Proxy-Reliance Control in Conformal Recalibration of One-Sided Value-at-Risk

TL;DR

This paper proposes a new framework for one-sided VaR recalibration that controls how much the adjustment depends on an imperfect volatility proxy, balancing responsiveness and robustness.

Contribution

It introduces a proxy-reliance parameter for VaR recalibration, providing a practical way to manage dependence on proxies and improve stressed-state robustness.

Findings

Larger proxy reliance increases tail responsiveness but risks fragility.

Empirical tests show proxy reliance improves stressed-state robustness.

Lower or intermediate reliance can outperform full reliance in stressed tail control.

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.