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When is volatility fair? Hölder regularity and financial risk
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DOI：10.1016/j.amc.2026.130223.png)
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Abstract
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• Financial risk is redefined as price irregularity rather than variability. • Fair volatility is defined as the level consistent with martingale model. • An analytical link connects regularity and price scale in the MPRE framework. • MPRE-implied volatility is compared to realized volatility across 14 indices. • Results reveal temporary market departures from the martingale condition.
Keywords:
Stochastic volatility
Financial risk
Hölder regularity
Hurst exponent
Multifractional processes with random exponent
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