[Necessary and sufficient conditions are determined under which a truncated approximation to generalized least squares is more efficient than ordinary least squares. For the general case, the necessary conditions are unlikely to be fulfilled. For a first order Markov model in a second order world, the sufficient conditions are satisfied only when one of the second order roots is very small, and therefore the first order assumption is approximately true. When the class of possible exogenous variables is limited to those typical of economic time series, the sufficient conditions are satisfied for a wider range of cases. Relative efficiencies are computed for a variety of cases.]

[We propose a new method for pricing options based on GARCH models with filtered historical innovations. In an incomplete market framework, we allow for different distributions of historical and pricing return dynamics, which enhances the model's flexibility to fit market option prices. An extensive empirical analysis based on S&P 500 index options shows that our model outperforms other competing GARCH pricing models and ad hoc Black-Scholes models. We show that the flexible change of measure, the asymmetric GARCH volatility, and the nonparametric innovation distribution induce the accurate pricing performance of our model. Using a nonparametric approach, we obtain decreasing state-price densities per unit probability as suggested by economic theory and corroborating our GARCH pricing model. Implied volatility smiles appear to be explained by asymmetric volatility and negative skewness of filtered historical innovations.]

[This article investigates empirically how returns and volatilities of stock indices are correlated between the Tokyo and New York markets. Using intradaily data that define daytime and overnight returns for both markets, we find that Tokyo (New York) daytime returns are correlated with New York (Tokyo) overnight returns. We interpret this result as evidence that information revealed during the trading hours of one market has a global impact on the returns of the other market. In order to extract the global factor from the daytime returns of one market, we propose and estimate a signal-extraction model with GARCH processes.]

This paper defines the news impact curve that measures how new information is incorporated into volatility estimates. Various new and existing ARCH models, including a partially nonparametric one, are compared and estimated with daily Japanese stock return data. New diagnostic tests are presented that emphasize the asymmetry of the volatility response to news. The authors' results suggest that the model by L. Glosten, R. Jagannathan, and D. Runkle (1989) is the best parametric model. The EGARCH also can capture most of the asymmetry; however, there is evidence that the variability of the conditional variance implied by the EGARCH is too high.

There have been two major classes of urban area models: nonspatial models of income, employment, and structural change; and land use models usually oriented toward transportation planning. Recent efforts have become relatively complicated and have employed quite sophisticated techniques, with particular attention being paid to the housing market. Nevertheless, most of the work done so far appears somewhat deficient; convincing behavioral relations forming the basic structure are absent; and there have been inadequate efforts to test and validate the models. Further, relatively few efforts have specified the institutional framework necessary to introduce policy actions directly, although some recent efforts have been made in this direction. We propose to construct a model of the Boston metropolitan area that contains three major parts: a macroeconomic nonspatial model of output, employment, and income distribution; a model of long-term adjustments of population and capital stocks; and a model of spatial allocation. The equations of the model will be econometrically estimated and the main thrust of our efforts will be devoted to specification and testing of structural relationships reflecting actions of households, busi nesses, and governments interacting within both market and nonmarket institutions. The purpose of building the model is to permit systematic evaluation of a very wide range of policy alternatives considered at national, state, metropolitan, or local jurisdiction levels. If this is to be accomplished, there are three requisites. First, the model must endogenously generate those variables that enter evaluative (social welfare) functions. In this model we consider income, income distribution, availability of public services to particular population groups, and residential segregation of racial and income groups to be such variables. Second, the model must be designed so that policy alternatives can be modelled by varying the levels of particular exogenous variables. Finally, the model structure and parameter estimates must provide a model with a high degree of predictive power if the enterprise is to be of any value for policy evaluation. This paper contains a general guide to our thinking about how to construct and implement such a model. Many crucial questions of specification remain unresolved. To date we have collected most of the data that will be needed for preliminary versions of the model and some equations have been estimated. Undoubtedly many compromises will have to be made between our plans and what * Massachusetts Institute of Technology. This research was supported by a grant from the Ford Foundation.

Implied volatility (IV) reflects both expected empirical volatility and also risk premia. Stochastic variation in either creates unhedged risk in a delta hedged options position. We develop EGARCH/DCC models for the dynamics of volatilities and correlations among daily IVs from options on twenty-eight large cap stocks. The data strongly support a general correlation structure and also a one-factor model with the VIX index as the common factor. Using IVs from stocks that are either highly correlated with the target stock’s IV or in the same industry together with the VIX can significantly improve hedging of individual IV changes.

A common finding in many of the recent empirical studies with the ARCH class of models applied to high frequency financial data concerns the apparent persistence of shocks for forecast of the future conditional variances. It is likely that several different variables share this same implied long-run component, however. In that situation, the variables are defined to be copersistent in variance. Conditions for copersistence to occur in the linear multivariate GARCH model are presented. These conditions parallel the conditions for linear cointegration in the mean. A simple empirical example with foreign exchange rate data illustrates the ideas. Copyright 1993 by The Econometric Society.

[Any misspecification of the disturbance error process in a linear regression may lead to an inefficient estimator. Although spectral methods proposed by Hannan will always be asymptotically efficient, they are frequently used because they are computationally demanding and very large samples are presumably required. This paper presents Monte Carlo evidence from a variety of typical econometric situations which indicates that the estimators perform quite well for moderate-sized samples (100) when the error process is highly dependent, and even for small samples when the error process is simple. The results are used to estimate a second order term in the asymptotic expansion for the variance.]

In the aftermath of the financial crisis, institutions have been asked to reduce leverage in order to reduce risk. To address the effectiveness of this measure, we build a model of equity volatility that accounts for leverage. Our approach blends Merton’s insights on capital structure with traditional time-series models of volatility. We estimate that precautionary capital needs for the entire financial sector reached $2 trillion during the crisis. We also investigate the long-standing observation that equity volatility asymmetrically responds to positive and negative news. Volatility asymmetry is mostly explained by exposure to the aggregate market, not a mechanical leverage effect. Received March 27, 2015; editorial decision February 25, 2017 by Editor Andrew Karolyi.

[The capital asset pricing model provides a theoretical structure for the pricing of assets with uncertain returns. The premium to induce risk-averse investors to bear risk is proportional to the nondiversifiable risk, which is measured by the covariance of the asset return with the market portfolio return. In this paper a multivariate generalized autoregressive conditional heteroscedastic process is estimated for returns to bills, bonds, and stock where the expected return is proportional to the conditional convariance of each return with that of a fully diversified or market portfolio. It is found that the conditional covariances are quite variable over time and are a significant determinant of time-varying risk premia. The implied betas are also time-varying and forecastable. However, there is evidence that other variables including innovations in consumption should also be considered in the investor's information set when estimating the conditional distribution of returns.]