Term Structure Arbitrage

Term structure exists because uncertainty isn't uniform across time. More time means more potential events and price moves, typically leading to higher IV for far expirations (contango). However, specific near-term events or stress can flip this to backwardation. The term structure reflects the market's aggregated view of time-varying risk.

Not primarily. ATM calendar spreads start with near-zero delta (no directional bias). However, they have negative gamma, meaning large moves in either direction hurt the position. The trade is primarily about time and term structure, not direction. The position does develop directional exposure as the underlying moves away from the strike.

Far-term options have more time value than near-term options at the same strike. When you buy the far-term and sell the near-term, you're buying more time value than you're selling, resulting in a net debit. This debit is your maximum loss and the 'cost' of the theta/term structure exposure.

At near-term expiration: if underlying is at strike, near-term expires worthless (you keep the premium) while far-term retains significant value (maximum profit). If underlying is far from strike, both options are either deep ITM (intrinsic offsets) or deep OTM (both worthless), resulting in loss of the debit.

You can trade term structure on any underlying with listed options at multiple expirations. UK single stocks, FTSE 100, and other indices all have term structures. However, liquidity varies significantly - FTSE options are more liquid than most single stocks. Check bid-ask spreads across expirations before trading.

Event-driven backwardation is usually localized: one or two expirations are elevated (around the event date), while others are normal. The event is identifiable (earnings, BoE meeting). Stress-driven backwardation affects the whole curve: all near-term expirations elevated vs all far-term. It correlates with VIX spikes and market selloffs.

Long calendars (positive vega) prefer stable or rising IV. Low IV environments are challenging because if IV drops further, the far-term option loses more value. High IV with backwardation is ideal for long calendars - you're selling expensive near-term IV expecting normalization. Be cautious in falling IV environments.

VIX term structure (VIX futures) is derived from SPX options term structure but traded as a separate product. They're related but not identical. VIX term structure is more tradeable directly (VIX futures), while SPX/FTSE term structure is traded through options calendars. Both show contango normally and backwardation in stress.

Term structure (across expirations) and skew (across strikes) are related. During stress, both typically steepen: near-term IV rises more (backwardation) AND put IV rises more (steeper skew). They can move independently, but often correlate in stress. Some advanced strategies trade both simultaneously.

Variance swaps provide 'purer' exposure to variance without gamma/delta complications. Options calendars have negative gamma (hurt by large moves) and changing delta (develop directional exposure). Variance swaps pay only on realized variance vs implied - cleaner for vol trading. Retail traders don't have access, so calendars are the alternative.

Calculate forward variance from the term structure: FV = [IV(far)²×T(far) - IV(near)²×T(near)] / [T(far)-T(near)]. Compare this to your expectation for realized variance over that period, considering: historical vol, upcoming events, mean reversion. If forward variance implies vol significantly different from expectation, opportunity may exist.

Size for worst-case scenario (VIX to 80+), not average case. Methods: (1) Maximum notional that survives a 3x VIX spike without devastating loss, (2) Volatility targeting where position size scales inversely with VIX level, (3) Kelly-based sizing given win rate and average win/loss. Most suggest keeping notional <10-15% of portfolio.

PCA-based factor models work well. Fit a smooth curve to the term structure, then analyze residuals for mean reversion. For trading: parallel shifts (factor 1) dominate, so net vega matters most. For relative value: slope (factor 2) and curvature (factor 3) create calendar and butterfly opportunities. Update factor loadings periodically as market regime changes.

Aggregate vega by expiration bucket across all positions. Track 'slope sensitivity' - how portfolio P&L changes with 1% change in near/far ratio. Set limits (e.g., max 1% NAV per 5% slope change). Balance exposures: if too concentrated in far-term vega, add near-term positions or calendars. Consider correlation with other risks (VIX, skew).

True calendar arbitrage (riskless profit) requires negative forward variance: IV(near)²×T(near) > IV(far)²×T(far). This is rare because market makers prevent it. Near-arbitrage exists when forward variance is very low (implying unrealistically low future vol) or very high (implying unrealistically high vol). Transaction costs must be considered - small violations aren't tradeable.