The core idea
A variance swap is a direct trade on realized variance versus implied variance.
Options quote implied volatility, but variance swaps are naturally written in variance. The floating leg is realized variance over the contract window. The fixed leg is the variance strike agreed at inception. If realized variance finishes above the strike, the long-variance side receives the difference.
The reason this belongs in a volatility surfacecluster is simple: the fair variance strike depends on market option prices across strikes and expiries. A single ATM implied volatility misses wing prices, skew, and convexity that matter for implied variance.
Define realized variance
The floating leg is based on squared log returns observed over the contract window and annualized by the contract convention.
Set the variance strike
The fixed leg is the variance level agreed at inception, usually interpreted as the market-implied fair variance for the period.
Compare realized with implied
The payoff depends on realized variance minus the variance strike, scaled by the variance notional.
Payoff formula
Variance swap payoff equals realized variance minus the variance strike.
Contract details vary, but the core payoff is the variance notional times realized variance minus the fixed variance strike. Realized variance is usually built from squared log returns over the sampling schedule.
Market-implied fixed variance level at trade inception.
Benefits when realized variance is above the fixed strike.
Benefits when realized variance is below the fixed strike.
Payoff conventions
Variance swap P&L depends on convention details, not only realized variance.
Two variance swaps can reference the same underlying and still produce different realized legs if their sampling, settlement, annualization, cap, corridor, or notional rules differ. A production variance workflow should treat those terms as part of the data model.
Variance notional
The variance notional converts variance-point differences into currency P&L, so it must be explicit in any payoff or API payload.
Annualization basis
Realized variance changes when the contract uses 365 days, 365.25 days, hour buckets, settlement windows, or another annualization rule.
Sampling calendar
Crypto trades continuously, so the sampling schedule should define UTC cutoffs, exchange source, missing ticks, and weekend handling.
Cap or corridor
Some variance products cap extreme observations or include only a strike or spot corridor; those rules should not be hidden behind one variance number.
Surface inputs
The fair variance strike uses the whole option surface.
In the continuous idealization, expected variance can be linked to a strip of out-of-the-money puts and calls, with strike weights that make the wings important. This is why SVI, SSVI, and quote-through-fit diagnostics matter before using a surface for variance work.
Dense strike coverage
Variance replication is sensitive to option prices across wings, not just ATM volatility.
Clean forwards
The split between put and call wings depends on the expiry forward used as the surface center.
Stable total variance
SVI and SSVI fits help convert noisy quotes into a coherent total-variance view before integration.
Wing discipline
Far-wing extrapolation can dominate variance estimates, so quote filters and model guardrails are essential.
The same total-variance logic appears in forward volatility. Forward variance compares total variance between expiries; variance swaps turn realized variance over a window into a payoff.
Option-strip replication
Variance swap replication uses the wings, so surface hygiene matters.
A fair variance strike is often estimated from an option strip, not from one quoted volatility. The practical implementation starts with accepted OTM puts and calls, the expiry forward, and a strike grid that is dense enough to make wing treatment auditable. This is why variance work should be tied to SVI fits, SSVI checks, and quote-through-fit diagnostics.
Split the strip around the forward
Use out-of-the-money puts below the forward and calls above it so the replication reads both wings of the smile.
Weight by strike spacing
Discrete strikes need spacing-aware weights. Thin or irregular crypto strike grids can otherwise overstate one wing.
Control the wings
Far-wing options can dominate the estimate because variance replication gives large importance to low-strike and high-strike tails.
Map to the target tenor
If the target horizon is between expiries, interpolate total variance rather than raw volatility.
accepted OTM puts/calls -> strike weights -> wing policy -> total variance integral -> fair variance strikeStrip contribution
The option-strip contribution should show which strikes moved the variance estimate.
A fair variance strike can be hard to audit if it appears as one final number. Derivasys-style diagnostics should make the accepted strike set, option strip contribution, wing contribution, interpolation, and source surface version visible before the value feeds a report or API response.
Accepted strike set
List which puts and calls entered the strip, which were rejected, and which intervals were interpolated or extrapolated.
Wing contribution
Show how much of the variance strike comes from put wings, ATM-adjacent strikes, and call wings before the value is trusted.
Spacing and liquidity
Irregular strike spacing and weak wing quotes should be visible because both can dominate the discrete replication estimate.
Surface version
The strip contribution should carry the source SVI or SSVI surface version so the estimate can be reproduced later.
Variance strike diagnostics
The variance strike should be decomposed into level, skew, curvature, and tenor effects.
Variance is not just ATM volatility squared. A surface-aware variance workflow should explain whether the estimate is moving because ATM total variance changed, skew moved through risk reversals, wing curvature changed through flies, or the relevant forward variance bucket shifted.
The same decomposition matters for corridor variance or conditional variance views, where the desk wants to include only part of the strike distribution instead of the full option strip.
ATM anchor
The ATM total variance sets the level, but it is not enough to price fair variance by itself.
Skew contribution
Risk reversals reveal whether put or call wings are making implied variance richer.
Fly contribution
Flies show how much smile curvature and wing richness add beyond the ATM point.
Forward variance bucket
Forward-volatility checks show whether the variance strike is consistent with neighboring maturities.
Variance vs volatility
Variance swaps are not the same as volatility swaps.
Variance is volatility squared. That difference matters because variance is additive through time and has a cleaner relationship with option-strip replication. Volatility swaps are easier to describe, but their square-root payoff is less directly replicated from vanilla options.
Variance swap
Pays realized variance minus a fixed variance strike. It is naturally expressed in variance units.
Volatility swap
Pays realized volatility minus a fixed volatility strike. The square root makes replication and hedging less direct.
VIX-style index
Uses an option strip to estimate expected variance over a target horizon, then quotes the square root as annualized volatility.
Production checks
Crypto variance work needs contract, venue, and surface discipline.
Crypto options add practical details: 24/7 trading, venue outages, futures basis, mark methodology, and sparse far-wing liquidity. A variance workflow should inspect these alongside fitted smiles, local volatility diagnostics, and realized-return sampling rules.
Sampling convention
Realized variance depends on whether returns are daily, hourly, close-to-close, exchange-specific, or based on another agreed schedule.
Corporate-action analogue
Crypto has forks, index methodology changes, venue outages, and settlement-source issues instead of equity corporate actions.
Jump and gap risk
Variance swaps pay squared returns, so jumps and sharp overnight-style gaps have an outsized effect.
Surface quality
The fair strike inherits every issue in the implied volatility surface: stale marks, crossed quotes, sparse wings, and unstable fits.
Monitoring workflow
Production variance systems need replayable realized variance and auditable implied variance.
The realized leg and implied leg fail in different ways. The realized leg needs exact sampling and settlement provenance. The implied leg needs strike acceptance, fit residuals, wing policy, and surface timestamp. A dashboard should show both before a variance estimate is used in trading, risk, or API output.
Realized sampling replay
A production stack should be able to recompute the realized variance leg from the exact settlement prices and timestamps.
Surface-to-strip audit
The dashboard should expose which strikes were accepted, rejected, interpolated, or extrapolated before a variance estimate is published.
Jump attribution
Large squared returns should be tagged by market event, venue outage, index change, or settlement-source issue.
API provenance
Implied-variance outputs should carry the source surface, fit timestamp, forward, expiry pair, and wing policy.
API output
A variance swap API should expose contract terms, implied variance, realized variance, and diagnostics.
A variance output is only useful if the consumer can reproduce both legs. The API should carry the contract conventions, source surface, accepted option strip, realized sampling state, and any holdback reason.
underlying, observation window, variance notional, annualization basis, sampling schedule, cap, corridor, and settlement source.
variance strike, source surface id, expiry pair, accepted strikes, wing policy, fit timestamp, and contribution breakdown.
realized variance to date, sampled prices, missing observations, replay id, and jump or venue-outage annotations.
stale surface flag, rejected quotes, interpolation-heavy wings, forward mismatch, and holdback reason.
The realized leg should support realized variance replay from exact sampled prices and timestamps. The implied leg should point back to SVI or SSVI surface versions and the monitoring checks that accepted them.
Failure modes
Variance workflows fail when wing policy, sampling rules, or replay state are hidden.
The largest errors usually come from shortcuts around the wings or from realized-leg conventions that are not recorded. Those failures are preventable when surface provenance and sampling provenance travel with the calculation.
ATM-only shortcut
Using ATM volatility as the variance strike ignores skew and wing curvature, which can be material in crypto options.
Unstable wing extrapolation
Sparse far-wing quotes can move the option-strip estimate more than the actively quoted strikes if wing policy is not controlled.
Sampling mismatch
A realized-variance leg built from a different settlement source or time grid will not match the contract definition.
Unreplayable calculation
If the accepted strikes, prices, forwards, and sampling observations are not versioned, the variance output cannot be audited later.
Dashboard workflow
Derivasys monitors the surface inputs behind implied variance.
Derivasys focuses the public dashboard on fitted SVI smiles, risk reversals, flies, fixed-tenor rows, quote-through-fit diagnostics, and API-ready surface state. Those are the inputs a variance workflow needs before estimating implied variance or comparing it with future realized variance.
Dashboard screenshots
Variance workflows should keep wing contribution and quote-through-fit health visible.
A variance estimate can look precise while depending on sparse wing marks or extrapolation. Derivasys keeps risk nodes, fitted-surface context, and through-fit diagnostics visible so the option strip can be reviewed before it feeds fair variance or forward-variance calculations.
Reading path
Move from total variance into variance derivatives.
Use total variance to isolate future variance buckets.
Read nextUnderstand the full strike and tenor surface used for variance estimates.
Read nextReview the one-expiry strike curve that feeds option-strip variance.
Read nextFit each expiry smile in total variance space before risk extraction.
Read nextTie slices together with a surface-level total-variance parameterization.
Read nextRead how signed skew changes the contribution of each wing.
Read nextUse smile curvature to understand wing richness in the option strip.
Read nextConnect variance exposure with vega, volga, and surface shock workflows.
Read nextFAQ
Common questions about variance swaps.
What is a variance swap?
A variance swap is a volatility derivative whose payoff is based on realized variance minus a fixed variance strike, multiplied by a variance notional.
How is realized variance calculated?
Realized variance is commonly based on squared log returns over the contract's sampling schedule, annualized according to the contract convention.
How is a variance swap strike related to options?
A fair variance strike can be estimated from a strip of out-of-the-money calls and puts, with option weights linked to inverse strike squared.
Why are variance swaps connected to volatility surfaces?
The option strip used for implied variance depends on the whole smile and term structure, so surface quality, wing behavior, and fit diagnostics matter.
Why do far wings matter for variance swaps?
Variance replication weights option prices across strikes, so sparse or extrapolated wings can move the fair variance strike even when ATM volatility looks stable.
How is forward variance related to variance swaps?
Forward variance compares total variance between expiries. Variance swap strikes and VIX-style estimates also rely on total variance over a defined horizon, so maturity interpolation should be done in variance space.
What should a variance swap API include?
A variance swap API should include contract terms, variance notional, annualization basis, sampling schedule, variance strike, source surface, accepted strikes, wing policy, realized variance to date, replay id, and diagnostics.
Why is realized variance replay important?
Realized variance replay lets a desk recompute the floating leg from the exact sampled prices, timestamps, settlement source, and missing-observation rules used by the contract.
Can ATM volatility approximate a variance swap strike?
ATM volatility can be a rough level indicator, but it misses skew, fly curvature, and far-wing contributions that can materially change an option-strip variance estimate.
References
Variance and surface references.
This page is written for the Derivasys surface workflow and connects variance swaps back to implied variance, fitted smiles, forward variance, and dashboard diagnostics.
- Variance swap overview
- Cboe VIX product overview
- Derivasys forward volatility guide
- Derivasys volatility surface guide
- Derivasys volatility smile guide
- Derivasys SVI guide
- Derivasys SSVI guide
- Derivasys risk reversal guide
- Derivasys flies guide
- Derivasys option Greeks guide
- Derivasys local volatility guide
- Derivasys production monitoring article
- Derivasys order-book construction article