Variance swap — overview
A variance swap is an over‑the‑counter derivative that lets two parties exchange payments tied to the realized variance (the square of volatility) of an underlying asset over a specified period. It provides a direct, cash‑settled exposure to how much the asset’s price moves, without taking a directional position in the asset itself.
How it works
- At contract initiation a fixed strike (often expressed as an annualized variance) and a variance notional are agreed.
- At maturity the realized variance over the contract period is measured (typically from daily log returns and annualized).
- The payoff to the long side is:
variance_notional × (realized_variance − strike_variance).
If realized variance exceeds the strike, the long receives a cash payment; if it is lower, the long pays. - Trades are settled in cash. Margining may occur during the life of the swap if mark‑to‑market exposures breach limits.
Mathematical intuition
- Variance is the average of squared deviations (roughly the mean of squared log returns). Annualized realized variance is commonly used.
- Volatility (standard deviation) is the square root of variance. Because variance squares returns, variance swaps amplify the impact of large price moves compared with volatility swaps.
Example: If a contract’s strike variance = 0.04 (implied volatility 20% → 0.20² = 0.04) and realized variance = 0.09 (30% vol → 0.30² = 0.09), the payoff equals variance_notional × (0.09 − 0.04).
Differences from volatility swaps and options
- Variance vs volatility swap: A variance swap pays based on variance; a volatility swap pays based on volatility (the square root). For the same underlying path, a variance swap’s payout is typically larger and more sensitive to large jumps.
- Versus options: Options expose traders to both volatility and directional price risk. Replicating a pure variance exposure with options requires a dynamic strip of options and hedging; variance swaps provide a more direct, static exposure without the same delta‑hedging needs. Replication of a variance swap can be approximated with a continuum (strip) of options across strikes.
Typical users
- Directional traders: speculate on future levels of realized volatility.
- Spread traders: trade the difference between realized volatility and implied volatility.
- Hedgers: manage risks from short volatility exposures (e.g., sellers of options).
Risks and considerations
- Jump risk: Large discrete price moves inflate realized variance disproportionately, producing unexpected payouts.
- Path dependence and model risk: Measurement method (sampling frequency, treatment of jumps) and assumptions affect payoff.
- Market and liquidity risk: Variance swaps are OTC instruments and can be less liquid or harder to price than exchange‑traded instruments.
- Counterparty risk: OTC settlement exposes participants to counterparty default risk (mitigated by collateral agreements).
Practical notes
- Strike setting: The strike is typically set so that the initial net present value is zero, based on prevailing implied variance.
- Notionals: Traders specify a variance notional (amount paid per point of variance) rather than a notional on the underlying price.
- Use cases: Efficient for pure volatility bets or hedges when one wants to avoid directional exposure and repeated hedging complexity.
Key takeaways
- A variance swap is a cash‑settled contract that pays based on realized variance minus a pre‑set strike.
- It provides pure volatility exposure, is more sensitive to large price moves than volatility swaps, and avoids the directional and hedging complexities associated with options.
- Important risks include jump sensitivity, measurement details, liquidity, and counterparty exposure.