A volatility swap pays on the difference between annualized realized volatility and a fixed strike, using a defined currency amount per volatility point.
A volatility swap is a derivative contract whose cash settlement depends on the difference between an underlying asset’s annualized realized volatility and a fixed volatility strike. A long-volatility buyer receives money when realized volatility finishes above the strike and pays when it finishes below the strike, subject to the contract’s notional, cap, and calculation terms.
The strike is agreed when the trade is executed. Option-implied volatility helps inform that strike, but the strike is not simply “the implied volatility” of one option.
| Term | What it controls |
|---|---|
| Underlying | The stock, index, currency, rate, commodity, or basket whose returns are measured |
| Observation period | The dates over which realized volatility is calculated |
| Observation schedule | Daily or other specified price observations |
| Volatility strike | Fixed annualized volatility level agreed at inception |
| Volatility or vega notional | Currency amount gained or lost for each volatility-point difference |
| Cap or floor | Contractual limit on recognized volatility or settlement, if any |
| Settlement terms | Valuation date, payment date, currency, and cash-flow direction |
| Disruption provisions | Treatment of missing prices, exchange closures, and extraordinary events |
A trade described only as “one-year index volatility” is incomplete. The exact observation and adjustment rules determine the floating value.
For a long-volatility position:
where:
The short-volatility payoff is the negative of this amount. Filed specifications may call (N_{\text{vol}}) vega notional, although this cash-flow multiplier should not be confused with every use of option vega. If the contract instead states volatility in decimals, all inputs and the notional must use that convention consistently. Mixing 0.20 with 20 volatility points creates a 100-fold unit error.
Suppose a swap is quoted at USD 10,000 per volatility point with a 20-point strike. Each one-point change in final realized volatility changes the settlement by USD 10,000:
| Realized volatility | Difference from strike | Long-volatility payoff |
|---|---|---|
| 12 points | -8 points | -USD 80,000 |
| 20 points | 0 points | USD 0 |
| 27 points | +7 points | +USD 70,000 |
| 35 points | +15 points | +USD 150,000 |
The contractual break-even before fees, funding, collateral remuneration, taxes, or unwind costs is the 20-point strike. The economic break-even can be higher for the buyer after those costs.
Because realized volatility cannot be negative, the long side’s lowest simplified settlement without another adjustment is:
For the example, that is -USD 200,000. The upper settlement is not similarly bounded unless the contract has a volatility cap or payment cap. This payoff bound does not limit losses or liquidity demands arising from other positions, closeout terms, or a counterparty default.
Realized volatility is the square root of realized variance. If observed prices are (S_0,S_1,\ldots,S_n), a log return is:
Under one simplified zero-mean convention:
where (A) is the annualization factor and multiplying by 100 expresses the result in volatility points. A result of 20 means 20% annualized volatility.
The governing formula may use different mean, denominator, observation-count, holiday, or disruption rules. Some contracts also prescribe treatment for stale prices, market closures, corporate actions, or early termination. Realized volatility should therefore be reproduced from the confirmation, not inferred from a charting platform’s default setting.
Volatility should not ordinarily be averaged arithmetically across periods. Variance aggregates first; volatility is then the square root of the combined variance.
Assume a one-year observation period has equal numbers of observations in two halves. Realized volatility is 30% annualized in the first half and 10% annualized in the second. Under a simplified equal-weight convention, full-period variance is:
Therefore, full-period realized volatility is:
The answer is not the 20% arithmetic average of 30% and 10%. With a 20-point strike and USD 10,000 per point, the simplified long-volatility payoff is approximately:
The example assumes equal observation weights and identical annualization conventions. Actual settlement must be rebuilt from the contract’s individual price observations.
| Contract choice | Potential effect |
|---|---|
| Log returns versus simple returns | Changes each measured observation |
| Zero mean versus sample-mean adjustment | Changes measured variance before taking its square root |
| Actual versus expected observation count | Changes annualization when observations are missing |
| Closing price versus special settlement value | Can change the final return materially |
| Dividend or corporate-action adjustment | Can prevent or create measured moves around ex-dates |
| Immediate versus forward start | Determines which price changes enter the calculation |
| Disrupted-day treatment | May omit, postpone, or replace an observation |
For review or dispute work, preserve source prices, timestamps, index versions, observation counts, adjustment notices, and the calculation output. A chart’s displayed historical volatility is not sufficient evidence unless its methodology matches the confirmation.
Assume a one-year long volatility swap has:
The payoff is:
The long-volatility buyer receives USD 50,000. If realized volatility finishes at 16 points instead, the payoff is:
The buyer then pays USD 40,000. These simplified calculations exclude collateral, discounting, fees, cap effects, and early termination.
Implied volatility is backed out from an option price for a particular strike and maturity under a pricing model. An underlying can have many implied volatilities at once because options across strikes form a volatility smile or skew.
A volatility-swap strike is one fixed contractual number for the swap’s observation period. Dealers may use the wider option surface, expected future variance, replication costs, convexity, liquidity, and supply and demand to determine it.
The strike should not be described as the current at-the-money implied volatility without qualification. Even if an at-the-money quote and a swap strike happen to be close, they represent different contracts and exposures.
Volatility is the square root of variance. Because the square-root function is nonlinear, the fair volatility-swap strike is generally not obtained by simply taking the square root of a fair variance-swap strike. The difference is commonly associated with a convexity adjustment.
This distinction also affects hedging. Under idealized assumptions, a variance payoff has a close relationship to a broad strip of options. A volatility payoff applies a square root to realized variance, making direct replication more difficult and model-dependent.
Suppose there are only two equally likely variance outcomes: 100 variance points or 900 variance points. These correspond to realized volatilities of 10 and 30 points.
The 2.36-point difference appears because taking an expectation and taking a square root do not commute. Since the square-root function is concave, the expected square root is no greater than the square root of the expected value. This is the core intuition behind the convexity adjustment between volatility and variance strikes.
This two-outcome example is not a pricing model. Market-implied probabilities, discounting, caps, jumps, volatility-surface dynamics, hedging costs, and risk premiums also affect an executable strike.
Assume the worked trade has a 35-point realized-volatility cap. The recognized volatility is:
If observed realized volatility reaches 42 points, settlement still uses 35 under this hypothetical term. The long side receives USD 150,000 rather than USD 220,000:
A cap on recognized volatility is not the same as a separate dollar-payment cap. The confirmation must state which variable is limited and how the cap interacts with disrupted observations and early termination.
| Feature | Volatility swap | Variance swap |
|---|---|---|
| Floating measure | Realized volatility | Realized volatility squared |
| Simplified payoff | Linear in volatility | Convex in volatility |
| Common size unit | Currency per volatility point | Currency per variance point or converted vega notional |
| Response to extreme moves | Direct through final realized volatility | Magnified through squared returns |
| Replication | More model-dependent | More directly linked to an option strip under idealized assumptions |
With a strike of 20, compare the unscaled payoff differences:
| Realized volatility | Volatility-swap difference | Variance-swap difference |
|---|---|---|
| 10 | (-10) | (10^2-20^2=-300) |
| 20 | (0) | (0) |
| 30 | (+10) | (30^2-20^2=+500) |
These are payoff units, not comparable dollar amounts. Each contract requires its own notional convention.
| Instrument | What primarily drives payoff | Important distinction |
|---|---|---|
| Volatility swap | Realized volatility over a defined period | OTC terms and linear final-volatility payoff |
| Variance swap | Realized variance over a defined period | Convex exposure to volatility |
| Option | Underlying price relative to strike, with time and volatility effects | Payoff is directional and nonlinear in price |
| VIX future | Futures price settling under the VIX methodology | Standardized exposure to a forward-looking option-implied volatility index, not the swap’s realized-volatility series |
A delta-hedged option position can have volatility exposure, but its outcome also depends on gamma, vega, theta, transaction costs, discrete hedging, and the path of the underlying. A volatility swap packages a different contract-defined exposure.
The VIX Index measures the option-implied market expectation of 30-day S&P 500 volatility under Cboe’s methodology. A VIX future settles through a special VIX quotation. Neither is a contract to pay the realized volatility of an arbitrary stock or portfolio over the same dates as a customized volatility swap.
Expressing a realized-volatility view. A trader can take a position on whether realized volatility will finish above or below a fixed strike.
Hedging volatility-sensitive portfolios. Long volatility may offset some losses in portfolios exposed to market turbulence, but the match depends on the underlying, horizon, path, and contract terms.
Relative-value analysis. Participants can compare volatility across assets, maturities, or related option markets. Different measurement and liquidity conventions prevent these comparisons from being risk-free arbitrage.
Separating direction from movement magnitude. The payoff does not directly depend on whether returns are positive or negative. However, volatility often changes asymmetrically with market direction, so practical exposures are not completely independent of directional conditions.
Final price alone does not determine realized volatility. Two paths can start and finish at the same values but produce very different volatility:
Timing also matters. A severe move before the observation period does not enter the calculation. A late large move can materially change the final annualized result. A position can also show a large interim mark-to-market gain and later settle below strike if subsequent observations are calm.
Partway through the contract, observed squared returns are known, but final realized volatility is not. The valuation must combine accrued realized variance with a distribution for remaining variance and then apply the square root, cap, discounting, and closeout terms.
This is more than adding “realized volatility so far” to “expected volatility later.” As the two-subperiod example shows, variance combines across time before the square root is taken. The nonlinear step makes interim value sensitive to the distribution of future variance, not only a single average forecast.
A large early move can increase expected settlement and trigger collateral from the short side. Later calm observations can dilute its annualized effect, so an interim gain is not the same as final cash settlement. Collateral reduces unsecured exposure but does not guarantee liquidity, eliminate gap risk, or make a bespoke position easy to replace.
The U.S. regulatory classification depends partly on the reference. A volatility swap based on a single security or narrow-based security index can fall under the SEC security-based-swap framework. A volatility swap based on a broad-based index or another non-security reference can fall under the CFTC swap framework. Product terms and current rules determine the result.
This article is general financial education, not personalized investment, trading, or legal advice. Volatility swaps are complex leveraged derivatives whose calculation and governing documentation determine the actual exposure.