Variance Swap Pricer
Compute the fair variance-swap strike from an implied-volatility smile by static replication, and see how much of it is the skew and convexity premium.
Interview Q&A — Volatility Trading
43 questions on delta-hedged gamma P&L, variance-swap replication, variance vs volatility swap convexity, and the product family.
A variance swap pays the difference between the realized variance of an underlying and a fixed strike. What makes it special is that its strike is not a forecast — it is a replication price. The realized variance of a diffusion can be manufactured from a static strip of out-of-the-money options plus a delta-one trade, so the fair strike is fully determined by today's option prices. This free calculator runs that replication — the Demeterfi-Derman-Kamal formula, the same one the CBOE uses to compute the VIX.
Why the strike sits above the ATM implied vol
The replication weights each strike by 1/K², which is a geometricfact, not a skew effect: an option's dollar-gamma area grows with K², so 1/K² flattens the strip into constant dollar gamma — the only profile whose delta-hedged P&L is pure realized variance. But those low strikes are exactly where equity skew makes puts expensive, and the squared payoff is convex in volatility. Both effects push the fair variance-swap strike above the at-the-money implied — the gap this tool reports as the skew-and-convexity premium.
How to read it
Set the skew to zero and the fair strike collapses back to the ATM volatility — the acceptance test for the replication. Make the skew negative (the usual equity case) and watch the premium open up, and the cumulative-variance curve steepen through the downside strikes. For the mechanics behind delta-hedged gamma P&L and the variance-vs-volatility swap convexity, the Coach volatility-trading questions work through it in depth; for the smile itself, start from the Heston & SABR models.