Show how volatility derivatives, including variance swaps, are used in practice

A variance swap pays variance notional × (realised variance − strike variance), where variance notional = vega notional ÷ (2 × strike volatility). With vega notional 1,000,000, strike 20 and realised volatility 25, variance notional is 25,000 and the payoff is 25,000 × (625 − 400) = 5,625,000, above the 5,000,000 a linear volatility bet pays: the payoff is convex. Before expiry, expected variance blends realised variance to date and implied variance for the remainder, weighted by time. The value is the variance notional × (expected variance − strike variance), discounted. Volatility index futures and options hedge equity sell-offs, since volatility spikes when stocks fall. The trap is carry: these futures usually sit in contango, so long hedges lose as they roll.