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| Variance swaps are derivative contracts whose payoff is proportional to the difference between realized variance and a preset variance strike, allowing pure volatility bets without the need for continuous Delta-hedging. |
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Volatility Trading with Variance Swaps
Section: 7.6 | Asset Class: Volatility | Type: Volatility / Derivatives
Overview
Variance swaps allow traders to bet on future realized variance without the operational burden of continuous Delta-hedging required by options-based volatility strategies. The payoff at maturity is proportional to the difference between the realized variance of the underlying and a preset variance strike K, scaled by a variance notional N.
Construction / Mechanics
Payoff at maturity T (for the long side):
P(T) = N × (v(T) - K) (434)
Realized variance over the period:
v(T) = (F/T) Σ_{t=1}^T R(t)² (435)
Log-return at time t:
R(t) = ln[S(t) / S(t-1)] (436)
where:
- t = 0, 1, ..., T: sample points (e.g., trading days)
- S(t): underlying price at time t
- F: annualization factor (F = 252 for daily data)
- N: variance notional (preset, in dollar terms)
- K: variance strike (preset at contract inception; determines the fair value entry price)
- Note: the mean return is NOT subtracted in v(T), so the denominator is T (not T-1)
Long variance swap: benefits when realized variance v(T) > K (realized vol was higher than expected). Short variance swap: benefits when realized variance v(T) < K (realized vol was lower than expected).
Fair value of K: at inception, K is set such that the swap has zero initial value; it equals the market's expected future variance (often proxied by the square of the VIX for equity index variance swaps).
Payoff / Return Profile
- Long variance swap profits when realized variance exceeds the variance strike K: v(T) > K.
- Typical use: hedge against a volatility spike; gains are convex in the volatility move (since variance is the square of vol).
- Short variance swap profits when realized variance is below K: v(T) < K.
- Typical use: harvest the volatility risk premium (implied vol > realized vol on average); earns N × (K - v(T)) in normal markets.
- The payoff is in units of variance (not volatility); a move from 10% to 20% vol generates 4× the payoff of a move from 10% to 15% vol.
Key Parameters / Signals
- K: variance strike (the break-even point)
- N: variance notional (dollar value per unit of variance)
- v(T): realized variance (the key realized outcome)
- F: annualization factor (252 for daily, 52 for weekly, etc.)
- T: number of observation periods
- v(T) - K: the net P&L per unit of notional
Variations
- Volatility swap: payoff based on sqrt(v(T)) - K_vol (realized volatility minus vol strike); less convex than variance swap; harder to replicate.
- Conditional variance swap: accumulates variance only on days when the underlying is within a specified range.
- Corridor variance swap: similar, accumulates variance only when the underlying is above (or below) a barrier.
Notes
- The key advantage over options-based volatility strategies: no Delta-hedging required, so the trader takes pure variance exposure with no directional risk (assuming no P&L drift from Delta).
- The convexity of the variance payoff (variance = vol²) means long variance swaps gain more from large vol spikes than short options positions gain from vol increases.
- Short variance swaps capture the volatility risk premium (K > expected realized variance) but have unlimited downside: if realized variance is very high (e.g., a market crash), N × (v(T) - K) can be very large.
- Variance swaps on equity indexes are liquid OTC instruments; single-stock variance swaps are less common.
- The mean is not subtracted in v(T) (Eq. 435), which is standard market convention; subtracting the mean would change the denominator to T-1.