Corridor Variance Swaps: Measuring Variance Inside a Price Range

For educational purposes only; not investment advice.

Direct answer

A corridor variance swap exchanges a fixed variance strike for realized variance accumulated only when the underlying satisfies a specified price-range condition. If the corridor is [L,H], returns observed while the contract’s reference price is outside that range receive zero weight.

It isolates volatility associated with a region of the price path rather than all realized volatility. That makes the lower and upper barriers, observation time, inclusion test, return definition, annualization, normalization, disruption rules, cap, and variance notional economically essential terms.

Conditional variance and settlement

For log return rᵢ = ln(Sᵢ/Sᵢ₋₁), one illustrative definition is:

RV_corr = A × Σ I(L ≤ Sᵢ₋₁ ≤ H) rᵢ² / D

A is an annualization factor, I(...) is 1 when the stated condition is true and 0 otherwise, and D is the contract’s normalization denominator. Settlement for a variance buyer can be written:

Payoff = N_var × (RV_corr − K_var)

Some contracts test the start price, end price, both endpoints, or an intraday observation. Some divide by all scheduled returns, while “conditional” variants may divide by the number of active observations. These choices are not interchangeable. A move that starts inside and jumps outside can be included under one rule and excluded under another.

Variance is squared volatility. A variance of 0.04 corresponds to a volatility equivalent of sqrt(0.04)=20%, but swap quotes and notionals may use decimal variance, volatility points squared, or vega-notional conversion. Units must be reconciled before calculating cash.

Five-return calculation

Assume an illustrative corridor [90,110], eligibility based on the start price, annualization A=252, and a denominator D=1 for this short demonstration. Five returns are 1%, −2%, 4%, −3%, and 1.5%; only the first, second, and fifth start inside the corridor.

Σ eligible rᵢ² = 0.01² + (−0.02)² + 0.015² = 0.000725

RV_corr = 252 × 0.000725 = 0.1827

Its volatility equivalent is sqrt(0.1827) ≈ 42.74%. If K_var=0.16 and N_var=$50,000 per decimal variance unit, the illustrative buyer payoff is:

$50,000 × (0.1827−0.16) = $1,135

This deliberately tiny sample is not a market convention or forecast. A real term sheet may divide by scheduled or active observations, cap realized variance, scale quoted variance by 10,000, or use different barrier tests; each would change the cash result.

Term-sheet and risk checklist

Record L, H, whether barriers are inclusive, and whether they are fixed, forward-relative, or reset.
Identify the exact price and timestamp used for eligibility and for calculating each return.
Confirm treatment of a return that crosses a barrier, touches it, gaps over it, or follows a market disruption.
Verify annualization factor, denominator, missing observations, holidays, corporate actions, rounding, cap, and settlement currency.
Translate variance notional into cash under the document’s quoting convention; do not substitute vega notional without the stated conversion.
Stress paths that hover near a barrier. A tiny price difference can switch a full squared return on or off.
Include jumps and sparse monitoring. Continuous-monitoring replication results do not eliminate discrete-observation hedge error.
Treat pricing as surface-wide. Corridor exposure depends strongly on skew and options near the barriers, not just at-the-money IV.
OTC contracts add counterparty credit, collateral, documentation, valuation-dispute, and unwind liquidity risk.
A variance seller can face very large losses unless the payoff is capped; excluding outside-corridor moves does not make exposure harmless.

Common misconceptions

“All volatility outside the corridor disappears.” Only returns assigned zero weight by the exact observation rule disappear from settlement.
“A jump across a barrier is automatically excluded.” Inclusion depends on whether the contract tests the start, end, both, or another reference.
“Corridor variance is ordinary variance with fewer days.” Normalization can use all days or active days, producing different economics.
“The square root is the cash payoff.” Settlement is normally linear in variance difference; volatility equivalent is descriptive.
“Narrower corridor always means less risk.” Concentration near a barrier and conditional normalization can make exposure unstable.
“It is a listed standardized option.” Corridor variance swaps are commonly customized OTC contracts; the signed term sheet controls.

Authoritative sources

Corridor Variance Swap - Roger Lee
Variance Swaps - International Swaps and Derivatives Association
S&P 500 Variance Futures Variance Calculator User Guide - Cboe