What is a Variance Swap? Definition, Formula, and Example

What is a Variance Swap?

A variance swap is a derivative contract that allows traders to speculate on or hedge the realized variance of an underlying asset without taking directional exposure. One party pays a fixed strike price (the variance strike) and receives the realized variance of the underlying over the contract term. The other party takes the opposite side. Unlike a volatility swap, which pays on the square root of variance, a variance swap pays linearly on variance itself, making it sensitive to large moves. Variance swaps are used by institutional traders and market makers to trade volatility directly, though synthetic versions can be constructed with listed options.

How a Variance Swap is Calculated

The payoff at expiration is:

Payoff = Notional × (Realized Variance − Variance Strike)

Realized variance is typically calculated as the sum of squared daily log returns over the contract period:

Realized Variance = (252 / n) × Σ (ln(Sₜ / Sₜ₋₁))²

where n is the number of observations and Sₜ is the closing price on day t. The annualization factor of 252 converts daily variance to annualized variance. The fair variance strike is set so that the swap has zero value at inception, derived from a strip of out-of-the-money options on the underlying.

Worked Example

A trader buys a one-month variance swap on SPY with a notional of $100,000 per variance point and a strike of 400 (which corresponds to 20% annualized volatility, since 20² = 400). Over the month, SPY realizes daily returns that produce an annualized realized variance of 625 (25% volatility).

Payoff = $100,000 × (625 − 400) = $22,500

The trader receives $22,500 at expiration. If realized variance had been 225 (15% volatility), the trader would pay $17,500. Because variance swaps pay on squared returns, a few large moves dominate the payoff; a single 5% day contributes far more than ten 0.5% days.

When Traders Use It

Variance swaps are used to trade the difference between implied and realized volatility, to hedge tail risk, and to construct dispersion trades where index variance is sold and single-stock variance is bought. They are also used by market makers to hedge options books. Because listed variance swaps are not widely available to retail traders, many replicate them using a strip of options weighted inversely to the square of the strike, though this requires frequent rebalancing. the live scanner

Limitations and Common Misconceptions

A variance swap is not the same as a volatility swap. Because it pays on variance, not standard deviation, it is more sensitive to extreme moves and has a different convexity profile. The contract is path-dependent and sensitive to the sampling frequency of realized variance. Retail traders face significant counterparty and margin risk if trading OTC versions, and synthetic replication carries roll and slippage costs. A low variance strike does not mean the underlying is calm; it only means the market is pricing low realized variance at inception.

Related Terms

realized volatility, implied volatility, volatility swap, dispersion trade, vix