Volatility skew and risk reversal

Measuring the tilt with delta

The smile tilts: in crypto the put side sits higher in sell-offs and bear phases, while in strong rallies the call side is often richer. To put a number on that tilt in a way that compares across expiries and volatility levels, traders use delta instead of strike. The 25-delta put is the put whose delta is −0.25; the 25-delta call, the call whose delta is +0.25. Both are roughly equally far out of the money, in probability terms, whatever the expiry.

• Risk reversal (RR) = 25-delta call IV − 25-delta put IV. Negative means puts are priced above calls: the market pays more for downside protection than for upside. Positive means calls are richer.
• Put skew = 25-delta put IV − ATM IV: how much more the downside wing costs than the money.

A worked example

A 30-day expiry with the forward at $100,000. ATM IV is 50%. The 25-delta put is the ≈ $91,000 strike, at 55% IV, worth about $2,551; the 25-delta call is the ≈ $110,500 strike, at 47%, worth about $1,882.

• Risk reversal: 47 − 55 = −8 points.
• Put skew: 55 − 50 = +5 points.
• Buying the 25-delta call and selling the 25-delta put, a long combo, brings in a credit of about $670: the skew pays you to own the upside and take on the downside. The reverse, a short combo, pays that $670: it is the overlay that hedges a holding with a protective put financed by a short call, and the skew makes the protection cost more than the call brings in.

What skew says

A deeply negative risk reversal is the market paying up for crash protection; it tends to deepen in sell-offs, when hedgers rush for puts. In strong rallies the risk reversal can turn positive as upside calls are chased. Skew moves with the price itself, so a position with legs on both wings, like a combo, has an exposure to skew as well as to direction. It is a reading of demand for protection, not a prediction of where the price goes.

How BOSS measures it

For each listed expiry, BOSS finds the IV at exactly −0.25 put delta and +0.25 call delta by interpolating, linearly in delta, between the two out-of-the-money quotes whose venue-reported deltas bracket the target. It never extrapolates past the listed strikes: if no pair brackets 25 delta, that expiry has no value. The per-expiry values are then interpolated to a constant 30 days in total variance, the same way as ATM IV 30d, so the numbers compare across days even as expiries roll.

The recorder stores them every 5 minutes and every hour, which is where the charts of put skew (25-delta put − ATM) and risk reversal (25-delta call − 25-delta put) over time come from. On Deribit, where the recording doesn't reach back far enough, a series rebuilt from Deribit's historical trades (the median IV of trades in each delta band) stands in, labeled as such.