Paper: arXiv 2610.13446

Authors: Keisuke Sasaki, Yasuhiro Omori

Abstract

A realized tail-risk conditional autoregressive expectile (RTCARE) model is proposed for joint forecasting of value-at-risk (VaR) and expected shortfall (ES). Realized tail measures such as the realized quantile and the realized ES, constructed from intraday high-frequency returns, are incorporated into the dynamics and measurement equations of the conditional expectile, allowing information about lower-tail risk to enter the forecasts. The parameters are estimated by Markov chain Monte Carlo, and we evaluate the resulting VaR-ES forecasts in numerical examples and in an empirical application using U.S. stock-return data. Across the considered tail levels, the RTCARE models deliver competitive and often superior forecasting performance relative to existing alternatives, with stable results across Monte Carlo replications and rolling forecast evaluations.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated model for tail-risk forecasting, incorporating advanced statistical techniques like MCMC. It rigorously evaluates the model through numerical examples and an empirical application with U.S. stock data, demonstrating strong statistical methodology and backtesting readiness. The integration of realized tail measures into conditional expectile models offers a novel approach to an important problem in quantitative finance.

Research Flowchart

  flowchart TD
    A[Research Goal: Joint Forecasting of VaR & ES] --> B{Proposed Model: RTCARE};
    B --> C{Methodology: Incorporate Realized Tail Measures};
    C --> D[Data: Intraday High-Frequency Returns];
    D --> E{Computational Process: MCMC Estimation};
    E --> F[Outcomes: Competitive/Superior Forecasting Performance & Stable Results];