Variance and Volatility Swap Mechanics

Variance swaps promise you the purest volatility exposure available in public markets. No delta to manage, no gamma to monitor, no theta bleeding out each night. You buy realized variance against an implied strike, and the market settles the difference in cash. Simple, elegant, and -- if you are on the wrong side of convexity -- capable of generating losses that make your vanilla options book look like a rounding error.

Before you trade your first variance swap (or even quote one to a client), you need to understand exactly how these instruments work, why they behave differently from volatility swaps, and where the bodies are buried. This guide walks you through the mechanics, the math that matters, and the risk management lessons the market has taught the hard way.

What a Variance Swap Actually Is

A variance swap is an OTC contract where two parties exchange the difference between realized variance and a pre-agreed strike variance at expiry. The long side profits when realized variance exceeds the strike; the short side profits when the market stays quiet.

The payoff at maturity is straightforward:

Settlement = Variance Notional x (Realized Variance - Strike Variance)

Realized variance is calculated from daily log returns of the underlying (typically an equity index like the S&P 500 or Euro Stoxx 50), annualized using the standard 252 trading days. Strike variance is quoted as volatility squared -- so a "20 vol" strike means a variance strike of 400.

Here is the critical distinction that separates beginners from practitioners: you do not trade variance swaps in variance notional terms day-to-day. You trade them in vega notional, which represents your approximate P&L for a one-point change in realized volatility from the strike.

Lesson 1: Vega notional is the language of the trading desk. Variance notional is the language of the confirm.

The conversion between the two is:

So if you are long $100,000 vega notional at a 20 strike, your variance notional is $100,000 / (2 x 20) = $2,500 per variance point.

A P&L Walkthrough You Should Memorize

Let's ground this with numbers. You go long a one-year S&P 500 variance swap at a strike of 20 (meaning a variance strike of 400) with $100,000 vega notional. Your variance notional is $2,500.

Scenario 1: Realized vol comes in at 25.

P&L = $100,000 x (25^2 - 20^2) / (2 x 20) = $100,000 x (625 - 400) / 40 = +$562,500

Scenario 2: Realized vol comes in at 15.

P&L = $100,000 x (15^2 - 20^2) / (2 x 20) = $100,000 x (225 - 400) / 40 = -$437,500

Lesson 2: Notice the asymmetry. You made $562,500 when vol moved 5 points in your favor but only lost $437,500 when it moved 5 points against you. That is convexity at work -- and it is the single most important concept in variance swap trading.

Scenario 3: The nightmare -- realized vol hits 50.

P&L = $100,000 x (50^2 - 20^2) / (2 x 20) = $100,000 x (2500 - 400) / 40 = +$5,250,000

If you were short that swap, you just lost $5.25 million on a $100,000 vega notional position. This is not a theoretical exercise. This is roughly what happened to short variance players during the 2008 financial crisis and again during the COVID crash in March 2020.

Why Convexity Is the Whole Game

The payoff of a variance swap is linear in variance but convex in volatility. Since most people think in volatility terms (not variance terms), this creates a systematic cognitive trap.

Lesson 3: Convexity means long variance positions always profit more from a vol increase than they lose from an equal vol decrease.

This is not an accident of the math -- it is built into the squared relationship between volatility and variance. When you double volatility from 20 to 40, variance quadruples from 400 to 1,600. When you halve volatility from 20 to 10, variance only drops to 100. The long side captures 1,200 variance points on the upside move but gives back only 300 on the downside.

This convexity premium is why variance swap strikes systematically trade above at-the-money implied volatility. The long side is paying extra for the asymmetric payoff profile. How much extra? That depends on the volatility of volatility (vol of vol) -- the more volatile volatility itself is expected to be, the wider the spread between var swap strikes and ATM vol.

(These are illustrative ranges for S&P 500 -- the actual premium depends on the skew environment and vol-of-vol conditions at the time.)

Variance Swaps vs. Volatility Swaps: Know What You Are Trading

A volatility swap pays the difference between realized volatility and a fixed strike -- no squaring involved. The payoff is simply:

Settlement = Vega Notional x (Realized Vol - Strike Vol)

This makes the payoff linear in volatility. Clean, intuitive, and lacking the convexity that makes variance swaps both powerful and dangerous.

Lesson 4: Volatility swaps are harder to replicate and therefore less liquid than variance swaps. This might seem counterintuitive -- the simpler payoff should be easier to hedge, right? Wrong.

Variance swaps dominate in practice because they can be replicated (hedged) using a static portfolio of options across all strikes, weighted inversely proportional to the square of the strike price. This theoretical replication (pioneered by Carr and Madan, and popularized by the Derman-Demeterfi-Kamal-Zou framework at Goldman Sachs in 1999) gives dealers a clear hedge, which translates to tighter bid-ask spreads and deeper liquidity.

Volatility swaps, by contrast, require model-dependent hedging. There is no clean, model-free replication. As a result, dealers charge wider spreads and the market remains thinner.

The Log Contract: How Dealers Actually Hedge

The theoretical foundation of variance swap pricing rests on a beautiful result: the fair value of realized variance equals the price of a log contract on the underlying. A log contract pays -ln(S_T/S_0) at maturity, and its expected value under risk-neutral pricing gives you the variance swap strike.

In practice, dealers replicate this log contract using a strip of out-of-the-money puts and calls across all available strikes:

• Puts below the current price, weighted by 1/K^2 (where K is the strike)
• Calls above the current price, weighted by 1/K^2
• Dynamic delta hedging of the residual exposure

Lesson 5: The 1/K^2 weighting means low-strike puts carry enormous weight in the replication. This is why variance swaps are heavily exposed to downside tail risk -- those deep OTM puts, weighted more aggressively, dominate the replication portfolio when the market crashes.

This also explains why the VIX (which uses a similar methodology) tends to spike asymmetrically during sell-offs. The heavy weighting of low-strike puts means that a 10% market decline has a much larger impact on implied variance than a 10% rally.

In the real world, the replication is imperfect because:

1. Strikes are finite. You cannot buy options at every possible strike. The truncation of the strip -- particularly the absence of very deep OTM puts -- introduces a systematic replication error.
2. Jumps break the hedge. The log contract replication assumes continuous price paths (geometric Brownian motion). When the market gaps overnight or crashes through multiple strikes, the delta hedge fails and the dealer takes a hit.
3. Bid-ask costs accumulate. Buying the full strip of options across 30-50 strikes is expensive in transaction costs, especially in less liquid single-stock names.

(This is why single-stock variance swaps typically trade with wider spreads and often include variance caps -- a maximum realized variance level that truncates the tail risk.)

The Mark-to-Market During the Life of the Swap

Lesson 6: A live variance swap's value blends realized variance already accrued with implied variance for the remaining term.

At any point before maturity, the fair value of a variance swap decomposes into two pieces:

• Accrued realized variance (what has already happened, which is fixed and known)
• Implied variance for the remaining period (what the market is pricing for the time left)

The weighting is proportional to time elapsed and time remaining. If you are 60 days into a 252-day swap, the mark-to-market is approximately:

MTM Variance = (60/252) x Realized Variance + (192/252) x Current Implied Variance

This means early in the swap's life, implied variance dominates the P&L. Late in the swap's life, realized variance dominates and the P&L is largely locked in (assuming the remaining days do not produce an extreme move).

(Experienced traders exploit this dynamic by initiating variance positions with a view on near-term catalysts -- earnings, FOMC meetings, elections -- knowing that the realized variance from those events will be "locked in" and will dominate the final settlement if the remaining time is short.)

Where Short Variance Has Blown Up

The history of short variance is a history of long stretches of steady income punctuated by catastrophic losses. If you only study the carry, you will miss the catastrophe.

February 2018 -- Volmageddon. The VIX doubled from 17 to 37 in a single session. The VelocityShares Daily Inverse VIX Short-Term ETN (XIV) collapsed from $1.9 billion in assets to $63 million overnight -- a loss exceeding 96%. The product was subsequently liquidated. While XIV was a VIX futures product rather than a variance swap, the underlying dynamics were identical: short convexity, short vol-of-vol, and a feedback loop where hedging activity amplified the very move that was causing losses.

March 2020 -- COVID crash. The VIX surged above 80 (the highest level since 2008), and S&P 500 realized volatility hit approximately 80-85% annualized over the peak two-week window. A short variance swap struck at 20 with $100,000 vega notional would have produced a loss of roughly:

P&L = $100,000 x (80^2 - 20^2) / (2 x 20) = $100,000 x (6400 - 400) / 40 = -$15,000,000

That is a $15 million loss on a position sized for approximately $100,000 per vol point. The 150-to-1 ratio of loss-to-vega-notional is the kind of outcome that ends careers and closes funds.

2008 Financial Crisis. Realized volatility on the S&P 500 exceeded 70% annualized during the peak of the crisis. Citadel, which accounted for roughly 30% of US equity options volume, lost approximately 50% of its asset value ($8 billion). While the losses came from multiple sources, the firm's massive short volatility and variance exposure through its options market-making operation was a central driver.

Lesson 7: Short variance is a concave payoff with no natural floor. Your maximum gain is capped (realized variance can only go to zero), but your maximum loss is theoretically unlimited. The only structural protection is a variance cap -- and many institutional variance swaps include one, typically set at 2.5x the strike (so a 20-strike swap would cap realized variance at 50^2 = 2,500).

Variance Caps and Corridor Variance Swaps

Because the tail risk of short variance is so extreme, the market has developed structural modifications:

Capped variance swaps limit the realized variance used in the settlement calculation. A cap at 2.5x the strike is standard for most institutional trades. This reduces the premium the long side pays (since the convexity upside is truncated) but also makes the product tradeable for risk-averse counterparties.

Corridor variance swaps only accumulate realized variance when the underlying is trading within a pre-defined price range. If the market moves outside the corridor, the swap stops accruing. This allows you to express targeted views -- for example, that volatility will be high only within a specific market range -- and limits both sides' tail exposure.

(Corridor var swaps are particularly popular in rates and FX markets, where dealers use them to monetize range-bound volatility views without taking on the full tail risk of a standard variance swap.)

Practical Sizing and Risk Management

Lesson 8: Size your variance exposure to the tail, not to the expected move.

Most traders make the mistake of sizing variance swaps based on the expected daily P&L at the strike level. This is exactly wrong. You need to size to the scenario where realized vol comes in at 2-3x the strike -- because that scenario, while rare, is the one that determines whether you survive.

A reasonable framework:

If your maximum tolerable loss is $1 million and your strike is 20, a 2.5x scenario (realized vol = 50) produces:

Vega Notional = $1,000,000 / [(2,500 - 400) / 40] = $1,000,000 / 52.5 = ~$19,048 vega notional

That is roughly one-fifth the size most traders would run based on "feel." The math does not care about your intuition.

Your Readiness Checklist

Tier 1 -- Before you look at a term sheet:

• You can convert between vega notional and variance notional without a calculator
• You can explain why var swap strikes trade above ATM implied vol
• You understand that short variance has a concave, not linear, payoff in vol terms

Tier 2 -- Before you execute a trade:

• You have sized the position to survive a 2.5x realized vol scenario
• You know whether your swap is capped or uncapped (and at what level)
• You have modeled the mark-to-market path under at least three vol scenarios
• You understand how the accrued-vs-implied blend shifts your P&L as time passes

Tier 3 -- Before you run a book:

• You can explain the log contract replication and where it breaks down
• You have studied at least two historical blowup episodes in detail
• You have a stop-loss or delta-hedging protocol for your variance book
• You understand how jump risk and strike truncation affect your replication error

Your concrete next step: Pull up an options chain on the S&P 500 (SPX). Calculate the theoretical variance swap strike by weighting OTM puts and calls by 1/K^2, summing the weighted prices, and comparing your result to the VIX squared. If your number is within 1-2 variance points of VIX^2, you understand the replication. If it is not, go back to the log contract derivation and work through the math until the numbers match. That exercise will teach you more about variance swaps than any article -- including this one.