Question

A stock is trading at $40. There are 3 three-month European calls on the stock with strikes of 35, 40 and 45. The prices of these calls are, respectively, 5.50, 3.85, and 1.50. Consider pursuing the butterfly spread strategy (buy the low and the high strike call and write 2 intermediate strike calls) and find the break-even points of the strategy as well as maximum losses and maximum gains. Any issues -comments? What is happening here?

Answer 1

Solution:

It is given that the three strike price are 35, 40 and 45 and their premium are 5.50, 3.85 and 1.50 respectively.

In order to create long butterfly strategy, we will buy 35 and 45 calls and pay a premium of 5.50 and 1.50 respectively. We will sell two 40 strike call and earn 2* 3.85 = 7.70.

Net cost of creating the butterfly spread = premium earned - premium paid = 7.70 - 5.5 - 1.5 = 0.7

In butterfly spread maximum profit happens when stock price is equal to the middle strike price. Maximum loss happens when share price is higher than the maximum strike price of lower than the lowest strike price.

:We can see that while creating the butterfly spread the maximum loss we can occur is the value of creating the spread and in this case it is positive 0.7. Hence the maximum loss is 0.7

Maximum profit case.

1. When strike price is 40 and stock price is 40.

Option 1. 35 strike price : it will be in the money and total earning in this option = stock price - strike price - premium paid = 40 - 35 - 5.5 = -0.5  

Option 2. 40 strike price: we will earn the premium as it is at the money and gain = 2* ( strike price - share price + premium earned) = 2* 3.85 = 7.70

Option 3 . 45 strike price ; we will lose the premium as it is out the money option and loss = Max( stock - strike , 0) - premium paid = Max ( 40-45,0) -1.5 = -1.5

Total profit = -0.5 + 7.70 -1.5 = 5.7

So maximum profit is 5.7 and maximum loss is 0.7

There is no break even point as this strategy never gives loss in this case as the net value of creating the strategy is positive 0.7.