Variance Swap
A variance swap is an over-the-counter derivative contract in which two counterparties exchange a fixed payment (the strike variance) for the realized variance of an underlying asset over the life of the contract, providing pure exposure to volatility without requiring delta-hedging.
Variance swaps allow traders and portfolio managers to take a direct position on the future realized volatility of an index or individual equity without holding a complex options portfolio. The payoff at expiration is the notional amount multiplied by the difference between realized variance and the strike variance agreed at inception. If realized variance exceeds the strike, the buyer receives a net payment; if realized variance falls short, the seller collects the difference.
Variance is defined as the square of volatility, which means variance swaps have convex payoffs relative to volatility itself. A volatility swap offers linear exposure, but a variance swap pays out more per unit of volatility increase when volatility is already high, because variance grows as the square of volatility. This convexity makes variance swaps particularly attractive to hedge funds expecting tail risk scenarios where volatility spikes sharply.
The strike price on a variance swap is typically set near the prevailing implied volatility level, derived from a model-free replication formula that synthesizes a strip of options across all strikes. This replication approach, developed in academic work that underlies the CBOE VIX methodology, means the variance strike essentially reflects the cost of owning the entire implied volatility surface rather than a single strike or maturity.
In the U.S. market, variance swaps on the S&P 500 index and individual large-cap equities trade in the OTC dealer market, subject to CFTC oversight as swaps under the Dodd-Frank Act. Dealer banks such as Goldman Sachs, Morgan Stanley, and JPMorgan act as market-makers, quoting strikes in volatility terms for clarity even though the actual payoff is variance-denominated. Notional sizes are quoted as vega notional, converting variance payoffs back into approximate dollar gains per point of volatility for ease of sizing.
The variance risk premium — the persistent gap between implied variance and subsequently realized variance — is the primary reason dealers willingly sell variance swaps. On average, implied variance has exceeded realized variance in the S&P 500 over long horizons, meaning systematic variance sellers collect a premium. Long-volatility hedge funds and tail-risk programs take the opposite side, accepting the average cost of the premium in exchange for large payoffs during crisis periods such as the 2008 financial crisis, the COVID-19 selloff in March 2020, and other vol spikes captured by the CBOE VIX index.