Term structure, and why calendars profit

Everything so far has used one expiration. A calendar spread uses two: you sell an option in a near expiration and buy the same strike in a later one. It is the first structure in this course that collects theta while being long vega, which makes it the natural tool for quiet markets where IV is low and condors pay too little. To understand it you need one new idea, the term structure of implied volatility.

Term structure

Each expiration has its own implied volatility. Plot them against days to expiration and you get the term structure:

• Upward sloping (contango): longer-dated IV is higher than near-dated. This is the normal state in calm markets. Near-term uncertainty is low; the far future is always uncertain.
• Downward sloping (backwardation): near-dated IV is higher. This happens around scheduled events (earnings, a central bank decision) and during sell-offs, when the next few weeks are what everyone fears.

IV by expiration (schematic)

  IV
  40% |  *                          backwardation (event or panic)
      |    *
  30% |      *  *  *  *  *  *  *  *  flat
      |   *  *
  25% | *                            contango (calm)
      +----+----+----+----+----+----
       7   30   60   90  120  180   days to expiration

A calendar spread is a position on this curve. Because you are short the near option and long the far one, you gain if near-dated IV falls relative to far-dated IV, and lose if it rises relative to it.

The long calendar

XYZ at $50. Sell the 30-day $50 call at $1.70 (IV 30%). Buy the 60-day $50 call at $2.45 (IV 30%, flat term structure for simplicity). Debit $0.75, which is the maximum loss.

The P&L is evaluated at the front expiration, 30 days from now, when the back-month call still has 30 days left. The front call is worth its intrinsic value; the back call is worth whatever a 30-day option is worth at that price, assuming IV is still 30%.

Max profit about $0.95 at $50, about 127% of the debit. Breakevens near $47.70 and $52.80. Max loss $0.75 at the extremes, where both calls converge to intrinsic and the spread goes to zero. The shape is a tent, like a butterfly, but with curved sides because the back option still has time value.

Long calendar $50, sell 30d / buy 60d, 0.75 debit

  +95  |            /\
       |          /    \
    0  |--------X--------X--------   X = 47.70 / 52.80
       |      /            \
  -75  |____/                \____
       +---+---+---+---+---+---+---+
       44  46  48  50  52  54  56   XYZ at front expiry

Why it profits

Two mechanisms, both visible in the Greeks.

Theta differential. Time decay runs at roughly 1/√T. The 30-day call at $1.70 will lose all $1.70 in the next 30 days. The 60-day call at $2.45 will lose only $0.75 in the same 30 days, ending at $1.70, because it goes from 60 days to 30 days rather than from 30 to zero. You are short the fast decay and long the slow decay. If XYZ does nothing, the spread you bought for $0.75 is worth $1.70.

Vega. The back call has more vega than the front. If IV rises across both months, the spread gains. That is the opposite of every credit structure in Modules 2 and 3.

Delta-neutral, short gamma, positive theta, positive vega. The short gamma is the same warning as everywhere else: a big move in either direction is the loss. The positive vega is what is new. A calendar in a low-IV environment is a position that earns while it waits for IV to rise, and both of those pay.

Where it fits

• Low IV rank. When condors collect too little, calendars are cheap to buy (the back month is cheap) and benefit from the IV recovery that low IV rank suggests.
• A price you expect the stock to sit near. The tent is narrow; the profit depends on the stock being close to the strike at the front expiration. Directional calendars use a strike above or below the price to add a mild lean.
• Contango helps entry, backwardation helps exit. You would rather buy the calendar when the back month is not much more expensive than the front (flat or slightly upward curve) and see the front month's IV rise relative to the back after entry.

The two risks are a large move (the tails of the table) and a fall in back-month IV relative to the front, covered in lesson 4. Neither can be defined in advance beyond the debit, which is the good news: the most you can lose is what you paid.

Key idea: A calendar sells the near expiration and buys the far one at the same strike. It profits because the near option decays faster and because the far option carries more vega, so it collects theta while being long volatility. Max loss is the debit; max profit is at the strike at the front expiration; the tent is narrow.

Try it: Build a 30/60-day ATM call calendar on a stock with low IV rank in the options profit calculator. Record the debit, the value at the front expiration if the stock is unchanged, and the breakevens. Then raise IV by 5 points and note the change; then lower it by 5 points. Compare that to the same test on an iron condor.

Recap

• Term structure is IV by expiration: upward sloping in calm markets, inverted around events and in sell-offs.
• A long calendar sells the near option and buys the far one at the same strike; the debit is the max loss.
• Profit comes from the front decaying faster than the back, and from the back's larger vega if IV rises.
• The calendar here nets +1 delta, −2.7 gamma, +$0.90 theta and +$2.40 vega per spread.
• Best used at low IV rank with a strike near where you expect the stock to sit at the front expiration.