Variance Swap - A Pure Forward on Realized Variance
By EC Assets Research Team, Volatility Research · Published · Updated
Variance Swap — A variance swap is a forward contract on realized variance: at maturity it pays the difference between the variance an asset actually realized and an agreed strike, scaled by a notional. It is the cleanest pure-volatility instrument, and its variance (squared) payoff gives it a convexity that makes it also a bet on volatility-of-volatility.
What a Variance Swap Is
A variance swap is a forward contract on realised variance. At inception the two parties agree a strike - the variance level the market is pricing - and at maturity the buyer receives (or pays) the difference between the variance the underlying actually realised and that strike, scaled by a notional. It is the cleanest way to take a direct, pure position on how volatile an asset will be, with none of the path-dependence and constant re-hedging that a delta-hedged option requires.
Payoff = N_var × (σ²_realized − K²_var)
where K_var is the variance strike (often quoted as a "fair volatility", e.g. 20), σ_realized is the volatility actually realised over the life of the swap, and N_var is the variance notional. Buy the swap and you are long volatility: you gain if realised variance exceeds the strike.
Variance, Not Volatility - and Why That Matters
The swap settles on variance (volatility squared), not volatility itself, and that squaring gives it a defining feature: convexity. Because the payoff is in σ², a long variance-swap holder gains more from a rise in volatility than they lose from an equal-sized fall. Big moves help the long disproportionately. This convexity is precisely why variance swaps trade rich to at-the-money implied volatility - the holder is being charged for the favourable asymmetry.
To make the sensitivity intuitive near the strike, desks quote a vega notional, the P&L per one vol point: N_vega ≈ N_var × 2·K_var.
Worked Example
Buy a one-year variance swap with a volatility strike of 20 (so the variance strike is 400) and a vega notional of 100,000. The variance notional is N_var = N_vega / (2·K_var) = 100,000 / 40 = 2,500 per variance point.
If realised volatility comes in at 25 (variance 625): payoff = 2,500 × (625 − 400) = +562,500. If realised volatility comes in at 15 (variance 225): payoff = 2,500 × (225 − 400) = −437,500.
Note the asymmetry: a 5-point rise in volatility paid 562,500, while a 5-point fall cost only 437,500. That gap is the convexity of variance - the structural reason a variance buyer is long not just volatility but volatility-of-volatility.
How It Is Priced and Replicated
The elegant result behind variance swaps is that the fair strike can be replicated model-free by a static portfolio of options - a strike-weighted strip of out-of-the-money puts and calls, each weighted in proportion to 1/K². Holding that strip and delta-hedging it reproduces the realised-variance payoff without assuming any particular volatility model. The VIX is computed from exactly this logic: it is essentially the fair 30-day variance strike of the S&P 500, expressed as a volatility.
[!key] A variance swap pays the gap between realised and implied variance in one clean number, with no path-dependence. It is the instrument that turns "I think the market will be more volatile than priced" into a direct trade - and its convexity means it is also a position on volatility-of-volatility.
When It Works and the Tail Caveat
Selling variance swaps harvests the variance risk premium - the same edge as selling options - and works in calm markets. Buying them is clean crash insurance that pays off precisely when realised volatility explodes. The danger sits with the seller: because the payoff is in variance, a single volatility spike produces a squared, convex loss. The 2008 and 2020 episodes punished short variance brutally, which is why most listed and dealer variance is sold as capped variance swaps (a maximum realised level, often 2.5× the strike) to bound the seller's tail.
[!warning] Short variance is the most convex way to be short volatility. An uncapped short variance-swap position can lose multiples of its premium in a single volatility shock, because losses scale with the square of realised volatility. Treat uncapped short variance as a tail-risk warehouse, not a yield trade.
Why It Matters for Institutional Investors
- Pure volatility exposure. Variance swaps let funds express a view on volatility without the daily delta-hedging burden of options - a cleaner, lower-maintenance vehicle for systematic volatility and dispersion strategies.
- Hedging. Long variance is an effective portfolio hedge: it is cheap in calm times and pays convexly in crises, when correlations spike and other hedges fail.
- Dispersion trading. Selling index variance against buying single-name variance (or vice versa) is a core relative-value volatility trade built entirely on variance swaps, expressing a view on correlation.
- Reading the VIX. Understanding that the VIX is a variance-swap-style construct clarifies what it does and does not say - it is the price of 30-day variance, a risk-neutral expectation inflated by the variance risk premium, not a forecast.
References
- Demeterfi, K., Derman, E., Kamal, M., & Zou, J. (1999). More Than You Ever Wanted to Know About Volatility Swaps. Goldman Sachs Quantitative Strategies Research Notes.
- Carr, P., & Madan, D. (1998). Towards a Theory of Volatility Trading. In Volatility (Risk Publications).
- Bossu, S., Strasser, E., & Guichard, R. (2005). Just What You Need to Know About Variance Swaps. JPMorgan Equity Derivatives.
- Cboe. VIX White Paper: The Cboe Volatility Index. Cboe Global Markets. (https://www.cboe.com/vix)
Frequently asked questions
What is the difference between a variance swap and a volatility swap?
A variance swap settles on realised variance (volatility squared); a volatility swap settles on realised volatility directly. The variance swap is more common because it can be replicated cleanly with a static strip of options, but it carries convexity - it gains more from a vol rise than it loses from an equal fall - which a volatility swap does not.
Why do variance swaps trade above at-the-money implied volatility?
Because of convexity. The variance payoff rewards large moves disproportionately, and it places weight on out-of-the-money options across all strikes, including the richly priced put wing. The buyer pays for that favourable asymmetry, so the variance strike sits above the at-the-money implied volatility.
How is a variance swap replicated?
By a static, strike-weighted portfolio of out-of-the-money options - puts below the forward and calls above it - each weighted in proportion to 1/K², combined with a delta hedge. This replication is model-free, which is why variance swaps and the VIX can be priced without assuming a particular volatility model.
Why is selling variance swaps so dangerous?
Because losses scale with the square of realised volatility. A volatility spike produces a convex, squared loss that can run to many times the premium collected. Episodes like 2008 and 2020 inflicted catastrophic losses on short-variance positions, which is why most are sold in capped form that limits the maximum realised level.
How is a variance swap related to the VIX?
The VIX is essentially the fair strike of a 30-day variance swap on the S&P 500, expressed as a volatility. It is computed from the same 1/K²-weighted strip of options that prices a variance swap, which is why the VIX is best understood as the price of 30-day variance rather than a forecast of it.
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