Calendars, read at the front expiry

A calendar spread uses two options with the same strike and different expiry dates. It profits when the stock sits near the strike as the nearer option runs out of time. Its payoff graph has a tent shape, and that graph only makes sense when it is read at the first expiry date, not the last.

What a call calendar is

A call option gives its owner the right to buy 100 shares at a fixed price, the strike, until a date called the expiry. A call calendar has two legs:

• Sell a call with a near expiry, called the front month.
• Buy a call at the same strike with a later expiry, called the back month.

The later option costs more, because it has more time for the stock to move. So you pay a net amount to open the trade, called a debit. A put calendar does the same with puts, and at the same strike its shape is very close to the call version.

The example: a 330 call calendar on AAPL

The figures are illustrative, model prices, with AAPL at 331.90 and implied volatility assumed flat at 28% for both expiries. Implied volatility is the size of future moves that option prices assume.

The debit of about $407 per calendar is the most the trade can lose in normal conditions, because the back option is worth at least as much as the front option at the same strike while both are alive.

Why the payoff is a tent

At the front expiry, the short call either expires worthless (stock below 330) or is worth the stock price minus 330 (stock above 330). The long call still has 28 days left. Its value depends on where the stock is:

• Stock at the strike. The front call expires worthless and the back call keeps the most time value, because an option at the strike has the most uncertainty left. This is the peak of the tent.
• Stock far below. Both calls are nearly worthless. You lose most of the debit.
• Stock far above. Both calls behave almost like shares, so their values nearly cancel. You also lose most of the debit.

So the graph rises to a peak near 330 and falls away on both sides. In the model example, with volatility unchanged, the back call would be worth about $10.70 at the front expiry if AAPL sat exactly at 330. The result is 10.70 − 4.07, a gain of about $6.63 per share, or about $663. Further away, at 315 or 345, the model still shows a small gain; at 300 or 360 it shows a loss.

Why it must be read at the front expiry

For most spreads, a risk graph draws a straight-line payoff at expiry, because every option is then worth only its intrinsic value: how far it is in the money. A calendar has two expiries. At the back expiry the front leg is long gone, so a graph drawn there describes a trade you no longer hold.

The useful moment is the front expiry. At that date the short call is settled, but the long call still has time value. Time value cannot be read off a straight line; it has to be priced with a model, using an assumed implied volatility and the days left. That is why the calendar's expiry line is curved, and why it moves when you change the volatility assumption.

Theta and vega: the two engines

Theta measures how much an option loses each day from the passing of time. Options near expiry lose value faster than options further out. The calendar is short the fast-decaying front call and long the slower-decaying back call, so near the strike its theta is positive: it gains from each day that passes, all else equal.

Vega measures how much an option's price changes for a one point move in implied volatility. Longer-dated options have more vega. Because the calendar owns the longer option, its net vega is positive: a rise in implied volatility, mostly in the back month, raises its value, and a fall lowers it.

What moves a calendar

• Price leaving the strike. The further the stock moves from 330 in either direction, the lower the tent. This is the main risk.
• Implied volatility changes. A rise in back-month volatility lifts the trade; a fall drags it down. A drop in volatility after an expected event, such as earnings, can hurt a calendar even if the stock stays still.
• Term structure. Term structure is the pattern of implied volatility across expiries. If the front month is priced with higher volatility than the back, you sell rich and buy cheaper, which helps the entry. If the back month is richer, the debit is larger. The two legs can also move separately after you open the trade.

The calendar is not a crash trade. A sharp fall moves the stock away from a strike near the money, and the gain from rising volatility usually does not make up for that. The crash band shows the size of that effect on your own legs.

Double calendars and diagonals

A double calendar places two calendars at once: usually a put calendar below the current price and a call calendar above it. The graph shows two peaks with a flatter area between them, which widens the zone where the trade does well, at the cost of a larger debit.

A diagonal uses different strikes as well as different expiries, for example selling a nearer call at a higher strike and buying a later call at a lower strike. This adds a directional lean. The poor man's covered call is a diagonal that uses a deep in-the-money long call in place of shares.

How Trident draws it

In the Strategy Lab, a calendar is built from the live chain with the front and back expiries you choose. The risk graph sets its expiry line at the front expiry and prices the remaining back leg with a model, so the tent appears in its true shape. A second line shows the trade today. You can shift the implied volatility assumption to see how the tent rises or sinks, and the Greeks panel shows the net theta and vega as you move the strike.

Frequently asked questions

What is the max loss on a call calendar?

In normal conditions it is the debit paid, about $407 in the example. Early assignment of the short call or extreme moves in volatility can change the result, so check the live graph.

Why does a calendar lose money if the stock rises a lot?

Deep in the money, both calls move almost one for one with the stock and carry little time value, so the back call's extra value shrinks toward zero and most of the debit is lost.

When should a calendar be closed?

A calendar is usually closed at or before the front expiry, because after that you hold only a single long call. The exact timing is part of your own plan.

Is a put calendar different from a call calendar?

At the same strike and expiries the shapes are very close. The choice often comes down to pricing, liquidity and assignment risk on the short leg.

To draw a calendar at the front expiry and test it against volatility changes on your own symbols, book a demo of Trident.

Illustrative example with model prices, not a recommendation. Options carry risk of loss. See the risk disclosure.