Calendar and diagonal spreads: trading time decay and the term structure

What you will learn

• How a calendar spread is built and why its value depends on both time and implied volatility.
• How to estimate its result at the front expiry for several prices.
• Why the term structure decides whether a calendar is cheap or expensive.
• How a diagonal spread replaces a covered call with far less capital, and what it gives up.

Explanation

A calendar spread (also "time spread") sells a near-term option and buys a longer-dated option of the same type and strike, for a net debit that is also the maximum loss. It profits when the front option expires or is bought back cheaply while the back option still holds time value, which happens when the underlying stays near the strike.

Two engines: theta and vega

The Greeks were introduced in the course Derivatives: Futures, Options, CFDs and Certificates; here they do real work. At-the-money time decay (theta) accelerates near expiry, so the short front option decays faster than the long back option: the calendar is net positive theta. Sensitivity to IV (vega) grows with time to expiry, so it is also net positive vega. This combination is rare; most short-premium trades are negative vega. The price is that large moves away from the strike hurt, because both options converge to intrinsic value.

Term structure decides the price

If the front expiry carries higher IV than the back (backwardation), the front option is relatively expensive and the calendar is cheap; in steep contango the calendar costs more. Comparing the two IVs is the first check before entry.

Diagonal spreads

A diagonal spread changes both expiry and strike. The common version buys a deep in-the-money, long-dated call (70 to 80 delta, 60 to 120 DTE) and sells a shorter-dated out-of-the-money call against it: a "poor man's covered call" that ties up a fraction of the capital. Trade-offs: no dividend, the long call decays, and the profit is capped above the short strike.

Worked example

Hypothetical example: a stock at $100. Front month: 30 DTE, IV 24 percent; back month: 60 DTE, IV 22 percent (mild backwardation). Model mid prices: 30-DTE 100 call 2.75; 60-DTE 100 call 3.55. Interest and dividends ignored.

Entry: sell the 30-DTE 100 call at 2.75, buy the 60-DTE 100 call at 3.55. Debit 0.80 ($80 per spread). Maximum loss $80.

Greeks at entry (per share, model-based): theta front -0.046 per day, back -0.030; net +0.016, about $1.60 per day per spread. Vega front 0.114, back 0.162 per volatility point; net +0.048, about $4.80 per spread per IV point.

Result at the front expiry (30 days later), IV of the back option unchanged at 22 percent:

For the $100 row: the front call expires worthless; the back call is now a 30-DTE at-the-money call at 22 percent IV, worth about 2.50; minus the 0.80 debit gives +1.70. For the $108 row: front call intrinsic 8.00 (you owe it), back call 8.35, spread 0.35, loss 0.45.

The profit zone is roughly 95 to 105; it widens if IV rises and narrows if IV falls. If back-month IV dropped to 18 percent with the stock at 100, the back call would be worth about 2.05 and the profit would shrink to about 1.25.

Diagonal for comparison: buy a 90-DTE 95 call at 7.20 (about 0.70 delta), sell a 30-DTE 105 call at 1.00. Debit 6.20 ($620) instead of $9,500 for 100 shares. If the stock is unchanged at the front expiry, the $100 premium is kept against roughly $65 to $70 of decay in the long call (model estimate); if the stock jumps to 112 the spread is worth at most the 10-point strike difference, so the gain is capped near 3.80 per share.

Exclusions: commissions, two-leg bid-ask costs, early assignment of the short call (lesson 10).

Common mistake

Practice activity

On paper: a stock is at $50. You sell a 30-DTE 50 put at 1.40 and buy a 60-DTE 50 put at 1.85. (a) State the debit and the maximum loss. (b) At the front expiry the stock is at $50 and the back put (now 30 DTE) is worth 1.30; compute the profit. (c) At the front expiry the stock is at $44 and the back put is worth 6.15; compute the result. (d) Which of the two situations would a rise in IV at the front expiry have improved, and why?

Key takeaways

• A calendar sells near-term time value and buys longer-term time value; its maximum loss is the debit.
• It is positive theta and positive vega: it wants the stock to stay near the strike and IV to stay or rise.
• Compare front and back IV before entry; backwardation makes calendars cheap, contango makes them expensive.
• A diagonal replaces a covered call with a deep in-the-money long call and a fraction of the capital, with a capped upside and no dividend.

Next step

Next you will apply the term-structure ideas to the most extreme short-term event in options: earnings, with straddles, strangles and the volatility crush.