[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.]

We study the information content of implied volatility from several volatility specifications of the Heath-Jarrow-Morton (1992) (HJM) models relative to popular historical volatility models in the Eurodollar options market. The implied volatility from the HJM models explains much of the variation of realized interest rate volatility over both daily and monthly horizons. The implied volatility dominates the GARCH terms, the Glosten et al. (1993) type asymmetric volatility terms, and the interest rate level. However, it cannot explain that the impact of interest rate shocks on the volatility is lower when interest rates are low than when they are high.

The authors use an extension of the equilibrium framework of M. Rubinstein (1976) and M. Brennan (1979) to derive an option valuation formula when the stock return volatility is both stochastic and systematic. Their formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options. If the 'mean,'volatility, and 'covariance' processes for the stock return and the consumption growth are predictable, the authors' option valuation formula can be written in 'preference-free'form. Further, many popular option valuation formulae in the literature can be written as special cases of their general formula.

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.

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.

We study the information content of implied volatility from several volatility specifications of the Heath–Jarrow–Morton (1992) (HJM) models relative to popular historical volatility models in the Eurodollar options market. The implied volatility from the HJM models explains much of the variation of realized interest rate volatility over both daily and monthly horizons. The implied volatility dominates the GARCH terms, the Glosten et al. (1993) type asymmetric volatility terms, and the interest rate level. However, it cannot explain that the impact of interest rate shocks on the volatility is lower when interest rates are low than when they are high.

We use an extension of the equilibrium framework of Rubinstein ( 1976 ) and Brennan ( 1979 ) to derive an option valuation formula when the stock return volatility is both stochastic and systematic. Our formula incorporates a stochastic volatility process as well as a stochastic interest rate process in the valuation of options. If the “mean,” volatility, and “covariance” processes for the stock return and the consumption growth are predictable, our option valuation formula can be written in “preference‐free” form. Further, many popular option valuation formulae in the literature can be written as special cases of our general formula.

This paper defines the news impact curve which 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 which emphasize the asymmetry of the volatility response to news. Our results suggest that the model by Glosten, Jagannathan, and Runkle 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.