What exactly is a variance swap and how does the payoff work relative to implied volatility?

A variance swap is an OTC derivative where one party pays a fixed rate (the 'strike variance') and receives the realized variance of an underlying asset over the contract period. It gives you pure exposure to volatility without the complications of delta-hedging options.

Payoff Formula:

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

Important: The notional is quoted in variance terms, not volatility terms. If you want exposure to volatility, you convert:

Vega Notional = Variance Notional x (2 x Strike Vol)

Worked Example:

Maplerock Capital enters a 3-month variance swap on the S&P 500:

• Strike volatility: 18% (so strike variance = 0.18^2 = 0.0324)
• Vega notional: $100,000 per volatility point
• Variance notional = $100,000 / (2 x 18) = $2,778 per variance point

At expiry, realized volatility turns out to be 22% (realized variance = 0.0484).

Payoff = $2,778 x (0.0484 - 0.0324) x 10,000 = $2,778 x 160 = $444,480

(Multiplied by 10,000 to convert from decimal to basis-point-squared convention.)

Why Not Just Trade VIX Futures?

Variance swaps have a convexity feature: because you're trading variance (vol squared), large volatility spikes produce outsized payoffs. A move from 18% to 30% realized vol pays much more than twice a move from 18% to 24%.

FRM Exam Tips:

• Know the difference between variance notional and vega notional
• Understand that the strike is typically set at implied variance, so the swap starts at zero value
• The convex payoff makes variance swaps popular for tail-risk hedging
• Mark-to-market uses the remaining implied variance plus the accrued realized variance

Practice variance swap calculations in our FRM question bank.