Time-varying distributions and dynamic hedging with foreign currency futures
01 Dec 1993-Journal of Financial and Quantitative Analysis (Cambridge University Press)-Vol. 28, Iss: 4, pp 535-551
TL;DR: In this article, a bivariate error correction model with a GARCH error structure was proposed to estimate the risk-minimizing futures hedge ratios for several currencies and a dynamic hedging strategy was proposed in which the potential risk reduction is more than enough to offset the transactions costs for most investors.
Abstract: Most research on hedging has disregarded both the long-run cointegrating relationship between financial assets and the dynamic nature of the distributions of the assets. This study argues that neglecting these affects the hedging performance of the existing models and proposes an alternative model that accounts for both of them. Using a bivariate error correction model with a GARCH error structure, the risk-minimizing futures hedge ratios for several currencies are estimated. Both within-sample comparisons and out-of-sample comparisons reveal that the proposed model provides greater risk reduction than the conventional models. Furthermore, a dynamic hedging strategy is proposed in which the potential risk reduction is more than enough to offset the transactions costs for most investors.
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TL;DR: In this paper, a new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations, and conditions suffcient to guarantee the positive deffniteness of the covariance matrices are developed.
Abstract: This paper presents theoretical results in the formulation and estimation of multivariate gen- eralized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations. Constraints suffcient to guarantee the positive deffniteness of the con- ditional covariance matrices are developed, and necessary and suffcient conditions for covariance stationarity are presented. Identifcation and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.
4,413Â citations
Cites background from "Time-varying distributions and dyna..."
...…literature, though usually without theoretical discussion (see, e.g., Bollerslev, Engle, and Wooldridge, 1988; Engel and Rodrigues, 1989; Engle, Granger, and Kraft, 1984; Kaminsky and Peruga, 1990; Kroner and Claessens, 1991; Kroner and Sultan, 1993; McCurdy and Morgan, 1991; among several others)....
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TL;DR: The third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time as discussed by the authors.
Abstract: This bestselling and thoroughly classroom-tested textbook is a complete resource for finance students. A comprehensive and illustrated discussion of the most common empirical approaches in finance prepares students for using econometrics in practice, while detailed case studies help them understand how the techniques are used in relevant financial contexts. Worked examples from the latest version of the popular statistical software EViews guide students to implement their own models and interpret results. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Building on the successful data- and problem-driven approach of previous editions, this third edition has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time. A companion website, with numerous student and instructor resources, completes the learning package.
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TL;DR: The authors compare the restrictions imposed by the four most popular multivariate GARCH models, and introduce a set of robust conditional moment tests to detect misspecification, and demonstrate that the choice of a multivariate volatility model can lead to substantially different conclusions in any application that involves forecasting dynamic covariance matrices (like estimating the optimal hedge ratio or deriving the risk minimizing portfolio).
Abstract: Existing time-varying covariance models usually impose strong restrictions on how past shocks affect the forecasted covariance matrix. In this article we compare the restrictions imposed by the four most popular multivariate GARCH models, and introduce a set of robust conditional moment tests to detect misspecification. We demonstrate that the choice of a multivariate volatility model can lead to substantially different conclusions in any application that involves forecasting dynamic covariance matrices (like estimating the optimal hedge ratio or deriving the risk minimizing portfolio). We therefore introduce a general model which nests these four models and their natural 'asymmetric' extensions. The new model is applied to study the dynamic relation between large and small firm returns. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.
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02 Sep 2002TL;DR: This third edition of this bestselling and thoroughly classroom-tested textbook has been updated with new data, extensive examples and additional introductory material on mathematics, making the book more accessible to students encountering econometrics for the first time.
Abstract: A complete resource for finance students, this textbook presents the most common empirical approaches in finance in a comprehensive and well-illustrated manner that shows how econometrics is used in practice, and includes detailed case studies to explain how the techniques are used in relevant financial contexts. Maintaining the accessible prose and clear examples of previous editions, the new edition of this best-selling textbook provides support for the main industry-standard software packages, expands the coverage of introductory mathematical and statistical techniques into two chapters for students without prior econometrics knowledge, and includes a new chapter on advanced methods. Learning outcomes, key concepts and end-of-chapter review questions (with full solutions online) highlight the main chapter takeaways and allow students to self-assess their understanding. Online resources include extensive teacher and student support materials, including EViews, Stata, R, and Python software guides.
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TL;DR: In this paper, multivariate GARCH models are used to model conditional correlations and to analyze the volatility spillovers between oil prices and the stock prices of clean energy companies and technology companies.
606Â citations
References
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TL;DR: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples.
Abstract: The relationship between co-integration and error correction models, first suggested in Granger (1981), is here extended and used to develop estimation procedures, tests, and empirical examples. If each element of a vector of time series x first achieves stationarity after differencing, but a linear combination a'x is already stationary, the time series x are said to be co-integrated with co-integrating vector a. There may be several such co-integrating vectors so that a becomes a matrix. Interpreting a'x,= 0 as a long run equilibrium, co-integration implies that deviations from equilibrium are stationary, with finite variance, even though the series themselves are nonstationary and have infinite variance. The paper presents a representation theorem based on Granger (1983), which connects the moving average, autoregressive, and error correction representations for co-integrated systems. A vector autoregression in differenced variables is incompatible with these representations. Estimation of these models is discussed and a simple but asymptotically efficient two-step estimator is proposed. Testing for co-integration combines the problems of unit root tests and tests with parameters unidentified under the null. Seven statistics are formulated and analyzed. The critical values of these statistics are calculated based on a Monte Carlo simulation. Using these critical values, the power properties of the tests are examined and one test procedure is recommended for application. In a series of examples it is found that consumption and income are co-integrated, wages and prices are not, short and long interest rates are, and nominal GNP is co-integrated with M2, but not M1, M3, or aggregate liquid assets.
27,170Â citations
TL;DR: In this article, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced, which are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances.
Abstract: Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.
20,728Â citations
TL;DR: In this article, the authors proposed new tests for detecting the presence of a unit root in quite general time series models, which accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend.
Abstract: SUMMARY This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
16,874Â citations
TL;DR: An overview of some of the developments in the formulation of ARCH models and a survey of the numerous empirical applications using financial data can be found in this paper, where several suggestions for future research, including the implementation and tests of competing asset pricing theories, market microstructure models, information transmission mechanisms, dynamic hedging strategies, and pricing of derivative assets, are also discussed.
4,206Â citations
TL;DR: In this article, a multivariate time series model with time varying conditional variances and covariances but with constant conditional correlations is proposed, which is readily interpreted as an extension of the seemingly unrelated regression (SUR) model allowing for heteroskedasticity.
Abstract: A multivariate time series model with time varying conditional variances and covariances but with constant conditional correlations is proposed. In a multivariate regression framework, the model is readily interpreted as an extension of the seemingly unrelated regression (SUR) model allowing for heteroskedasticity. Each of the conditional variances are parameterized as a univariate generalized autoregressive conditional heteroskedastic (GARCH) process. The descriptive validity of the model is illustrated for a set of 5 nominal European-US dollar exchange rates following the inception of the European Monetary System (EMS). EMS results are compared to estimates obtained for the same model using data over the pre-EMS period, July 1973 to March 1979. When compared to the pre-EMS free float period, the comovements between the currencies are found to be significantly higher over the later period.
3,662Â citations