Paper: arXiv 2603.22569

Authors: Tenghan Zhong

Abstract

We introduce a proxy-reliance-controlled conformal recalibration framework for one-sided Value-at-Risk (VaR), and study a question that existing state-aware methods do not usually isolate: how strongly should the recalibration adjustment depend on an imperfect volatility proxy? We formalize this through a proxy-reliance parameter that continuously interpolates between an approximately constant-shift correction and a fully proxy-scaled correction. This makes proxy reliance a distinct and practically interpretable design choice in one-sided VaR recalibration. We show theoretically that larger proxy reliance increases the responsiveness of the tail adjustment to proxy scale, but also increases stressed-state fragility when the proxy underreacts. Empirically, in rolling out-of-sample tests on a six-ETF panel with VIX-linked state variables, and with supporting evidence from SPY, we find that the empirical value of proxy-reliance control lies in improved stressed-state robustness rather than uniform overall dominance. In particular, when the baseline forecast remains exposed to proxy imperfection in stressed states, lower or intermediate proxy reliance can outperform fully proxy-scaled recalibration in stressed left-tail VaR control.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical and empirical evaluation of conformal prediction applied to risk management, specifically focusing on VaR recalibration using proxy variables like the VIX. It successfully balances formal risk theoretical derivations with rolling out-of-sample testing across an ETF panel, demonstrating clear practical utility in stressed market states.

Research Flowchart

  flowchart TD
    A["Research Question: How strongly should VaR recalibration depend on an imperfect volatility proxy?"] --> B["Framework: Proxy-Reliance-Controlled Conformal Recalibration"]
    
    C["Inputs: 6-ETF Panel, SPY, VIX-linked State Variables"] --> D["Methodology: Interpolate via Parameter γ<br/>(Constant Shift vs. Fully Proxy-Scaled)"]
    
    B --> D
    D --> E["Evaluation: Theoretical Fragility Analysis & Rolling Out-of-Sample Tests"]
    
    E --> F["Key Findings: High γ increases responsiveness but adds stress fragility;<br/>Lower/Intermediate γ improves stressed-state VaR robustness"]

Cited References (38)

  1. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation (1982) — link
  2. Generalized autoregressive conditional heteroskedasticity (1986) — link
  3. Incorporating volatility updating into the historical simulation method for value-at-risk (1998) — link
  4. VaR without correlations for portfolios of derivative securities (1999) — link
  5. Elements of financial risk management (2012)
  6. Quantile regression (2005) — link
  7. CAViaR : Conditional autoregressive value at risk by regression quantiles (2004) — link
  8. DeepVol : volatility forecasting from high-frequency data with dilated causal convolutions (2024) — link
and 30 more
  1. Predicting VIX with adaptive machine learning (2024) — link
  2. Options-driven volatility forecasting (2025) — link
  3. A semi-parametric dynamic conditional correlation framework for risk forecasting (2025) — link
  4. Forward-looking physical tail risk: a deep learning approach (2026) — link
  5. Techniques for verifying the accuracy of risk measurement models (1995) — link
  6. Evaluating interval forecasts (1998) — link
  7. Algorithmic learning in a random world (2005) — link
  8. Conformal prediction: A gentle introduction (2023) — link
  9. Exact and robust conformal inference methods for predictive machine learning with dependent data (2018) — link
  10. Adaptive conformal inference under distribution shift (2021) — link
  11. Practical adversarial multivalid conformal prediction (2022) — link
  12. Conformal prediction for multi-dimensional time series by ellipsoidal sets (2024) — link
  13. Adaptive conformal inference for computing market risk measures: An analysis with four thousand crypto-assets (2024) — link
  14. Taming tail risk in financial markets: conformal risk control for nonstationary portfolio VaR (2026) — link
  15. Temporal conformal prediction ( TCP ): A distribution-free statistical and machine learning framework for adaptive risk forecasting (2025) — link
  16. Conformal predictive portfolio selection (2024) — link
  17. Reliable real-time value at risk estimation via quantile regression forest with conformal calibration (2026) — link
  18. The extreme value method for estimating the variance of the rate of return (1980) — link
  19. On the estimation of security price volatilities from historical data (1980) — link
  20. Answering the skeptics: yes, standard volatility models do provide accurate forecasts (1998) — link
  21. Modeling and forecasting realized volatility (2003) — link
  22. Understanding the VIX (2009) — link
  23. Forecasting volatility in financial markets: A review (2003) — link
  24. A new approach to the economic analysis of nonstationary time series and the business cycle (1989) — link
  25. International asset allocation with regime shifts (2002) — link
  26. CoVaR (2016) — link
  27. Measuring systemic risk (2017) — link
  28. Stress scenario selection by empirical likelihood (2015) — link
  29. Forecasting risk with Markov-switching GARCH models: A large-scale performance study (2018) — link
  30. Minimum capital requirements for market risk (2019) — link

0 of 38 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.