Volatility Swaps

A regular option gives you a view on a stock's direction, and volatility is just a side effect of how that view is priced. A volatility swap flips that around — it's a bet purely on how choppy the stock turns out to be, with no view on direction at all. Two counterparties agree today on a fixed volatility level; at expiry, whoever guessed closer to the volatility that actually happened gets paid by the other side, regardless of whether the stock went up, down, or sideways to get there.

The payoff

$$\text{Payoff} = N \times (\sigma_{\text{realized}} - K_{\text{vol}}),$$

In words: $\sigma_{\text{realized}}$ is the annualized realized volatility actually measured over the contract's life (computed from the underlying's day-to-day returns), $K_{\text{vol}}$ is the fixed volatility level, called the vol strike, agreed at the start, and $N$ is the notional per volatility point ("vega notional"). The long side of the swap profits when realized volatility comes in above the strike — they were "long vol" and the market delivered more chop than priced in — and loses when it comes in below. Nothing about the stock's price direction enters the formula at all; only how much it wiggled, in either direction, matters.

Worked example 1 — a simple settlement

A one-year volatility swap on an index has vol strike $K_{\text{vol}} = 18\%$ and vega notional $N$ = $50,000 per volatility point. Over the year, realized volatility actually comes in at 24%. Payoff to the long side $= 50{,}000 \times (24-18) = 50{,}000 \times 6 =$ $300,000. If instead realized vol came in at 13%, the long side pays the short side $50{,}000\times(13-18) = 50{,}000\times(-5) =$ -$250,000 — a loss, even if the index itself had a great year for returns, because the swap only cares about how much it bounced around along the way.

Worked example 2 — why vol swaps aren't just replicated with straddles

A trader might think a long vol swap is roughly the same as delta-hedging a long straddle, since both profit from big moves. They're close but not identical: a delta-hedged option position's P&L from realized volatility is not linear in $\sigma_{\text{realized}}$ — it depends on the path of realized volatility over time (how it's distributed day by day), not just the final annualized number, and it also carries gamma that isn't constant across strikes. A true vol swap's payoff, by contrast, is exactly linear in the single number $\sigma_{\text{realized}} - K_{\text{vol}}$, with no path dependence beyond that final realized-vol calculation. This is precisely why market makers actually replicate vol swaps using a portfolio of options across many strikes (a "variance swap" replication, described in the variance swaps page) rather than a single straddle, then convert the resulting variance exposure into volatility exposure — an extra step, because variance is what actually replicates cleanly, and volatility is its square root.

Generate a few paths above and picture measuring how choppy each one is, independent of where it ends up — two paths can end at the exact same final price with very different realized volatility, and a vol swap only cares about the second thing, never the first.

What this means in practice

Volatility swaps let a trader take a pure, linear view on realized volatility without any of the direction-related bookkeeping (delta hedging, gamma scalping) that comes with running an options position to the same end. They're used to hedge a vol-trading book's convexity risk, to speculate directly on an event's volatility impact, or by variance-swap dealers who want to offer clients a volatility-quoted product while still hedging in variance terms underneath. Liquidity is thinner than for listed options — most volatility swaps trade over the counter between institutions, not on an exchange.