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Variance Swap: Payoff, Realized Variance, and Notional Conventions

For educational purposes only; not investment advice.

Direct answer

Section titled “Direct answer”

A variance swap is typically an over-the-counter cash-settled derivative whose long side receives a payment when realized return variance over a specified observation period exceeds a fixed variance strike, and pays when it falls below that strike. Under a decimal-variance convention:

long payoff = N_var × (RV − K_var)

RV is realized annualized variance, K_var is the contractual variance strike, and N_var is cash per one unit of decimal variance. Often the strike is quoted as a volatility number K_vol, with K_var=K_vol².

The contract provides more direct exposure to variance than one plain-vanilla option, but “direct” does not mean linear in volatility: squaring makes extreme moves disproportionately important. Exact economics depend on the confirmation’s return formula, observation calendar, disruption rules, cap, notional, and settlement source.

Contract mechanics and notional

Section titled “Contract mechanics and notional”

Realized variance is commonly based on sampled log returns:

RV = A × Σᵢ [ln(Sᵢ/Sᵢ₋₁)]²

A is an annualization factor specified by the contract. A confirmation must define observation dates and times, closing or settlement levels, holidays, missing prices, dividends or corporate actions, and whether the sample mean is removed. Two contracts called “variance swaps” can settle differently.

At inception, the fair variance strike is set so the swap has approximately zero value, excluding fees and credit adjustments. Option prices across strikes can support a model-light estimate of this strike, but finite strikes, jumps, discrete sampling, and execution create gaps between theory and a live contract.

Variance notional and vega notional are not interchangeable. If volatility is expressed as a decimal, the local sensitivity of payoff to realized volatility near strike is:

dPayoff/dσ ≈ 2 × N_var × K_vol

For a one-volatility-point move, Δσ=0.01, so:

VegaNotional_per_point ≈ 0.02 × N_var × K_vol

This is a local conversion around the strike, not a constant sensitivity. Some confirmations quote volatility in whole points, producing numerically different notionals for the same economics. Never use a notional without its unit convention.

Payoff and vega-notional examples

Section titled “Payoff and vega-notional examples”

Assume K_vol=20%=0.20, so K_var=0.20²=0.0400. Let decimal variance notional be N_var=$100,000 per one unit of variance. If realized volatility is 30%=0.30, then RV=0.30²=0.0900 and the long receives:

$100,000 × (0.0900 − 0.0400) = $5,000

If realized volatility is 10%, the long payoff is:

$100,000 × (0.0100 − 0.0400) = −$3,000

The move from 20% to 30% creates a larger absolute variance difference than the move from 20% to 10%, even though both are 10 volatility points. That asymmetry comes from squaring volatility.

At the 20% strike, this contract’s approximate vega notional is:

0.02 × $100,000 × 0.20 = $400 per volatility point

This local estimate would predict about $4,000 for a 10-point rise, while the exact variance payoff is $5,000; convexity accounts for the difference. A contract cap, if present, can limit the long payoff and the short’s loss, but only according to its precise terms.

Risks and controls

Section titled “Risks and controls”
  • Read the confirmation before using any payoff formula: underlying, start and end dates, samples, annualization, strike, notional, cap, currency, settlement, and disruption rules are contractual.
  • Normalize whole-volatility-point and decimal-volatility conventions before comparing notionals or strikes.
  • Recalculate realized variance independently from the exact observation series; do not substitute a chart’s historical volatility.
  • Stress jumps and clustered volatility. Squared returns let a few observations dominate the final settlement.
  • A short variance position may have very large loss without a cap; historical calm does not bound a future jump.
  • OTC exposure includes counterparty credit, collateral, documentation, valuation, liquidity, unwind, and legal risk.
  • The fair strike can change sharply with downside skew and tail-option prices, not just at-the-money IV.
  • A listed-option replication is imperfect because strikes are discrete and finite, hedging is discontinuous, and Bid/Ask costs accumulate.
  • VIX is an index under a published methodology, not the realized leg or confirmation of every variance swap.
  • Compare expected payoff with financing, fees, capital, margin, and stress liquidity rather than treating a positive historical variance risk premium as free carry.

Common misconceptions

Section titled “Common misconceptions”
  • “A variance swap pays realized volatility minus implied volatility.” It normally pays a notional times a difference in variance.
  • “A 10-point move up and down has symmetric P&L.” Squaring volatility makes the payoff convex.
  • “Variance notional is a dollar amount by itself.” Its meaning requires a variance-unit convention; vega notional is different.
  • “The long side cannot lose more than premium paid.” A swap may have no upfront option premium and can create a payment obligation at settlement.
  • “The short side’s loss is always capped.” Only an explicit contractual cap limits it.
  • “VIX at inception is the exact strike.” Index methodology, maturity interpolation, contract terms, credit, and execution may differ.
  • “No daily Delta hedge means no path risk.” Realized variance is built from the path of sampled returns, and unwind value changes before maturity.
Section titled “Related topics”

Authoritative sources

Section titled “Authoritative sources”