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

What is a Volatility Swap?

A volatility swap is a derivative contract that pays the difference between realized volatility and a fixed volatility strike. Unlike a variance swap, which pays on variance (volatility squared), a volatility swap pays linearly on volatility itself. This makes it a cleaner instrument for traders who want direct exposure to realized volatility without the convexity overweighting of large moves that variance swaps impose. One party pays a fixed strike and receives annualized realized volatility over the contract term; the other party takes the opposite position. Volatility swaps are primarily over-the-counter instruments used by institutional traders and market makers.

How a Volatility Swap is Calculated

The payoff at expiration is:

Payoff = Notional × (Realized Volatility − Volatility Strike)

Realized volatility is calculated as the annualized standard deviation of daily log returns:

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

where n is the number of return observations, Sₜ is the closing price on day t, and 252 annualizes the daily figure. The volatility strike is set at inception so the swap has zero initial value, typically derived from the fair value of a variance strip or options portfolio.

Worked Example

A trader sells a three-month volatility swap on QQQ with a notional of $200,000 per volatility point and a strike of 22. Over the contract period, QQQ realizes annualized volatility of 18.

Payoff to the seller = $200,000 × (22 − 18) = $80,000

The seller keeps the difference because realized volatility came in below the strike. If realized volatility had been 26, the seller would pay $80,000. Because the payoff is linear in volatility, a move from 20 to 25 has the same dollar impact as a move from 30 to 35, unlike a variance swap where higher volatility levels are penalized more heavily.

When Traders Use It

Volatility swaps are used to express a pure view on realized volatility without directional risk. They are common in relative value strategies where traders compare realized volatility across assets or between implied and realized volatility. Market makers use them to hedge vega exposure in options books. Because they are OTC contracts, retail traders rarely access them directly, but they can approximate exposure using options strips or volatility ETFs, though with tracking and rebalancing differences. the live scanner

Limitations and Common Misconceptions

A volatility swap is not a variance swap. The linear payoff means it underweights extreme moves relative to variance swaps, which can be either an advantage or a disadvantage depending on the trader’s view. The contract is sensitive to the sampling method and frequency of realized volatility, and early termination can be costly. OTC counterparty risk and collateral requirements are significant. Traders should not assume a volatility swap tracks the VIX or any other published volatility index; it is based on the realized volatility of a specific underlying over a specific window.

Related Terms

variance swap, realized volatility, implied volatility, vix, vega