Modeling and Forecasting Tail Risk Spillovers: A Component-Based CAViaR Approach

Abstract

This paper introduces a new extension of the Conditional Autoregressive Value at Risk (CAViaR) model aimed at improving tail risk forecasting across assets. The proposed component-based model, CAViaR with Spillover Effects (CAViaR-SE), decomposes the conditional Value at Risk into a proper-risk component and a spillover component driven by a linear combination of tail risks from influential assets. These assets are selected via a recursive partial correlation algorithm, allowing multiple spillover sources with minimal parameterization. The spillover component acts as a predictable quantile shifter, directly affecting the conditional quantile dynamics rather than the volatility scale. Empirical results on Dow Jones Industrial Average stocks show that spillover effects account for a substantial share of total tail risk and significantly improve out-of-sample tail risk forecasts. Backtesting procedures, together with Model Confidence Set (MCS) analysis, confirm that CAViaR-SE provides well-calibrated risk measures and statistically superior forecasts compared to standard and augmented CAViaR models.