Straddles, strangles, strips and straps
1. The idea
Some strategies buy both calls and puts. They gain when the share moves far, in either direction, and lose when it stays near the strike price. So they are bets on how far the share will move, whichever way it goes.
- A straddle is a call and a put with the same strike price and expiry.
- A strangle is a put with a lower strike price and a call with a higher one, with the same expiry. Compared with a straddle at the strike price halfway between, on the same share and with the same expiry, it costs less, and the share must move further before it gains.
- A strip is one call and two puts with the same strike price and expiry: its payoff grows twice as fast with a fall as with a rise.
- A strap is two calls and one put with the same strike price and expiry: its payoff grows twice as fast with a rise as with a fall.
Every option is bought, so the largest loss is the premiums paid, if the share ends at the strike price, or anywhere between the two strike prices of a strangle. Below the put’s strike price only the puts have a payoff, which grows $1 per put for each $1 the share falls; above the call’s strike price only the calls have one. So a straddle with a strike price \(K\), a call premium \(c\) and a put premium \(p\) makes a profit when the share price at expiry, \(S_T\), ends outside its two break-even share prices:
\[ S_T = K - (c + p) \qquad\text{and}\qquad S_T = K + (c + p). \]
An example. With a share at $50, three-month options with a strike price of $50 cost $2.74 for the call and $2.24 for the put. A straddle costs \(2.74 + 2.24 = \$4.98\), so it makes a profit if the share ends below $45.02 or above $54.98, and loses at most $4.98. A strip of the same options costs \(2.74 + 2 \times 2.24 = \$7.22\); below $50 its two puts repay that cost twice as fast, so it makes a profit below \(50 - 7.22/2 = \$46.39\).
Selling these positions is the opposite bet: the seller of a straddle keeps the premiums if the share stays near the strike price, and loses more the further it moves, without limit if it rises.
2. Try it
If an answer is wrong, we will see what went wrong and how to fix it.
3. The straddle on a chart
First, what the straddle costs.
Now move the share price at expiry. The payoff is a V with its point at the strike price, and the profit is the V moved down by the premiums paid.
4. One worked example, then your turn
The worked example is a strangle.
Now a strip, with hints, one step at a time.
And one on your own: a strap.
5. Practice
Each question has new numbers. You master the skill when you get three right in a row, with at least one right answer for a straddle, a strangle, and a strip or a strap. You can always open the solution, but then that question does not count.
6. Coming back to it
When you have mastered a skill, it comes back on the start page for a short review after 1 day. After each right answer the next review comes later: after 3, 7, 14 and then 30 days. After a wrong one, the reviews start again at 1 day.
This skill: