Variance Swap

What Is a Variance Swap?

A Variance Swap is an OTC derivative contract in which two counterparties agree to exchange the difference between realized variance — the actual squared daily returns of an underlying asset over the contract life — and a pre-agreed variance strike (also called the fixed leg), multiplied by a notional vega amount. Unlike vanilla options, a variance swap delivers pure volatility exposure: there is no underlying delta to manage, no path-dependency from discrete rebalancing, and no sensitivity to the direction of the underlying asset.

The payoff at expiry is: (Realized Variance − Variance Strike) × Vega Notional / (2 × ATM Volatility). In practice, the variance strike is set so the contract has zero upfront cost, and it approximates the square of the implied volatility for the relevant tenor — but it is not identical. The variance strike trades at a variance risk premium above the expected realized variance, reflecting the fact that sellers of variance bear convex exposure to volatility spikes.

The key mathematical property of variance swaps is convexity: a long variance position gains more from a spike in realized vol above strike than it loses from realized vol falling below strike by the same absolute amount. This asymmetry is the source of the volatility risk premium that variance sellers harvest over time.

Why It Matters for Traders

Variance swaps are the primary instrument through which institutional traders and dealer gamma exposure managers express views on the level versus the surface of volatility. Unlike straddles or strangles, variance swaps have no vega decay in the traditional options sense — their P&L is entirely a function of the difference between what volatility does versus what was priced in.

The spread between the variance swap strike and at-the-money implied volatility is a direct measure of the volatility skew's contribution to the variance risk premium. In equity markets, this spread tends to be 2–4 volatility points in normal regimes — a structural premium that quantitative volatility funds systematically harvest by selling variance. When this spread compresses dramatically (e.g., during low-vol regimes), it signals the variance risk premium has been arbitraged toward exhaustion and the risk/reward of being short variance deteriorates sharply.

How to Read and Interpret It

• Variance swap strike significantly above realized vol (spread > 4 vol points): Elevated volatility risk premium — historically favorable entry for short variance strategies. Monitor for convexity of convexity risk before sizing.
• Strike near or below recent realized vol: Premium compressed; short variance risk/reward poor. Often seen entering earnings seasons or macro event clusters.
• Implied correlation via dispersion trades: Comparing index variance swap strikes to single-stock variance swap strikes reveals the implied correlation — a divergence signals potential dispersion trade opportunities.
• Track vol surface roll — a steep term structure of variance strikes (front < back) suggests the market anticipates vol normalization, which typically benefits short-dated variance sellers.

Historical Context

The most catastrophic variance swap episode was the February 5, 2018 'Volmageddon' event. Products like the XIV ETN (inverse VIX) and short-variance strategies had accumulated massive short positions, effectively short variance at strikes around 11–12 vol points. When the VIX spiked from ~17 to ~38 intraday — a move of roughly 21 vol points — the convex payoff structure of variance swaps meant losses were dramatically larger than linear vol models predicted. The XIV ETN lost over 90% of its value in after-hours trading and was subsequently liquidated. Dealers who were long variance as hedges against structured product vol exposure fared well, illustrating the instrument's asymmetric payoff structure.

Limitations and Caveats

Variance swaps are OTC instruments with significant counterparty credit risk — during the 2008 financial crisis, several dealer defaults created unwind problems for variance swap books. The convexity of variance exposure means that extreme realized vol events can produce losses that dwarf initial VaR estimates, a structural limitation of standard volatility risk premium harvesting frameworks. Additionally, variance swaps are sensitive to jump risk (discontinuous price moves) in a way that implied volatility models often underestimate — a 10% overnight gap contributes more to realized variance than 10 days of 1% moves.

What to Watch

• VIX vs. VVIX divergence — VVIX pricing elevated while VIX is low signals the market is pricing in potential variance spikes.
• Equity factor dispersion — rising dispersion often precedes index variance compression, affecting dispersion trade P&L.
• Dealer gamma exposure — when dealers are short gamma, they are effectively long realized variance, which competes with and can amplify variance swap dynamics.
• Correlation between realized and implied variance across asset classes as a regime indicator.