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Volatility Swap: Payoff, Convexity, and Variance-Swap Differences

Understand a volatility swap's linear realized-volatility payoff, contract conventions, convexity adjustment, and differences from variance swaps and listed options.

Updated

For educational purposes only; not investment advice. Investing may result in loss.

Direct answer

A volatility swap is typically a customized, cash-settled over-the-counter derivative whose long side receives or pays an amount approximately linear in an agreed measure of realized volatility:

long payoff = N_vol × (σ_realized − K_vol)

K_vol is the volatility strike and N_vol is cash per volatility point, often called Vega notional in the confirmation. If realized volatility finishes above the strike, the long side receives; if it finishes below, the long side pays, subject to any cap, floor, disruption, collateral, and close-out terms.

The legal confirmation controls the underlying, observation window, price source, return definition, annualization, corporate-action treatment, calculation agent, settlement date, and early termination. A volatility swap is not one standardized U.S. listed equity option, and bilateral swap protections should not be inferred from listed-option clearing rules.

This page describes the product generally, not a live quote or an offer. Availability, eligible counterparties and accounts, collateral or margin, reporting, tax, and legal treatment vary by product, market, dealer, account type, and jurisdiction. Examples are illustrative as of 2026-08-23. Historical data, index methodologies, and model outputs apply only to their stated dates, inputs, sampling rules, and assumptions; they do not determine an executable price or a particular contract’s settlement. Nothing here is individualized investment, legal, or tax advice.

Why volatility is not variance

Realized variance commonly takes a form such as:

V_realized = A/N × Σ[ln(S_i/S_(i−1))]²

and realized volatility is σ_realized = √V_realized. The exact A, observations, holidays, missing prices, and return adjustments come from the confirmation. Under point quotation, one point means one percentage point, so 30% − 25% = 5 points, not 0.05 points.

A variance swap pays linearly in V_realized − K_var, while a volatility swap pays linearly in √V_realized − K_vol. Because square root is nonlinear, the square root of a fair variance strike generally is not a fair volatility strike:

E[√V] ≠ √E[V]

This gap is commonly called a convexity adjustment. Its size depends on the risk-neutral distribution of future realized variance, including volatility-of-volatility, skew, and jumps. A strip of options supports idealized variance replication, but transforming variance into a square-root payoff introduces additional model and dynamic-hedging risk. Finite strikes, discrete trading, transaction costs, and market discontinuities add further error.

Do not confuse contractual Vega notional with an option’s local Vega Greek. N_vol directly converts settlement points into cash; option Vega is a model-based sensitivity that changes with market state and inputs.

Settlement and notional conversion

Assume a long volatility swap has:

  • volatility strike K_vol = 25%;
  • notional N_vol = $10,000 per volatility point;
  • realized volatility at maturity σ_realized = 30%.

Then:

payoff = $10,000 × (30 − 25) = $50,000

If realized volatility were 21%, the uncapped long payoff would be $10,000 × (21 − 25) = −$40,000. Percentages are converted to points according to the confirmation; multiplying $10,000 × 0.05 would understate the first payoff by a factor of 100.

For comparison, 25%² = 625 variance points and 30%² = 900 variance points. Under a matching simplified convention, a variance swap would settle on a 275 variance-point difference, but variance notional uses a different unit. Equal-looking notionals do not create equal cash risk.

Contract and risk checklist

  • Read the confirmation: underlying, observation window, price source, holidays, annualization, return type, caps, floors, and payment mechanics.
  • Verify whether quotes and payoff use decimal volatility or volatility points before converting cash.
  • Separate volatility notional, variance notional, option Vega, and gross contractual notional.
  • Recalculate realized volatility from the contract’s exact price series and adjustment rules.
  • Stress jumps, clustered returns, volatility-of-volatility, missing observations, market disruption, and corporate actions.
  • Model the convexity adjustment; do not set K_vol = √K_var without explicit assumptions and evidence.
  • Include skew, wings, discrete strikes, transaction costs, and rebalancing error in any option-based hedge.
  • Assess counterparty, collateral, close-out, valuation-dispute, liquidity, funding, and legal-documentation risk.
  • Check mark-to-market exposure before maturity; a linear terminal payoff does not imply a stable interim value.
  • Do not assume OCC clearing protections apply to a bilateral OTC swap.
  • Compare alternatives only after normalizing horizon, sampling, annualization, caps, and cash units.

Common misconceptions

  • “A volatility swap is a listed option strategy.” It is generally a separately documented OTC derivative.
  • “The fair volatility strike is the square root of the variance strike.” The expectation and square root do not commute.
  • “Vega notional is the same as option Vega.” One is a contractual cash conversion; the other is a local model sensitivity.
  • “Realized volatility is universal.” Sampling, annualization, holidays, adjustments, and price source change the result.
  • “Linear payoff means low risk.” Large volatility-point moves can create large, potentially uncapped cash obligations.
  • “Variance replication perfectly hedges volatility.” The square-root payoff, jumps, discrete trading, wings, and costs leave basis risk.
  • “25% to 30% is a 0.05-point move.” It is five volatility points under standard point quotation.
  • “A model mark is an executable exit.” Customized swaps can be illiquid and subject to valuation disputes.

Authoritative sources

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