Browsing by Author "Bollerslev, T"

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    A Framework for Exploring the Macroeconomic Determinants of Systematic Risk
    (2005) Andersen, TG; Bollerslev, T; Diebold, FX; Wu, J; Brandt, M
    The increasing availability of high-frequency asset return data has had a fundamental impact on empirical financial economics, focusing attention on asset return volatility and correlation dynamics, with key applications in portfolio and risk management. So-called "realized" volatilities and correlations have featured prominently in the recent literature, and numerous studies have provided direct characterizations of the unconditional and conditional distributions of realized volatilities and correlations across different assets, asset classes, countries, and sample periods. For overviews see Andersen et al. (2005a, b). In this paper we selectively survey, unify and extend that literature. Rather than focusing exclusively on characterization of 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.
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    A multivariate generalized ARCH approach to modeling risk premia in forward foreign exchange rate markets
    (Journal of International Money and Finance, 1990-01-01) Baillie, RT; Bollerslev, T
    Assuming that daily spot exchange rates follow a martingale process, we derive the implied time series process for the vector of 30-day forward rate forecast errors from using weekly data. The conditional second moment matrix of this vector is modelled as a multivariate generalized ARCH process. The estimated model is used to test the hypothesis that the risk premium is a linear function of the conditional variances and covariances as suggested by the standard asset pricing theory literature. Little supportt is found for this theory; instead lagged changes in the forward rate appear to be correlated with the 'risk premium.'. © 1990.
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    Bid-ask spreads and volatility in the foreign exchange market. An empirical analysis
    (Journal of International Economics, 1994-01-01) Bollerslev, T; Melvin, M
    Consistent with the implications from a simple asymmetric information model for the bid-ask spread, we present empirical evidence that the size of the bid-ask spread in the foreign exchange market is positively related to the underlying exchange rate uncertainty. The estimation results are based on an ordered probit analysis that captures the discreteness in the spread distribution, with the uncertainty of the spot exchange rate being quantified through a GARCH type model. The data sets consists of more than 300,000 continuously recorded Deutschemark/dollar quotes over the period from April 1989 to June 1989. © 1994.
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    Correcting the errors: Volatility forecast evaluation using high-frequency data and realized volatilities
    (Econometrica, 2005-01-01) Andersen, TG; Bollerslev, T; Meddahi, N
    We develop general model-free adjustment procedures for the calculation of unbiased volatility loss functions based on practically feasible realized volatility benchmarks. The procedures, which exploit recent nonparametric asymptotic distributional results, are both easy-to-implement and highly accurate in empirically realistic situations. We also illustrate that properly accounting for the measurement errors in the volatility forecast evaluations reported in the existing literature can result in markedly higher estimates for the true degree of return volatility predictability.
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    Daily House Price Indexes: Construction, Modeling, and Longer-Run Predictions
    (Economic Research Initiatives at Duke (ERID), 2013-06-11) Bollerslev, T; Patton, AJ; Wang, W
    We construct daily house price indexes for ten major U.S. metropolitan areas. Our calculations are based on a comprehensive database of several million residential property transactions and a standard repeat-sales method that closely mimics the procedure used in the construction of the popular monthly Case-Shiller house price indexes. Our new daily house price indexes exhibit similar characteristics to other daily asset prices, with mild autocorrelation and strong conditional heteroskedasticity, which are well described by a relatively simple multivariate GARCH type model. The sample and model-implied correlations across house price index returns are low at the daily frequency, but rise monotonically with the return horizon, and are all commensurate with existing empirical evidence for the existing monthly and quarterly house price series. A simple model of daily house price index returns produces forecasts of monthly house price changes that are superior to various alternative forecast procedures based on lower frequency data, underscoring the informational advantages of our new more finely sampled daily price series.
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    Equity trading volume and volatility: Latent information arrivals and common long-run dependencies
    (Journal of Business and Economic Statistics, 1999-01-01) Bollerslev, T; Jubinski, D
    This article examines the behavior of equity trading volume and volatility for the individual firms composing the Standard and Poor's 100 composite index. Using multivariate spectral methods, we find that fractionally integrated processes best describe the long-run temporal dependencies in both series. Consistent with a stylized mixture-of-distributions hypothesis model in which the aggregate “news”-arrival process possesses long-memory characteristics, the long-run hyperbolic decay rates appear to be common across each volume-volatility pair. © 1999 Taylor & Francis Group, LLC.
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    Estimating stochastic volatility diffusion using conditional moments of integrated volatility
    (Journal of Econometrics, 2002-07-01) Bollerslev, T; Zhou, H
    We exploit the distributional information contained in high-frequency intraday data in constructing a simple conditional moment estimator for stochastic volatility diffusions. The estimator is based on the analytical solutions of the first two conditional moments for the latent integrated volatility, the realization of which is effectively approximated by the sum of the squared high-frequency increments of the process. Our simulation evidence indicates that the resulting GMM estimator is highly reliable and accurate. Our empirical implementation based on high-frequency five-minute foreign exchange returns suggests the presence of multiple latent stochastic volatility factors and possible jumps. © 2002 Elsevier Science B.V. All rights reserved.
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    From zero to hero: Realized partial (co)variances
    (Journal of Econometrics, 2021-01-01) Bollerslev, T; Medeiros, MC; Patton, AJ; Quaedvlieg, R
    This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen et al. (2010) and Bollerslev et al. (2020a) to allow for a finer decomposition of realized (co)variances. The new “realized partial (co)variances” allow for multiple thresholds with various locations, rather than the single fixed threshold of zero used in semi (co)variances. We adopt methods from machine learning to choose the thresholds to maximize the out-of-sample forecast performance of time series models based on realized partial (co)variances. We find that in low dimensional settings it is hard, but not impossible, to improve upon the simple fixed threshold of zero. In large dimensions, however, the zero threshold embedded in realized semi covariances emerges as a robust choice.
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    Long-term equity anticipation securities and stock market volatility dynamics
    (Journal of Econometrics, 1999-09-01) Bollerslev, T; Mikkelsen, HO
    Recent empirical findings suggest that the long-run dependence in U.S. stock market volatility is best described by a slowly mean-reverting fractionally integrated process. The present study complements this existing time-series-based evidence by comparing the risk-neutralized option pricing distributions from various ARCH-type formulations. Utilizing a panel data set consisting of newly created exchange traded long-term equity anticipation securities, or leaps, on the Standard and Poor's 500 stock market index with maturity times ranging up to three years, we find that the degree of mean reversion in the volatility process implicit in these prices is best described by a Fractionally Integrated EGARCH (FIEGARCH) model. © 1999 Elsevier Science S.A. All rights reserved.
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    "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange"
    (2003) Andersen, TG; Bollerslev, T; Diebold, FX; Vega, C
    Using a new dataset consisting of six years of real-time exchange rate quotations, macroeconomic expectations, and macroeconomic realizations (announcements), we characterize the conditional means of U.S. dollar spot exchange rates versus German Mark, British Pound, Japanese Yen, Swiss Franc, and the Euro. In particular, we find that announcement surprises (that is, divergences between expectations and realizations, or “news”) produce conditional mean jumps; hence high-frequency exchange rate dynamics are linked to fundamentals. The details of the linkage are intriguing and include announcement timing and sign effects. The sign effect refers to the fact that the market reacts to news in an asymmetric fashion: bad news has greater impact than good news, which we relate to recent theoretical work on information processing and price discovery.
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    "Modeling and Forecasting Realized Volatility"
    (2003) Andersen, TG; Bollerslev, T; Diebold, FX; Labys, P
    We provide a general framework for integration of high-frequency intraday data into the measurement, modeling, and forecasting of daily and lower frequency return volatilities and return distributions. Most procedures for modeling and forecasting financial asset return volatilities, correlations, and distributions rely on potentially restrictive and complicated parametric multivariate ARCH or stochastic volatility models. Use of realized volatility constructed from high-frequency intraday returns, in contrast, permits the use of traditional time-series methods for modeling and forecasting. Building on the theory of continuous-time arbitrage-free price processes and the theory of quadratic variation, we develop formal links between realized volatility and the conditional covariance matrix. Next, using continuously recorded observations for the Deutschemark / Dollar and Yen / Dollar spot exchange rates covering more than a decade, we find that forecasts from a simple long-memory Gaussian vector autoregression for the logarithmic daily realized volatilities perform admirably compared to a variety of popular daily ARCH and more complicated high-frequency models. Moreover, the vector autoregressive volatility forecast, coupled with a parametric lognormal-normal mixture distribution implied by the theoretically and empirically grounded assumption of normally distributed standardized returns, produces well-calibrated density forecasts of future returns, and correspondingly accurate quantile predictions. Our results hold promise for practical modeling and forecasting of the large covariance matrices relevant in asset pricing, asset allocation and financial risk management applications.
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    Multivariate Leverage Effects and Realized Semicovariance GARCH Models
    (2018-04-16) Bollerslev, T; Patton, AJ; Quaedvlieg, R
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    Periodic Autoregressive Conditional Heteroskedasticity
    (1996) Bollerslev, T; Ghysels, E
    Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P-ARCH, models is directly related to the class of periodic autoregressive moving average (ARMA) models for the mean. The implicit relation between periodic generalized ARCH (P-GARCH) structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in forecast efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. Two empirical examples with daily bilateral Deutschemark/British pound and intraday Deutschemark/U.S. dollar spot exchange rates highlight the practical relevance of the new P-GARCH class of models. Extensions to discrete-time periodic representations of stochastic volatility models subject to time deformation are briefly discussed.
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    Realized Semi(Co)Variation: Signs that All Volatilities are Not Created Equal
    (Economic Research Initiatives at Duke (ERID) Working Paper, 2021-06-17) Bollerslev, T
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    Realized semibetas: Disentangling “good” and “bad” downside risks
    (Journal of Financial Economics, 2021-01-01) Bollerslev, T; Patton, AJ; Quaedvlieg, R
    We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the “right” semibetas.
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    Realized Semicovariances: Looking for Signs of Direction Inside the Covariance Matrix
    (Economic Research Initiatives at Duke (ERID) Working Paper, 2017-09-05) Bollerslev, T; Li, J; Patton, AJ; Quaedvlieg, R
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    Risk, jumps, and diversification
    (2008) Bollerslev, T; Law, TH; Tauchen, G
    We test for price discontinuities, or jumps, in a panel of high-frequency intraday stock returns and an equiweighted index constructed from the same stocks. Using a new test for common jumps that explicitly utilizes the cross-covariance structure in the returns to identify non-diversifiable jumps, we find strong evidence for many modest-sized, yet highly significant, cojumps that simply pass through standard jump detection statistics when applied on a stock-by-stock basis. Our results are further corroborated by a striking within-day pattern in the significant cojumps, with a sharp peak at the time of regularly scheduled macroeconomic news announcements.
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    Semiparametric Estimation of Long-Memory Volatility Dependencies
    (Journal of Econometrics, 2000) Bollerslev, T; Wright, JH
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    The forward premium anomaly is not as bad as you think
    (Journal of International Money and Finance, 2000-08-01) Baillie, RT; Bollerslev, T
    The forward premium anomaly refers to the widespread empirical finding that the slope coefficient in the regression of the change in the logarithm of the spot exchange rate on the forward premium is invariably less than unity, and often negative. This "anomaly" implies the apparent predictability of excess returns over uncovered interest rate parity (UIP), and is conventionally viewed as evidence of a biased forward rate and /or of evidence of a time-varying risk premium. This paper presents a stylized model that imposes UIP and allows the daily spot exchange rate to possess very persistent volatility. The model is calibrated around realistic parameter values for daily returns and the slope coefficient estimates in the anomalous regressions with monthly data are found to be centered around unity, but are very widely dispersed, and converge to the true value of unity at a very slow rate. This theoretical evidence is shown to be consistent with the empirical findings for the monthly sample sizes typically employed in the literature. Hence, the celebrated unbiasedness regression does not appear to provide as much evidence as previously supposed concerning the possible bias of the forward rate. © 2000 Elsevier Science Ltd. All rights reserved.