Surface

Quoted Vol

An arbitrage-free volatility surface for quoting SPX, carried by 135 numbers on nine permanent maturities. Butterfly and calendar arbitrage are properties of the construction, not results checked afterwards. It prices any maturity inside the quoted range, listed or not. how it works, and where it fails →

Reading

starting…

This date

Any maturity

What the repair cost

1 · The funding the market is pricing?

Funding and dividend-plus-borrow, from today to each expiry

 

← the figure is wider than this screen — drag it sideways →

2 · The density being quoted?

At the expiry nearest your maturity slider

 

3 · The variance-swap curve?

Spot, and the same swap starting forward

 

4 · One surface, any maturity?

135 numbers. The white smile is decoded at whatever maturity you ask for — listed or not.

 

← the figure is wider than this screen — drag it sideways →

5 · Level and skew, across the grid?

At-the-money volatility and central skew, across the permanent grid

 

← the figure is wider than this screen — drag it sideways →

Eighteen days of SPX chains, chosen around events. Everything drawn here is computed in your browser from the quoted bids and asks; only the linear programs run offline.

No forecast, no regime, no signal. This is the marginal law of one day, in coordinates that survive the expiry cycle. What it costs and where it fails.

Föllmer & Schied, Stochastic Finance Convex order, Kellerer's theorem, and why the calendar condition on discrete laws is a finite test rather than an approximation.
Davis & Hobson (2007) The range of traded option prices — necessary and sufficient conditions for a finite set of quotes to admit no arbitrage. The question this page asks of every adjacent pair.
Breeden & Litzenberger (1978) The risk-neutral density as the second strike-derivative of the call price. Every marginal here starts there, and every difficulty here comes from doing it on real quotes.
Carr & Madan (1998) The log-contract, and why it is an integral of the smile rather than the smile — which is exactly why forward variance cannot certify a condition that must hold at every strike.
Gatheral & Jacquier (2014) Arbitrage-free SVI volatility surfaces. The power-law SSVI tested here and rejected at this granularity: price RMSE 42.08, median 7.12 volatility points.