Backtesting Risk Measures for Digital Assets

Abstract:

This paper presents a practical framework for backtesting hourly refreshed risk forecasts in digital-asset markets. We study one-day-ahead downside and upside tail measures produced by the Talos historical simulation engine, namely Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR), Gain-at-Risk (GaR), and Conditional Gain-at-Risk (CGaR), across multiple confidence levels. The goal is operational: to verify that these risk figures remain reliable as new market data arrive.

The framework addresses calibration, stability through time, and comparative forecast accuracy. Calibration is assessed through joint identification functions for the threshold and tail mean, allowing frequency errors and tail-severity errors to be diagnosed separately. Comparative accuracy is evaluated with the Fissler–Ziegel FZ0 score and Diebold–Mariano tests. The same methodology is applied symmetrically to downside and upside measures. Because forecasts are updated hourly while the horizon remains one day, overlapping horizons induce serial dependence, making heteroskedasticity- and autocorrelation-consistent inference essential.

The paper also shows how the same risk measures can support one-hour outlier detection through normalized exceedance scores and simple rarity bounds. Overall, the methodology provides a unified and operationally transparent approach to monitoring digital-asset risk measures for tokens, derivatives, and portfolios.

Download the full PDF to learn how Talos verifies that its digital asset risk forecasts stay reliably calibrated as market conditions change.

‍