How do variance swaps let traders bet on realized volatility?

Question

AcadiFi · Accepted Answer

A variance swap pays the difference between realized variance and a variance strike, times a notional.

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Suppose Harrowmere Capital believes the S&P 500 will move more than implied over three months. They buy a variance swap from Delstrom Derivatives at a strike of 20 vol (variance = 400), $5,000 vega notional. Vega notional converts to variance notional = vega notional / (2 × strike vol) = $5,000 / 40 = $125. Realized vol = 25 → realized variance = 625. Payoff = $125 × (625 − 400) = $28,125.

Dealers hedge variance swaps via static replication using a portfolio of out-of-the-money puts and calls weighted by 1/K² plus a dynamic delta-hedge in the underlying. The replication exploits the result that a log-contract's gamma is proportional to 1/S², making the hedge variance-linear.

Advantages over vanilla options: pure volatility exposure without path-dependency of delta-hedged positions, no dependence on where the underlying ends up. Risks: gap risk from large single-day moves (since squared returns compound), jump risk not captured by the log-contract replication.

How do variance swaps let traders bet on realized volatility?

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