Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two-step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results.

/pdf/dynamic-conditional-correlation-a-simple-class-of-1s5avcbk8r.pdf

Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models

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.

https://www.jstor.org/stable/pdfplus/3532933.pdf

Multivariate Simultaneous Generalized ARCH

ARCH modeling in finance: A review of the theory and empirical evidence

Time varying correlations are often estimated with Multivariate Garch models that are linear in squares and cross products of returns. A new class of multivariate models called dynamic conditional correlation (DCC) models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two step methods based on the likelihood function. It is shown that they perform well in a variety of situations and give sensible empirical results.

/pdf/dynamic-conditional-correlation-a-simple-class-of-35boqnouqg.pdf

Dynamic Conditional Correlation - A Simple Class of Multivariate GARCH Models - eScholarship

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.

Modeling Asymmetric Comovements of Asset Returns

Optimal dynamic hedging portfolios and the currency composition of external debt

Commodity prices have historically been among the most volatile of international prices. Measured volatility (the standard deviation of price changes) has not been below 15 percent and at times has been more than 50 percent. Often the volatility of commodity prices has exceeded that of exchange rates and interest rates. The large price variations are caused by disturbances in demand and supply. Stockholding leads to some price smoothing, but when stocks are low, prices can jump sharply. As a result, commodity price series are not stationary and in some periods they jump abruptly to high levels or fall precipitously to low levels relative to their long-run average. Thus it is difficult to determine long-term price trends and the underlying distribution of prices. The volatility of commodity prices makes price forecasting difficult. Indeed, realized prices often deviate greatly from forecasted prices, which has led to the practice of giving forecasts probability ranges. But assigning probability ranges requires forecasting future price volatility, which, given uncertainties about true price distribution, is difficult. One potentially useful source of information for forecasting volatility is the volatility forecasts imbedded in the prices of options written on commodities traded in exchanges. Options give the holder the right to buy (call) or sell (put) a certain commodity at a certain date at a fixed (exercise) price. Options prices depend on several variables, one of which is the expected volatility up to the maturity date. Given a specific theoretical model, the market prices of options can be used to derive the market's expectations about price volatility and the price distribution. The authors systematically analyze different methods'abilities to forecast commodity price volatility (for several commodities). They collected the daily prices of commodity options and other variables for seven commodities (cocoa, corn, cotton, gold, silver, sugar, and wheat). They extracted the volatility forecasts implicit in options prices using several techniques. They compared several volatility forecasting methods, divided into three categories: (1) forecasts using only expectations derived form options prices; (2) forecasts using only time-series modeling; (3) forecasts that combine market expectations and time-series modeling (a new method devised for this purpose). They find that the volatility forecasts produced by method 3 outperform the first two as well as the naive forecast based on historical volatility. This result holds both in and out of sample for almost all commodities considered.

Kenneth F. Kroner

Papers

Optimal dynamic hedging portfolios and the currency composition of external debt

Forecasting volatility in commodity markets