Instead of assuming the distribution of return series, Engle and Manganelli (2004) propose a new Value-at-Risk (VaR) modeling approach, Conditional Autoregressive Value-at-Risk (CAViaR), to directly compute the quantile of an individual asset's returns which performs better in many cases than those that invert a return distribution. In this paper we explore more flexible CAViaR models that allow VaR prediction to depend upon a richer information set involving returns on an index. Specifically, we formulate a time-varying CAViaR model whose parameters vary according to the evolution of the index. The empirical evidence reported in this paper suggests that our timevarying CAViaR models can do a better job for VaR prediction when there are spillover effects from one market or market segment to other markets or market segments. * We thank the editor (Bruce Mizrach) and the three anonymous referees for constructive suggestions that guided us in improving the paper. We are also grateful to Simone Manganelli for providing his CAViaR codes.
As a benchmark for measuring market risk, Value-at-Risk (VaR) reduces the risk associated with any kind of asset to just a number (amount in terms of a currency), which can be well understood by regulators, board members, and other interested parties. This paper employs a new kind of VaR approach due to Engle and Manganelli [4] to forecasting oil price risk. In doing so, we provide two original contributions: introducing a new exponentially weighted moving average CAViaR model and developing a least squares regression model for multi-period VaR prediction.
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