Calendar Spread

A calendar spread is a position made of two contracts on the same underlying asset that differ in their expiry or delivery date. One contract is bought and the other is sold. The trader is not betting mainly on the direction of the underlying price but on how the price difference between the two dates will change. The strategy is also called a time spread or horizontal spread.

Calendar spreads exist in both options and futures. In options, the two legs have the same strike and different expiry months, and the position draws on the fact that short-dated options lose value faster than long-dated ones. In futures, the two legs are different delivery months, and the position reflects the shape of the futures price curve. In both markets the trade is a basic form of spread trading.

A long calendar spread sells an option that expires soon and buys an option of the same type and strike price that expires later. The longer-dated option always costs more, so the trade is opened for a net debit:

• $P_{\text{far}}$ is the premium paid for the longer-dated option.
• $P_{\text{near}}$ is the premium received for the shorter-dated option.

The net debit is the most the position can lose, provided it is closed when the near option expires. The position profits when the near option decays faster than the far one. That happens most strongly when the underlying price sits at the strike as the near option expires: the option sold is then worthless, while the option held still has its full time value. Unlike a vertical spread, the maximum profit cannot be stated in advance, because it depends on what the far option is worth on that date, and that depends on implied volatility at the time.

A share trades at $100. A trader sells a one-month $100 call option for $2.50 and buys a three-month $100 call for $4.50. The net debit is 4.50 − 2.50 = $2.00.

One month later the share is still at $100. The call sold expires worthless. The call held now has two months left and, if volatility is unchanged, might be worth about $3.60. Selling it gives a profit of 3.60 − 2.00 = $1.60 per share. If the share had moved to $85 or $115 instead, the two calls would be worth nearly the same as each other, the spread would be close to zero, and most of the $2.00 would be lost.

A long calendar spread has positive theta while the price is near the strike, because the short option decays faster than the long one. It has positive vega: longer-dated options respond more to a change in implied volatility, so a general rise in volatility helps and a fall hurts. Its gamma is negative, so large price moves in either direction work against it.

The two expiries do not always move together. Implied volatility for the near month can jump ahead of an earnings report or other event while the far month barely changes. A calendar spread is therefore a position on the term structure of volatility, one slice of the volatility surface. The implied volatilities of the two legs together define a forward volatility for the period between the two expiry dates, and traders use calendar spreads to take a view on it.

In futures, a calendar spread buys one delivery month and sells another in the same commodity, index or interest rate product. Exchanges list many such spreads as instruments that trade at a single price, the difference between the two months. Because the legs tend to move together, exchanges usually set lower margin for the spread than for either leg alone.

The spread reflects the cost of carrying the asset from one date to the other: financing, storage and insurance, less any income. When later months are priced above nearer ones the market is in contango, and the reverse is backwardation. A trader who expects supply to tighten may buy the near month and sell the far month, a bull spread. Calendar spreads are also the tool for rolling a position: a holder of an expiring futures contract sells it and buys the next month in one trade.

• Reverse calendar spread. The trader buys the near option and sells the far one, gaining from a large price move or a fall in implied volatility.
• Diagonal spread. The two options differ in strike as well as in expiry, adding a directional lean.

The main risk of a long options calendar is a sharp move in the underlying before the near expiry. A second is a fall in implied volatility, which lowers the value of the long option that remains. Early assignment is possible on the short leg where the contracts are of the American option type. Once the near option has expired, the trader holds a single long option, and the position is no longer a spread unless another near-dated option is sold against it.

Futures calendar spreads are often described as low risk because the legs offset each other, but the difference between months can move violently when physical supply is disrupted or when storage runs short, and the loss on such a spread has no fixed limit.