Question

1. A trader creates a long butterfly spread from put options with strike prices of $160, $170, and $180 per share by trading a total of 20 option contracts (5 contracts at $160, 10 contracts at $170 and 5 contracts at $180). Each contract is written on 100 shares of stock. The options are worth $22, $28, and $36 per share of stock.
   1. What is the value (payoff) of the butterfly spread at maturity as a function of the then stock price?
   2. What is the profit of the butterfly spread at maturity as a function of the then stock price?

Answer 1

The butterfly strategy is a more complex options spread built from options bought and sold at three different strike prices.All three positions are of the same type; either all puts or all calls, and all with same expiration date.

Long put 1 with strike price $160 and premium paid $22

Long put 1 with strike price $170 and premium paid $28

Long put 1 with strike price $180 and premium paid $36

1 contract = 100 shares

Strike Price	Contracts	Premium	Contract Value	Profit
160	5	22	22*500 = 11000	160*500-11000 = 69000
170	10	28	28*1000 = 28000	170*1000-28000 = 142000
180	5	36	36*500 = 18000	180*500-18000 = 72000
Total	20	86	57000	283000

The value of the butterfly spread at maturity as a function of the stock price is $57000.

The profit of the butterfly spread at maturity as a function of the stock price is $283000.