Crossing penalised CAViaR

ArXiv ID: 2501.10564 “View on arXiv”

Authors: Unknown

Abstract

Dynamic quantiles, or Conditional Autoregressive Value at Risk (CAViaR) models, have been extensively studied at the individual level. However, efforts to estimate multiple dynamic quantiles jointly have been limited. Existing approaches either sequentially estimate fitted quantiles or impose restrictive assumptions on the data generating process. This paper fills this gap by proposing an objective function for the joint estimation of all quantiles, introducing a crossing penalty to guide the process. Monte Carlo experiments and an empirical application on the FTSE100 validate the effectiveness of the method, offering a flexible and robust approach to modelling multiple dynamic quantiles in time-series data.

Keywords: Conditional Autoregressive Value at Risk (CAViaR), Dynamic Quantiles, Joint Estimation, Crossing Penalty, Monte Carlo Experiments, Equity Indices

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 6.0/10
• Quadrant: Holy Grail
• Why: The paper introduces a novel penalised objective function for joint quantile estimation and uses a sophisticated global optimizer (CMA-ES), demonstrating high mathematical complexity. It validates the method via Monte Carlo simulations and an empirical application on the FTSE100, showing practical data handling and backtesting readiness.

  flowchart TD
    A["Research Goal: Joint Estimation<br>of Multiple Dynamic Quantiles"] --> B{"Data Input:<br>FTSE100 Time-Series"};
    B --> C["Methodology:<br>CAViaR with Crossing Penalty"];
    C --> D["Computational Process:<br>Simultaneous Optimization"];
    D --> E{"Monte Carlo<br>Simulations"};
    E --> F["Key Outcomes:<br>Robust & Flexible<br>Dynamic Quantile Modeling"];
    D --> G{"Empirical Application:<br>FTSE100 Data"};
    G --> F;