Variance swap
A variance swap is an over-the-counter contract that pays the difference between the realized variance of an underlying over its life and a strike agreed at inception, times a notional. Its fair strike can be replicated with a strip of out-of-the-money options weighted by 1/K², the same construction behind the VIX.
Senzoukria · Glossary · Updated September 2026
At a glance
- Payoff
- N_var × (σ²_realized − K_var)
- Vega notional
- N_vega = N_var × 2 × K_vol
- Replication
- Out-of-the-money options weighted by 1/K² (plus a forward position)
Payoff
At maturity, the buyer receives the variance notional times the difference between the annualised realized variance of daily log returns and the variance strike. Strikes are usually quoted in volatility terms, K_vol, with K_var = K_vol². Because the payoff is in variance, it is convex in volatility: gains when realized volatility exceeds the strike grow faster than losses when it falls short. Contracts are often sized by vega notional, the approximate gain per volatility point near the strike, equal to N_var × 2 × K_vol.
Worked example
A variance swap struck at 20 volatility with a vega notional of 100,000 dollars has a variance notional of 100,000/(2 × 20) = 2,500 dollars per variance point. If realized volatility is 25, the buyer receives 2,500 × (625 − 400) = 562,500 dollars. If it is 15, the buyer pays 2,500 × (400 − 225) = 437,500 dollars. The same 5-point deviation produces an asymmetric result: that is the convexity.
| Realized volatility | Realized variance | Payoff to buyer |
|---|---|---|
| 15 | 225 | −437,500 dollars |
| 20 | 400 | 0 |
| 25 | 625 | +562,500 dollars |
Replication and the VIX
A portfolio of out-of-the-money puts and calls across all strikes, each weighted by the inverse of its strike squared, has a value proportional to the market's risk-neutral expected variance, which gives the fair variance strike. The Cboe VIX formula applies this construction to SPX options and cites the research on volatility swaps behind it; the squared VIX divided by 10,000 approximates the 30-day fair variance of the S&P 500. In practice the strip is finite and discrete, and jumps make the replication imperfect.
- Because the strip includes deep out-of-the-money puts, fair variance usually exceeds at-the-money implied variance on equity indices.
- Short variance positions carry large losses in crashes; capped variance swaps were developed to limit that exposure.
Relevance and the Senzoukria view
Futures traders rarely trade variance swaps, but the concept explains what the VIX measures and why its level sits above at-the-money volatility. Senzoukria does not price variance swaps. Its realized-volatility tools, such as the Realized Vol chart indicator, measure the realized side of the comparison, and its GEX module shows the implied volatility smile from which a strip could be built.
Related
In the same section
- Short volatility
- Variation margin
- Vanna and charm flows
- Vega
- Vanna
- Vega exposure
- Value migration
- Velocity logic
Sources
This page in other languages
Frequently asked questions
- Why trade variance rather than volatility?
- Because variance can be replicated statically with options and a forward position, while a pure volatility payoff cannot. The price of that tractability is convexity: the payoff grows with the square of realized volatility.
- Is the VIX a variance swap rate?
- Approximately. The VIX squared divided by 10,000 corresponds to the 30-day variance implied by the SPX option strip used in its calculation, which is the fair strike of a theoretical variance swap on the index, subject to discretization and to how the strip is truncated.