Selling strangles

Quantitative Finance Level 1

Let Y be the strangle that consists of the $45 put and the $55 call. An investor sold the strangle for $5. What is the range of values of the stock on expiration, such that the investor would have made money?

$ 0 ≤ P < $ 45 or P > $ 55 \$0 \leq P < \$45 \text{ or } P > \$55 $ 40 < P < $ 60 \$40 < P < \$60 $ 45 < P < $ 55 \$45 < P < \$55 $ 0 ≤ P < $ 40 or P > $ 60 \$0 \leq P < \$40 \text{ or } P > \$60

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Calvin Lin by Calvin Lin

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2 solutions

Chew-Seong Cheong
Mar 21, 2015

This is a short strangle. The short party makes profit if Put strike - Premium < Underlying price < Call strike + Premium ⇒ $ 45 − $ 5 < P < $ 55 + $ 5 ⇒ $ 40 < P < $ 60 \text{Put strike - Premium < Underlying price < Call strike + Premium} \\ \Rightarrow \$45 - \$5 < P < \$55 + \$5 \quad \Rightarrow \boxed{\$40 < P < \$60} .

15 Helpful 1 Interesting 2 Brilliant 1 Confused

Nice inequality to use to express the condition

Calvin Lin Staff - 6 years, 2 months ago

I'm confused. My understanding is that for someone to be profitable in a strangle they hoave to be outside of the range(45 to 55). but being greater than 40 still puts them in range of 45-55. What am i missing?

michael bye - 5 years, 10 months ago

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Your statement is false. Here are the facts:

  1. If someone buys a 45-55 strangle, it would be worth something on expiration if the stock is outside of the range.
  2. If someone buys as 45-55 strangle for $5, then it would be profitable if it is worth more than $5 on expiration (assuming nothing else is done). This means that the stock is < 40 or > 60.
  3. If someone sells a 45-55 strangle, it would be worth nothing if the stock lies within the range.
  4. If someone sells a 45-55 strangle for $5, then it would be profitable if it is worth less than $5 on expiration (assuming nothing else is done). This means that the stock price is 40 < S < 60.

This problem is set in scenario 4. I believe you are thinking about the scenario 1.

Calvin Lin Staff - 5 years, 10 months ago

Your statement would be true if someone had BOUGHT the strangle. Bought the problem states the investor Sold the strangle. I made the same mistake the first time through!

Jon Wacker - 1 year, 10 months ago

I made the same mistake as well. But my risk tolerance is much lower so I'm a BUYER of strangles. SELLING has too much risk in that it is infinite.

Howard Agster Jr. - 1 year, 9 months ago
Jeff Carter
Apr 24, 2016

Think about a logical solution to this problem. The person sold a 45/55 strangle and received $5 in credit to assume the risk of holding the position. (When you write or buy options, your account is debited and the amount it's debited is the most you can lose) Because I received $5 in credit, it lengthens the width of the possible range for my trade to make a profit by the amount of the credit.

Another way to think about this is by the action of the option. I sold a 45 put, and sold a 55 call. If the opposite party exercises my 45 put, I am "long" the stock from $45. As long as the stock stays above $45 I have a winning trade-but I also received a $5 credit for assuming the risk-so it's really $40. Conversely, if my call is exercised I am "short" the stock from $55. As long as it stays below $55 I am winning-but because I received the $5 credit the stock can go up to $60 before I lose money.

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