Modeling variance risk in financial markets using power-laws : new evidence from the Garman-Klass variance estimator

Abstract

This study examines the range-based variance risk of five key financial asset markets—S&P 500, gold, crude oil, the USD/GBP exchange rate, and Bitcoin—using the noise-efficient Garman-Klass variance estimator. Our findings corroborate previous research by demonstrating that range-based asset variances adhere to power-law behavior generating variance behavior that is effectively infinite in practical terms. Furthermore, we provide novel evidence that the widely accepted log-normal model is unequivocally rejected for all range-based asset variances, underscoring its inadequacy in capturing the statistical properties of financial asset variances. A key contribution of this study is the discovery that a power-law function with α ≈ 2.8 represents a universal law governing the cross-sectional variances of otherwise unrelated asset markets. These findings have significant implications for risk management frameworks that rely on models developed within the mean-variance space, as they highlight the limitations of traditional approaches in assessing and managing financial risks.