Variance Swap

What is Variance Swap?

Variance Swap A variance swap is an OTC derivative that allows traders to take pure exposure to realized variance (the square of realized volatility) over a specified period. The buyer of a variance swap pays a fixed "variance strike" at maturity and receives the actual realized variance; the seller does the opposite. The product enables direct trading of volatility without the strike, expiration, and Greeks complications of options. Mechanics: - Two counterparties agree on a variance strike (typically expressed as σ²) - Over the swap's tenor, realized variance is calculated daily based on close-to-close returns - At maturity, the payoff is: (realized variance − variance strike) × variance notional Worked example structure: - Counterparty agrees: 30-day SPX variance swap with strike 256 (16% σ) - Daily realized variance accumulates: each day's squared log-return contributes to the running variance calculation - If realized variance comes in at 324 (18% σ), the long-variance party receives 324 − 256 = 68 variance points × notional - If realized variance comes in at 196 (14% σ), the long-variance party pays 256 − 196 = 60 variance points × notional Variance swaps were invented to address limitations of using options for pure-vol trading: - **Path-independent**: option vol P&L depends on the path the underlying takes; variance swap P&L only depends on aggregate variance over the period - **No Greeks management**: variance swaps have linear exposure to realized variance, no delta hedging required - **No strike or expiration concerns**: a variance swap is just a single contract on aggregate variance - **Convex in volatility**: variance swaps have convex payoffs (variance = σ²), giving leveraged exposure to large vol moves Variance swaps are dominant in institutional volatility trading: - **Dispersion trading**: variance swaps on index vs basket of single-stock variance swaps - **Volatility arbitrage**: pure vol bets without delta management - **VIX trading mechanics**: VIX is calculated from a basket of variance swaps (theoretically), making variance swaps the building blocks of VIX Retail access to variance swaps is essentially zero. They're OTC products requiring institutional credit lines and counterparty risk management. Retail proxies include: - **VIX futures**: linear exposure to VIX (which is calculated from variance swaps) - **VIX ETPs (VXX, UVXY)**: track VIX futures with roll-yield characteristics - **Long straddles**: option-based approximation of long variance, but with path dependence - **Calendar spreads**: relative-value variance plays across time The mathematical foundation of variance swaps connects directly to options pricing theory. A long variance swap can be replicated (in theory) by buying a portfolio of options weighted by 1/strike². This replication relationship is why volatility traders care about variance swaps even when they don't directly trade them — the pricing of variance swaps informs the pricing of options portfolios. Famous variance swap blow-ups during financial crises (LTCM 1998, Long-Term Capital Management's exposure to variance swaps, multiple hedge fund losses in March 2020) underscore the convex nature of variance — variance moves more violently than volatility in stress regimes.