Journal of Financial Economics, 61, 43-76. Andersen, T. Bollerslev, T., Diebold, F.X. and Labys, P. (2001), "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, 96, 42-55. Andersen, T., Bollerslev, T., Diebold, F.X. and Labys, P. (2000), "Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian," Multinational Finance Journal, 4, 159-179. Andersen, T., Bollerslev, T., Diebold, F.X. and Labys, P. (1999), "(Understanding, Optimizing, Using and Forecasting) Realized Volatility and Correlation," Manuscript, Northwestern University, Duke University and University of Pennsylvania. Published in revised form as "Great Realizations," Risk, March 2000, 105-108.
Range-Based Volatility Brandt, M.W. and Diebold, F.X. (2006),"A No-Arbitrage Approach to Range-Based Estimation of Return Covariances and Correlations," Journal of Business, 79, 61-74. We generalize the Alizadeh-Brandt-Diebold (2002) range-based approach to volatility to the multivariate case by exploiting no-arb conditions. Absence of triangular arbitrage in foreign exchange, for example, implies that dollar rate covariances may be expressed in terms of dollar rate volatilities and cross rate volatility, all of which may be estimated by the range, and then plugged in. Alizadeh, S., Brandt, M. and Diebold, F.X. (2002), "Range-Based Estimation of Stochastic Volatility Models," Journal of Finance, 57, 1047-1092.
GARCH-Based Volatility Diebold, F.X. (2003), "The ET Interview: Professor Robert F. Engle," Econometric Theory, 19, 1159-1193. Diebold,. F.X. and Nerlove, M. (1989), "The Dynamics of Exchange Rate Volatility: A Multivariate Latent-Factor ARCH Model,” Journal of Applied Econometrics, 4, 1-22. Diebod, F.X. (1988), Empirical Modeling of Exchange Rate Dynamics. New York: Springer-Verlag. (Lecture Notes in Economics and Mathematical Systems No. 303.) Diebold, F.X. (1986), "Modeling the Persistence of Conditional Variances: A comment," Econometric Reviews, 5, 51-56.
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