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

Paper: arXiv 2603.25217

Authors: 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.

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper introduces an innovative extension to the CAViaR framework by incorporating a component-based tail risk spillover mechanism via recursive partial correlation. The empirical evaluation is robust, utilizing Model Confidence Set analysis and formal backtesting on DJIA stocks to demonstrate statistically superior out-of-sample forecasting.

Research Flowchart

  flowchart TD
    A[Research Goal: Improve Tail Risk Forecasting via Spillover Effects] --> B[Input Data: Dow Jones Industrial Average Stocks]
    B --> C[Select Spillover Sources: Recursive Partial Correlation Algorithm]
    C --> D[Model Formulation: Decompose VaR into Proper-Risk & Spillover Components CAViaR-SE]
    D --> E[Out-of-Sample Evaluation: Backtesting & Model Confidence Set MCS Analysis]
    E --> F[Key Findings: Spillovers drive significant tail risk & CAViaR-SE yields superior forecasts]

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0 of 292 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.