### Introduction

No, we are not going to talk about strangling people here. Rather, this node is on an option combination known as a strangle in the jargon. It consists of a call and a put on the same underlying, with the same expiry, but different strikes. This write-up assumes some basic familiarity with options. It's also a bit of a technical subject, so don't expect clever quips or revolutionary insights.

### The out the money and the in the money strange

As mentioned in the introduction, the options have different strikes. There are two possibilities: the strike of the call could be lower than the strike of the put, or it could be higher. If the strikes are the same, it is called a straddle, and that is something else again.

The simplest case is the case in which the call has higher strike than the put. In this case, we can compute how much money our strangle returns at expiry.

1. The underlying is below the strike of the put. In this case, we can exercise the put, sell the shares for the strike price, buy them back at the market price, and pocket the difference between the expiry price and the strike.
2. The underlying is between the strikes. In this case, exercising either option means we will incur a loss. As such, they expiry worthlessly - we won't exercise them. Our investment in the strangle is lost, though.
3. The underlying is above the strike of the call. In this case, we exercise the call, sell the shares, and make the difference between the stock price and the strike.
So, with this strangle, we make money when we are below the low strike or above the high strike. If we are between the strikes, we make nothing - our investment is lost. Because this strangle does not always make money, it is called an out the money strangle.

Now, imagine that the call has the lower strike. In that case, at expiry, there are three possibilities:

1. The underlying is below the strike of the call. In this case, we exercise the put, selling shares. In this case, we can buy back the stock, and make an amount of money equal to the difference between the strike of the put and the level of the stock. Note that this is at least as much as the difference between the strike of call and put.
2. The underlying is between the strike of the call and that of the put. In that case, we exercise both options, selling at the strike of the put and buying at the strike of the call. We make an amount of money equal to the difference of the strikes.
3. The underlying is above the strike of the put. We only exercise the call, selling the shares in the market. We pocket an amount of cash equal to the difference between the strike and the shares. Note, again, that this amount is at least equal to the difference between the strikes.
With this strangle, we have a payoff that is equal to the difference between the strikes, plus the payoff of the out the money strangle. This combination is called an in the money strangle.

As such, the price of the in the money strangle and the out the money strangle should be closely related; in principle, the in the money strangle should be worth more by an amount equal to the difference between the strikes. There are two caveats here:

1. You pay the option premium now, but only get this extra cash at expiry. As such, you forfeit interest on the cash if you buy the strangle. This interest can be computed using the risk-free interest rate, and the market price of options is discounted for this.
2. If the options are American, the in the money strangle could be a candidate for early exercise. This subject is very complex and well beyond the scope of this node, but it drives up the price of the options.
In general, you don't want to buy an in the money strangle. There is almost never a good reason for it, and if you do know what you are doing, this writeup was probably stuff you knew already, anyway.

### Strangles in investing

Still with us? Good! Now that we covered the boring theory on strangles, let's look at some ideas on how strangles can be used in investing. I'm not claiming that these are good ideas!

##### Long strangle

Here, someone buys a strangle. Normally, this strangle has strikes that are around the current level of the stock. The buyer pays the option premium, and hopes that your stock will move in such a way that he makes money. Now, if the strikes are further away, the strangle is cheaper. However the chance of making money is correspondingly less. As such, it becomes more like a "lottery ticket". If the buyer buy the same number of strangles, it is more risky to buy a strangle with strikes that are closer to at the money; if he buys for a certain cash amount, it is more risky to buy straddles that have strikes that are further away.

A long strangle is essentially a bet that the market will move more than the people selling the strangle \ think. The buyer doesn't take a bet on the direction, just on the amount of movement.

##### Short Strangle

Here, someone sells the strangle. This is the opposite of buying it; it is hoped the market won't move as much. The problem here is that if the market violently moves in one direction, the seller could lose a lot, far more than was gained from selling the strangle. This risk is proportional to the number of strangles you sold; as such, especially selling a large number of strangles with strikes that are far out the money can be quite risky. Worse, most private investors cannot bear this risk, and cannot hedge it, either.

##### Short Strangle with shares

Here, someone buys shares, and sell a strangle on them. You immediately pocket cash. If the market moves up, her first make a bit, and then the short call kicks in and tops off the profit. If the market goes, the first loss is cushioned by the premium. The, at the strike of the put, the loss accelerates, losing from both the shares and the put.

Because there is a large initial cash investment, the risk per euro or dollar invested is lowered somewhat as opposed to the simple short strangle. With proper stoplosses, diversification and cash to act as a cushion, this strategy, set up with long-dated options, can be an interesting choice to get pretty steady behavior in any market but a sharp crash.

### Conclusion

In this writeup, we have briefly discussed what a strangle is in option trading. Essentially, it is a combination of a call and a put with a different strike, but the same time to expiry. Normally, the call has a strike above the current level of the underlying, and the put has a strike below the current level of the underlying. Straddles can be used in investing, although a simple short straddle is quite risky for an investor.

Stran"gle (?), v. t. [imp. & p. p. Strangled (?); p. pr. & vb. n. Strangling (?).] [OF. estrangler, F. 'etrangler, L. strangulare, Gr. , , fr. a halter; and perhaps akin to E. string, n. Cf. Strain, String.]

1.

To compress the windpipe of (a person or animal) until death results from stoppage of respiration; to choke to death by compressing the throat, as with the hand or a rope.

Our Saxon ancestors compelled the adulteress to strangle herself. Ayliffe.

2.

To stifle, choke, or suffocate in any manner.

Shall I not then be stifled in the vault, . . . And there die strangled ere my Romeo comes? Shak.

3.

To hinder from appearance; to stifle; to suppress.

"Strangle such thoughts."

Shak.

Stran"gle, v. i.

To be strangled, or suffocated.

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