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

Demetrio Lacava

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.

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.

Paper Structure

This paper contains 8 sections, 11 equations, 3 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Conditional Autoregressive Value at Risk models
  3. CAViaR with Spillover Effects
  4. Identifying Sources of Risk
  5. The Data Set
  6. Empirical Application
  7. Out-of-sample Evaluation
  8. Final remarks

Figures (3)

  • Figure 1: Heatmap representing the sample cross-quantilogram Han:Linton:Oka:Whang:2016. Sample period: March 19, 2008 -- November 14, 2025
  • Figure 2: Spillover component $q^s_{i,t}$ from SAV CAViaR-SE (green line), AS CAViaR-SE (blue), and IG CAViaR-SE (red) models, for selected tickers. Sample period: March 19, 2008 -- November 14, 2025.
  • Figure 3: Spillover effect estimated coefficient from the SAV-X and the AS-X. Sample period: March 19, 2008 -- November 14, 2025.