Skip to content
Financial Context Wiki

Corridor Variance Swaps: Observation, Normalization, and Units

Calculate indicator-weighted realized variance inside a corridor while controlling observation rules, denominators, variance units, notionals, caps, jumps, and OTC settlement.

Updated

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

Direct answer

A corridor variance swap is an indicator-weighted variance contract. It accumulates squared returns only for intervals that satisfy a contractually defined price-range test. The name does not determine whether the test uses the interval’s start price, end price, both endpoints, or an intraday condition, nor whether the denominator counts all scheduled returns or only active returns.

Let official adjusted observation levels be P₀,…,P_N and log return r_i=ln(P_i/P_{i−1}). For corridor [L,H], illustrative weights are w_i^start=I(L≤P_{i−1}≤H), w_i^end=I(L≤P_i≤H), and w_i^both=w_i^start×w_i^end. Inclusive versus strict barriers, touches, crossings, gaps, observation times, and fallback prices are confirmation terms.

With annualization factor A, scheduled count N_sched, and active count N_active=Σw_i, two economically different definitions are RV_sched=(A/N_sched)Σw_i r_i² and RV_active=(A/N_active)Σw_i r_i². The active formula needs an explicit rule when N_active=0. These are realized quadratic-variation measures; they normally do not subtract a sample mean unless the signed terms say so.

How to specify and calculate the swap

  1. Lock the legal claim and parties: master agreement, transaction confirmation, underlier and index version, price or total-return basis, currency, effective date, observation period, valuation and payment dates, business-day convention, calculation agent, governing law, and buyer or seller direction.
  2. Lock the observation grid and corridor: official price source and timestamp, L, H, fixed or resetting levels, inclusive or strict touches, start, end, both-endpoint or intraday weight, and treatment of crossings and gaps.
  3. Define each return and adjusted level. Record log, simple, gross, or net return; dividends, splits, corporate actions, index rebalances, FX or quanto terms; missing observations; market disruption, postponement, fallback, and correction rules.
  4. Produce an auditable interval table containing P_{i−1}, P_i, r_i, r_i², w_i, and w_i r_i². Then apply the stated A, N_sched, valid-observation count, N_active, zero-active fallback, day count, and rounding convention without switching denominators after observing the path.
  5. Normalize all cash units. If volatility is quoted in numerical volatility points, K_var,points=K_vol²; in decimal units, K_var,decimal=(K_vol/100)², and 1 decimal variance unit=10,000 variance points. Record variance notional, vega notional, buyer or seller sign, strike, floor, realized-variance cap, per-return cap, payment cap, and their exact order of application.
  6. Price and hedge from the relevant forward, full volatility surface and skew, barrier region, rates, dividends, jumps, and observation grid. Separate idealized continuous-monitoring replication from finite strikes and maturities, discrete sampling, barrier switching, local-time effects, transaction costs, and actual unwind liquidity.
  7. Independently recalculate every observation and cash flow. Reconcile the calculation-agent statement, mark-to-market, model version, valuation reserve, confirmation, CSA threshold and collateral, netting, dispute, default closeout, fees, tax, settlement currency, and final payment.

For a variance buyer with decimal-unit variance notional N_var,decimal, strike K_var, optional realized-variance floor F_var, and cap C_var, one possible signed payoff is Π=N_var,decimal×(min(max(RV,F_var),C_var)−K_var). A seller receives the negative of that amount. A cap on cash, a cap on each return, and a cap on annualized RV are not interchangeable.

Variance is squared volatility. Decimal variance 0.04, variance level 400 variance points, and volatility 20 vol points describe the same level because 0.04×10,000=400=20². They do not share the same cash notional. Near a strike expressed as K_vol volatility points, one common local convention is N_vega≈2×K_vol×N_var,points; the exact variance payoff remains quadratic rather than linear in volatility.

Worked examples

  • Start, end, and both-endpoint tests. Use inclusive corridor [90,110], levels P=[100,105,115,108,88], annualization A=252, and scheduled denominator N_sched=4. The four log returns are [0.04879016417,0.09097177821,−0.06280090124,−0.20479441265], with squares [0.00238048012,0.00827586443,0.00394395320,0.04194075145]. Start weights [1,1,0,1] give sum 0.05259709600, RV_start=3.31361704804, and volatility equivalent 182.0334%. End weights [1,0,1,0] give RV_end=0.39843929892 and 63.1220%; both-endpoint weights [1,0,0,0] give RV_both=0.14997024754 and 38.7260%. The jump from 108 to 88 is included only by the start test.
  • Scheduled versus active normalization. Five scheduled return intervals have weights [1,0,1,0,1]; their eligible returns are +3%, −2%, and +1%, so Σw_i r_i²=0.0014. With A=252, scheduled normalization gives RV_sched=252×0.0014÷5=0.07056 and volatility equivalent 26.5631%. Active normalization gives RV_active=252×0.0014÷3=0.1176 and 34.2929%. The eligible numerator is identical, but the contracts are not economically equivalent.
  • Variance points, decimal units, and vega notional. Let K_vol=20, so K_var=400 variance points=0.04 decimal variance, and let realized volatility be 22, so realized variance is 484 points=0.0484. If N_vega=$10,000 per vol point, the local strike conversion gives N_var,points=$10,000÷(2×20)=$250 per variance point, equivalent to N_var,decimal=$2,500,000 per decimal variance unit. Exact buyer payoff is (484−400)×$250=$21,000; the linear vega estimate is (22−20)×$10,000=$20,000. The $1,000 difference is the quadratic curvature term, not a rounding error.
  • A jump, a switch, and a realized-variance cap. Use corridor [80,120], a start-price test, 4 scheduled returns, A=252, log returns [2%,−1%,−45%,3%], and weights [1,1,1,0]. The inside-to-outside −45% jump is included, the following return is excluded, and eligible squared-return sum is 0.203, so raw RV=252×0.203÷4=12.789. With K_var=0.04, N_var,decimal=$100,000, and no cap, buyer payoff is (12.789−0.04)×$100,000=$1,274,900. If the confirmation instead caps annualized realized variance at C_var=0.64, payoff is (0.64−0.04)×$100,000=$60,000. This does not describe a per-return or cash-payment cap.

Term-sheet, model, and lifecycle risks

  • Verify the underlier, index version, price-return or total-return basis, and calculation agent.
  • Lock settlement currency, FX or quanto terms, and the currency of both corridor barriers.
  • Record the observation calendar, timestamp, timezone, holiday, and official price source.
  • Define missing, delayed, disrupted, postponed, fallback, and corrected observations.
  • Specify log, simple, gross, or net returns and any mean adjustment.
  • Specify dividend, split, corporate-action, index-rebalance, and adjusted-level treatment.
  • Record fixed, forward-relative, or resetting L and H for every interval.
  • Distinguish inclusive and strict barriers and define an exact touch.
  • Distinguish start, end, both-endpoint, average, and intraday eligibility rules.
  • Stress overnight gaps and jumps that switch the indicator for a full squared return.
  • Do not mix scheduled, valid, and active observation denominators.
  • Define the result when N_active=0 or very few active observations remain.
  • Lock annualization, day count, observation count, precision, and rounding.
  • Distinguish decimal variance, variance points, volatility points, and quoted percentages.
  • Distinguish variance notional from vega notional and validate any local conversion.
  • Apply per-return caps, realized-variance caps, floors, and payment caps in the stated order.
  • Stress the full skew and surface, barrier concentration, jumps, and model calibration.
  • Allow for finite-option-strip, discrete-monitoring, transaction-cost, and hedge-slippage error.
  • Include unwind liquidity, valuation reserves, model differences, and calculation disputes.
  • Include counterparty credit, CSA collateral, thresholds, netting, default closeout, fees, and tax.

Common misconceptions

  • Every price move outside the corridor automatically disappears from settlement.
  • A return that crosses a barrier is always excluded.
  • Scheduled-day and active-day normalization produce the same result from the same eligible returns.
  • Volatility 20% means variance 0.20, or vega notional can replace variance notional directly.
  • A narrower corridor is necessarily safer and continuous replication eliminates jump or hedge risk.

Authoritative sources

Navigation

Search the wiki...