# Variance and Volatility Swaps > Variance swaps pay the difference between realised variance and a fixed strike. Learn how variance and volatility swaps work, how they are priced and their risks. Source: https://learn.tradelabsai.com/volatility/variance-and-volatility-swaps/ Track: Volatility · Level: Advanced · Updated: 2026-10-03 Publisher: TradeLabs AI (https://tradelabsai.com). Education, not financial advice. Cite as: TradeLabs Learn, "Variance and Volatility Swaps", https://learn.tradelabsai.com/volatility/variance-and-volatility-swaps/ A variance swap is a contract that pays the difference between the realised variance of an asset over a period and a fixed variance level agreed at the start. A volatility swap does the same with volatility (the square root of variance). Unlike options, these swaps give exposure to realised volatility without any need to delta hedge and without depending on where the price ends up. They are mostly traded over the counter between banks and institutions, especially on equity indices. ## How a variance swap works At maturity, the payoff to the buyer (long variance) is: ``` payoff = variance notional × (σ²_realised - K²_var) ``` - **σ_realised:** annualised realised volatility over the period, computed from daily log returns. - **K_var:** the strike, quoted in volatility points. - **Variance notional:** usually set from a vega notional: variance notional = vega notional / (2 × K_var). **Example: A one year variance swap** A trader buys a one year S&P 500 variance swap with a strike of 20 and a vega notional of $100,000. Variance notional = 100,000 / (2 × 20) = $2,500 per variance point. - **Realised volatility 25:** payoff = 2,500 × (625 minus 400) = $562,500. - **Realised volatility 15:** payoff = 2,500 × (225 minus 400) = minus $437,500. - **Realised volatility 40 (a crisis year):** payoff = 2,500 × (1,600 minus 400) = $3,000,000. Because the payoff is in variance (volatility squared), gains grow faster than losses: a 5 point rise earns more than a 5 point fall loses. For short variance positions, that convexity works against you. ## Volatility swaps A volatility swap pays vega notional × (σ_realised minus K_vol). The payoff is linear in volatility, which is easier to understand, but volatility swaps are harder to hedge and price. Because of convexity, the fair volatility swap strike is slightly below the variance swap strike for the same period. ## How variance swaps are priced A key result, developed in work by Demeterfi, Derman, Kamal and Zou at Goldman Sachs (1999) and others, is that variance can be replicated with a portfolio of out of the money options across all strikes, weighted by 1/K², plus a delta hedge. The fair variance strike can be read from the option prices: ``` K²_var ≈ (2 / T) × Σ (ΔK / K²) × e^(rT) × Q(K) ``` where Q(K) is the price of the out of the money option at each strike. This is essentially the same calculation Cboe uses for the VIX, which is why the VIX squared approximates the 30 day S&P 500 variance swap rate. See [The VIX](https://learn.tradelabsai.com/volatility/the-vix/). Because the replication puts weight on far out of the money puts, variance swap strikes on equity indices sit above at the money implied volatility, reflecting the skew. See [Volatility Smile and Skew](https://learn.tradelabsai.com/volatility/volatility-smile-and-skew/). ## Uses - **Pure volatility views:** profit from realised volatility without delta hedging. See [Volatility Trading](https://learn.tradelabsai.com/volatility/volatility-trading/). - **Volatility risk premium harvesting:** selling variance has historically earned a premium on average. See [Theta Harvesting](https://learn.tradelabsai.com/options/theta-harvesting/). - **Hedging:** long variance protects against volatile, crashing markets. - **Relative value:** comparing variance swaps with options, across indices, or across maturities. See [Dispersion and Correlation Trading](https://learn.tradelabsai.com/volatility/dispersion-trading/). ## Risks - **Short variance tail risk:** in a crash, realised variance can explode. Many dealers and funds selling variance suffered heavy losses in 2008, after which the market shrank and caps became standard. - **Caps:** most single stock variance swaps, and many index ones, now cap realised variance at a multiple of the strike (often 2.5 times the strike in volatility terms), limiting losses for sellers and gains for buyers. - **Jumps:** replication assumes continuous prices; large gaps break the hedge for dealers. See [Fat Tails](https://learn.tradelabsai.com/math/fat-tails/). - **Liquidity and counterparty risk:** over the counter contracts depend on the counterparty. See [Market, Credit and Counterparty Risk](https://learn.tradelabsai.com/portfolio/counterparty-risk/). - **Realised volatility calculation details:** missing days, market closures and dividend adjustments are defined in the contract. ## Listed alternatives VIX futures give exposure to forward implied volatility, not realised volatility. Some exchanges have listed variance futures at times, but liquidity has been limited compared with the over the counter market. ## Frequently asked questions ### What is a variance swap? A contract that pays the difference between the realised variance of an asset over a period and a fixed variance strike, multiplied by a notional. ### What is the difference between a variance swap and a volatility swap? A variance swap pays on volatility squared, giving convex payoffs; a volatility swap pays linearly on volatility and is harder to hedge. ### How is the VIX related to variance swaps? The VIX is calculated with a method closely related to variance swap replication, so VIX squared approximates the fair 30 day variance swap rate on the S&P 500. You have finished the Volatility track. Continue with futures, starting with [How Futures Contracts Work](https://learn.tradelabsai.com/futures/how-futures-contracts-work/). ## Continue learning - Previous lesson: [Volatility Arbitrage](https://learn.tradelabsai.com/volatility/volatility-arbitrage/) - Related: [Volatility Arbitrage](https://learn.tradelabsai.com/volatility/volatility-arbitrage/): Volatility arbitrage trades the gap between implied volatility and a forecast of realised volatility with delta hedged options. Learn how it works and its risks. - Related: [The VIX](https://learn.tradelabsai.com/volatility/the-vix/): The VIX measures expected 30 day volatility of the S&P 500 from option prices. Learn how it is calculated, what levels mean, VIX futures and how traders use it. - Related: [Volatility Trading](https://learn.tradelabsai.com/volatility/volatility-trading/): Volatility trading profits from the size of price moves, not their direction. Learn implied vs realised bets, the main instruments and how to manage risk. - Related: [Historical and Realized Volatility](https://learn.tradelabsai.com/volatility/historical-volatility/): Historical volatility measures how much a price actually moved, using past returns. Learn the standard formula, range based estimators and how traders use it. - Related: [Fat Tails](https://learn.tradelabsai.com/math/fat-tails/): Fat tails mean extreme market moves happen far more often than the normal curve predicts. Learn the evidence, the causes, how to measure them and how to manage them.