Derive VRP (IV minus realized vol) and classify whether options are rich, fair, or cheap
Answers whether crypto options are overpriced or underpriced relative to how much the market has actually been moving. For BTC and ETH it computes 30-day realized volatility from daily price candles and reads at-the-money implied volatility from the options data, then takes the difference (implied minus realized). It classifies the premium as rich (over +5), fair, or cheap (below -5) per asset. Use rich and cheap readings as context on options pricing relative to realized moves; note this compares implied volatility with past realized moves, while the academic variance risk premium compares expectations over the same future window.
An implied-minus-trailing-realised VOLATILITY SPREAD, and the care needed before calling it anything grander.
Realised volatility here is the standard deviation of daily log returns over the past 30 days, annualised by multiplying by sqrt(365) for a continuously traded market (sqrt(252) for equities). It is BACKWARD-looking.
Implied volatility is the number that, put into an option pricing model, reproduces the option's traded price. Black-Scholes-Merton (Black and Scholes 1973; Merton 1973) has no closed form for it, so it is solved numerically. It is FORWARD-looking, and it is not itself a price - it is a model-dependent PARAMETER inferred from one, so it changes if the model or its inputs change. Nor is it a pure forecast: it embeds both an expectation of future movement and the compensation demanded for bearing that risk.
WHAT THIS IS NOT. The academic variance risk premium is the difference between the risk-neutral and physical expectations of realised variance over THE SAME FUTURE WINDOW - roughly E^Q[RV] - E^P[RV] - and it is measured in variance, not volatility points. Carr and Wu (2009) and Bollerslev, Tauchen and Zhou (2009) construct exactly that, on equity indexes, with matched horizons; Carr and Wu's sign convention also runs opposite to "implied minus realised". What this analysis computes is forward-looking implied volatility minus TRAILING realised volatility - a different pair of objects over non-matching windows. It is a legitimate and widely used trader's gauge, and it is not the quantity in those papers. Name it accurately: an implied-to-trailing-realised spread.
Reading it as "options are overpriced" is the common error. A positive spread does not identify an arbitrage; it is consistent with the market pricing higher future volatility than the recent past, with compensation for variance risk, or with both. Risk compensation is a plausible interpretation of a persistently positive average, not something this spread alone demonstrates.
Comparability still requires the two figures to share an annualisation convention, and the horizon mismatch above should be stated whenever the number is quoted.
The +5 / -5 cut-offs in annualised volatility points are our own convention and are not risk-adjusted.
One caution on framing: a positive average spread is a property of the STATISTIC, and it is not a return. Turning it into a return requires a position - typically a short-volatility strategy - and that strategy's payoff, small gains in most periods and large losses in a few, belongs to the strategy rather than to the measurement. Do not read the spread as money available.
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