Time Spreads & Diagonals

Long Call Time Spread:
Short 1 XYZ Sep 50 call @ $2.00, Long 1 XYZ Dec 50 call @ $5.00
Cost	$300 Debit
Maximum Loss:	$300
Maximum Profit:	Depends on value of Dec 50 call at time of Sep expiration
Short Call Time Spread
Long 1 XYZ Sep 50 call @ $2.00, Short 1 XYZ Dec 50 call @ $5.00
Cost	$300 Credit
Maximum Loss:	Depends on value of Dec 50 call at time of Sep expiration
Maximum Profit:	$300
Long Put Time Spread
Short 1 XYZ Sep 50 put @ $1.00, Long 1 XYZ Dec 50 put @ $3.00
Cost	$200 Debit
Maximum Loss:	$200
Maximum Profit:
Short Put Time Spread
Long 1 XYZ Sep 50 put @ $1.00, Short 1 XYZ Dec 50 put @ $3.00
Cost	$200 Credit
Maximum Loss:	Depends on value of Dec 50 put at time of Sep expiration
Maximum Profit:	$200

Explanation and Application

Time spreads are so called because they are positions with options in two different expiration months, with the options being either both calls or both puts. Time spreads involve buying an option in one expiration month and selling another option in a different expiration month but with the same strike as the first option. Specifically; a long call time spread is selling a call in a front month at a certain strike, and buying a call in a deferred month at the same strike. A put time spread is selling a put in a front month at a certain strike, and buying a put in a deferred month at the same strike. A short call time spread or put time spread is simply the reverse of the long time spread: long front month and short deferred month. In time spreads, one option in the position expires before the other. You have to keep this in mind because it does present certain risks and necessary adjustments that other types of positions might not.

Time spreads, whether they are call time spreads or put time spreads, maximize their value when the stock is at the strike price of the options, and the front month option is expiring. Time spreads have their minimum value when the stock is very far away from the strike price of the options. If you buy a time spread you want the stock price to be at the strike price at expiration. If you sell a time spread you want the stock price to be as far away as possible from the strike price at expiration.

Therefore, a long time spread might be a good position if you think the stock price is going to move to, then stay at, a particular strike price until expiration of the front month option. The maximum risk of a long time spread is the amount paid for it. The maximum value depends on the value of the deferred month option when the front month option expires. That depends largely on the implied volatility of the deferred month options.

Another risk of time spreads is that of assignment of the short option, which will transform your time spread into another position. For example, a long put time spread has the risk of assignment on the short front month put. If the short put is assigned, you will receive long stock in your account. That, along with the remaining deferred month put, is a synthetic long call. This position does not have unlimited risk. But it is significantly different from the original long put time spread and could require a great deal of cash or margin in your account to be able to hold the long stock position. You must be aware, then, of the sometimes significant risks due to assignment when you have short ITM options in any position.

Greeks

Delta

The delta of a time spread is determined by where the stock price is relative to the strike price of the options. Depending on where the price of the stock is relative to the strike price of the time spread, the delta of the time spread can go from positive, to neutral, to negative.

When the stock price is equal to the strike price, the deltas of the time spread, whether it's long or short, are pretty neutral. This is due to the fact that the deltas of ATM calls (or puts) are very similar to each other no matter how much time there is until expiration, and are relatively unaffected by volatility. The differences between ATM deltas across expirations are relatively small, and depend largely on the carrying costs.

But as the stock price moves away from the strike price of the options, the deltas of the time spread change very much. No matter if it's a call time spread or put time spread (their P&L profiles are very similar), when the stock price is less than the strike price, a long time spread has positive deltas and a short time spread has negative deltas. When the stock price is greater than the strike price, a long time spread has negative deltas (it wants the stock to come down to its strike price) and a short time spread has positive deltas (it wants the stock to come up away from its strike price). It's interesting to see why the deltas of call and put time spreads are the same. When the stock price is less than the strike price, the calls are OTM and the puts are ITM. Deltas on ITM options get closer to 1.00 the closer the option is to expiration. Deltas on OTM options get closer to 0.00 the closer the option is to expiration. A long OTM call time spread is short a front month OTM call that generates fewer negative deltas than the positive deltas generated by the long back month OTM call. Therefore the long OTM call time spread has positive deltas. A long ITM put time spread is short a front month ITM put that generates more positive deltas than the negative deltas generated by the long back month ITM put. Therefore the long ITM put time spread has positive deltas also.

Gamma

The gamma of a time spread, like its delta, depends on where the stock price is relative to the strike price of the options. When the stock is equal to the strike price, a long time spread has negative gamma. Remember, when the stock price is equal to the strike price the time spread maximizes value. Any movement by the stock away from the strike price will cause the time spread to fall in value. The reason is that negative gamma manufactures positive delta if the stock price falls, and negative delta if the stock price rises – both cause the time spread to theoretically lose value.

The negative gamma is due to the fact that the gamma of an ATM option increases as time goes by. A long ATM time spread, whether it's a call or put, has a short front month option that generates more negative gamma than the positive gamma generated by the long deferred month option. The difference between gamma in the different months is most pronounced for the ATM strike, and diminishes the more OTM or ITM an option becomes until, at a certain point, the deferred month option generates more positive gamma than the negative gamma generated by the front month. That's due to the curvature of gamma. No matter how much time to expiration, gammas for ITM and OTM options are low relative to ATM options. But gammas for ITM or OTM options with more days to expiration are relatively higher than the gammas for ITM or OTM options with fewer days to expiration. And the gamma for ATM options with more days to expiration is relatively lower than the gamma for ATM options with fewer days to expiration. The result is that OTM and ITM time spreads have positive gammas, indicating that they want the stock to move (to their respective strike).

Theta

The theta, or time decay, of a time spread corresponds inversely to its gamma. Theta has the same type of curvature as gamma. But where the gamma of a long time spread is negative, its theta is positive. An ATM time spread wants the stock to stay where it is (equal to the strike price) and for time to pass – that's indicated by the positive theta. When the gamma turns positive for long OTM and ITM time spreads, theta turns negative – if the stock stays where it is, and the time spread continues to be OTM or ITM, the value of the time spread will fall as time passes.

Vega

Just as deferred month options have greater extrinsic value than front month options, they also have greater vega, or sensitivity to changes in volatility. Like gamma and theta, vega is greatest for the ATM time spreads but unlike gamma and theta, vega is greater in the deferred month at every strike price. Because different option expirations can have different implied volatilities, fluctuations in volatilities between the different months can have a large impact on the value of time spreads. Long time spreads have positive vega, meaning if volatility increases, their value increases, and if volatility decreases, their value decreases. To add to the vega issue, if volatility rises in the front month, and either stays the same or falls in the deferred month, a time spread could lose value. That's why if you're contemplating trading time spreads, you should have an idea of how volatility can change from expiration month to expiration month, because this can be a significant source of risk.

Structure

The relationship between a call time spread and a put time spread at the same strike and in the same months is directly related to the 'jelly roll' spread or simply, the "roll". If your position is a long call time spread, and you sell roll, the resulting position will be a long put time spread. If your position is a long put time spread, and you buy a roll, the resulting position will be a long call time spread. The only difference, then, between a long call time spread and a long put time spread at the same strike is a market-neutral position, the roll.

The interrelationships of the structures of jelly rolls and time spreads are shown in Exhibit–1. The structure of this short jelly roll consists of a long 100 strike call time spread, spread against a short 100 strike put time spread, which is also equivalent to a far month long combo versus the near month short combo. Simply put; a call time spread is synthetically a put time spread because the difference is a jelly roll (two synthetic underlyings against each other).

Pricing

A time spread's value is determined by the difference in extrinsic values of the front month option and the deferred month option. (The intrinsic values of the options are the same, therefore, they cancel each other out.) All other things (stock price, strike price, dividends, interest rate, and volatility) being equal, an option with more days to expiration will have more extrinsic value than an option with fewer days to expiration. ATM options, whether they are puts or calls, have more extrinsic value than OTM or ITM options. Therefore, the ratio of extrinsic value between the deferred month and front month (which is the value of the time spread) depends on how close the stock price is to the strike price of the options and the difference between the number of days to expiration for the two options.

The effect of theta on extrinsic value, or how much time decay erodes the extrinsic value of options, is non- linear. That is, the closer an option is to expiration, the greater the effect of time decay on its extrinsic value. Therefore, the ratio of extrinsic value between the deferred month and the front month is also inversely proportional to how close the front month option is to expiration. In practice, an ATM time spread whose front month option is, say 10 days to expiration, will be increasing in value faster than an ATM time spread whose front month option is 90 days to expiration.

The relationship between a call time spread and a put time spread at the same strike and in the same expiration months depends on the roll. Because the value of the roll is basically a function of the carrying costs between the two expiration dates, and because the difference between a call time spread and a put time spread is a roll (as described above), the difference between the call and put time spreads is also a function of carrying costs.

The values of time spreads can be better understood with respect to jelly rolls. Jelly rolls in equities are interesting because the early exercise feature causes put spreads to collapse when cheap calls approach a value that is less than the cost of carry. The differences between the call and put time spread prices as well as the conversion/reversal differences become larger as the strikes increase, and then they start to collapse.

The main thing is that ATM time spreads have the most value because ATM is where they like to be. They get cheaper the farther away from the money that they get. Although call time spreads are synthetically put time spreads via the roll, their pricing and properties differ because of interest rates/dividends and related early exercise valuations.

DIAGONALS

A diagonal can be a confusing position. It has long and short options in two different months (like a time spread) but at two different strikes (like a vertical). Therefore, it is helpful to think of a diagonal in terms of a vertical and a time spread. Perceiving diagonals in this way will help you to understand how you can control the risk and understand the Greeks.

Using a diagonal spread, is simply another way to modify a bull vertical spread or bear vertical spread and for a trader to optimize his or her market objectives based on an analysis of implied volatility levels.

Diagonal back spreads and ratio spreads also attempt to modify the Greeks to better fit the traders' opinion of what will happen in the market. For example, if traders think that volatility is low and they are going to buy a call spread, then they would buy the far month low strike call rather than the close month on a vertical spread in order to add vega sensitivity to their spread. In this case, they will probably also benefit from a positive theta.

Conclusion

Multiple expiration spreads offer the trader a gamut of configurations to choose from. It is recommended to stress-test ratioed time spreads and ratioed diagonal time spreads in the options analyzer to get familiar with their properties. It is these options' relationships that are generally overlooked and thereby have a tendency to become attractive for speculative strategies.