Abstract
Persistently high negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. In the event of having more than one hedging instrument, multivariate covariances need to be calculated. Optimal hedge ratios are unlikely to remain constant using high frequency data, so it is essential to specify dynamic covariance models. These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. Analytical developments are occasionally promulgated for multivariate conditional volatility models. The primary purpose of the paper is to analyze purported analytical developments for the most widely-used multivariate dynamic conditional covariance model to have been developed to date, namely the Full BEKK model, named for Baba, Engle, Kraft and Kroner. Dynamic models are not straightforward (or even possible) to translate in terms of the algebraic existence, underlying stochastic processes, specification, mathematical regularity conditions, and asymptotic properties of consistency and asymptotic normality, or the lack thereof. The paper presents a critical analysis, discussion, evaluation and presentation of caveats relating to the Full BEKK model, and an emphasis on the numerous dos and don’ts in implementing the Full BEKK and related non-Diagonal BEKK models, such as Triangular BEKK and Hadamard BEKK, in practice.
Highlights
High negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses
The results in the previous section allow a clear discussion of the caveats associated with the widely-used Full BEKK
(3) The Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)(1,1) parameters must satisfy the regularity conditions of positivity as they are the unconditional variances from a univariate random coefficient autoregressive process
Summary
High negative covariances between risky assets and hedging instruments are intended to mitigate against risk and subsequent financial losses. Modeling, forecasting and evaluating dynamic covariances between hedging instrument and risky financial assets requires the specification and estimation of multivariate models of covariances These values can either be determined analytically or numerically on the basis of highly advanced computer simulations. For the variety of detailed possible outcomes mentioned above, where problematic issues arise constantly, and sometimes unexpectedly, a companion paper by the author evaluates the recent developments in modeling dynamic conditional correlations on the basis of the Dynamic Conditional correlation (DCC) model (see McAleer 2019) Both papers are intended as Topical Collections to bring the known and unknown results pertaining to Full BEKK and associated non-diagonal multivariate conditional volatility models, such as Triangular BEKK and Hadamard BEKK, into a single collection.
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