Vol Surface Lab

Today against its own year

Where the current readings sit in their own twelve-month distribution. A level says little on its own — 34% implied volatility is high for equities and quiet for bitcoin — so the range it comes from is the context.

Since this page started measuring

One reading per day, written by the daily run. Each series keeps its own scale: they share a time axis, not a unit.

The implied volatility surface

Surface

Implied volatility across log-moneyness k = ln(K/F) and expiry, from an SVI fit per slice. Cells outside the strike range each expiry actually quotes are dimmed: there the surface is extrapolation, not price.

Smile detail

Exchange marks against the calibrated slice, with the fit residual below in vol points — the unit that can be compared against the bid-ask width.

Term structure

ATM vs model-free, log time axis

At-the-money implied volatility against the fair variance-swap strike. The gap between them is the convexity of the smile — the part of the price that ATM vol cannot see.

Wing structure and skew

25-delta risk reversal & butterfly

RR25 is the difference between the 25-delta call and put volatilities: what the market charges for asymmetry, largely independent of the level of vol. BF25 is the average wing over the ATM: what it charges for convexity.

Variance risk premium

By expiry

Fair variance-swap strike against realized volatility over a matched trailing window. The bar between them is the premium; the t-column is that premium in standard errors of the realized leg alone.

Ex post, through time

DVOL on each date against the variance actually realized over the following 30 days. The shaded band is the premium the variance seller was paid — filled toward the seller when positive, against them when negative.

Risk-neutral density

Breeden–Litzenberger

Market-implied price cone

The same distributions read across time: where the option market prices the terminal price of each listed expiry. It is not a forecast. This is the risk-neutral measure — what the market charges, premium included — so its mean is the forward by construction, and demand for crash protection fattens the lower band beyond any real-world estimate of it.

The second derivative of the call price with respect to strike is the risk-neutral density; the first derivative is the probability of finishing above a level. Both are exact identities, differentiated off the calibrated smile rather than off raw quotes.

q(K) = e^rT · ∂²C/∂K² Q(S_T > X) = −e^rT · ∂C/∂K |_K=X

Positioning

Open interest by strike: how many contracts are outstanding, and where. Calls above the axis, puts below. This is the one panel that does not come from the fit — it reads the raw chain, in-the-money strikes included.

Calibration and arbitrage diagnostics

every claim above depends on these

A density read off a slice that violates the butterfly condition is meaningless, so the checks run before the results rather than after. Durrleman's g(k) ≥ 0 is the butterfly condition; total variance non-decreasing in maturity is the calendar condition; Roger Lee's moment formula caps wing slopes at 2.