When volatility skews are regimes, not mispricings

A surface before a signal

Options on a single underlying typically do not share one implied-volatility, so the strike-wise implied-volatility pattern is used to judge relative richness when raw premiums cannot be compared directly. That pattern is the volatility-skew: the strike-by-strike reading for options that share an underlying and an expiration.

On one illustrated session, cattle, Eurodollar, and bond-futures options showed higher implied volatilities out of the money than at the money. The equity-index skew made out-of-the-money puts look rich versus out-of-the-money calls. The yen skew was nearly flat.

Why a strike gap can be a regime

Three commonly cited reasons for skews are lasting or temporary demand to buy some strikes and sell others, heavier-tailed returns than a normal percentage-change assumption, and the possibility that a constant percentage volatility implies different absolute price variation at different price levels. The extra implied-volatility often assigned to out-of-the-money strikes because realized percentage changes have heavier tails than that normal assumption is fat-tail-compensation.

At a fixed 20 percent volatility assumption, crude oil at 15 implies a 3-unit annual price standard deviation while crude oil at 20 implies a 4-unit standard deviation, so higher strikes may carry lower implied volatilities if absolute variability is not expected to rise one-for-one with price.

Tenor, averages, and seasons

Shorter-dated skews are typically more pronounced than longer-dated ones. Longer-dated implied volatilities tend to sit closer to a longer-run average of the underlying's volatility, including seasonal effects in agricultural contracts.

Editorial reading: a short-dated strike gap can be hedging demand, fat-tail-compensation, and tenor mean-reversion sitting on the surface, not a standalone claim that one contract is mispriced.

A pair becomes a rule only after that isolation

A volatility-spread procedure sells the higher-implied-volatility option and buys the lower one, each delta-hedged, then estimates the model gap by repricing both contracts with one shared remaining-life volatility forecast. That model price discrepancy is the black-scholes-theoretical-edge. The book that sells the richer implied-volatility, buys the cheaper one, and offsets residual directional exposure with a futures holding is a delta-hedged-volatility-spread.

In a June 22, 1989 settlement table of September 1989 bond options, a 10 percent shared forecast made the 92 puts 3/64 rich and the 94 puts 4/64 cheap, a 7/64 model gap that a 0.18 long futures holding per spread would keep approximately delta-neutral. Listed alternatives were a 90/94 put combination at 10/64 and a 92/96 call combination at 9/64.

Costs, friction, and leftover path risk

Institutional round-turn commissions of 15 dollars per option reduced that 92/94 model gap to less than 5/64. Unwinding a three-legged option-plus-futures package adds execution friction that can erase the remaining discrepancy.

One-by-one spreads remain exposed to gap or limit moves beyond the short strike because the futures hedge is unbounded. The 92/94 example is short volatility below the 93 midpoint and long volatility above it, so a decline with rising implied-volatility is adverse for that construction.

A 7.7 percent volatility path was shown as a break-even-volatility for that spread. Break-even-volatility is a single volatility path at which a named spread's modeled profit and loss is zero under a stated assumption about where price is centered. The distance from current implied-volatility to that path depends on how close the underlying is to the strike midpoint, so the metric is not a robust risk indicator and is not a complete risk measure. Similar front-month put spreads may routinely show model discrepancies between 0 and 10/64, making a 3/64 gap possibly ordinary compensation rather than an outlier.