Question

2. Three-month European put options with strike prices of $50, $55, and $60 cost $2, $4, and $7, respectively.

a) What is the maximum gain when a butterfly spread is created from the put options?

b) What is the maximum loss when a butterfly spread is created from the put options?

c) For what two values of St does the holder of the butterfly spread break even with a profit of zero, where St is the stock price in three months?

Answer 1

Buy put of strike 50 and 60 and sell 2 put of strike 55

1.
=MAX(50-S,0)-2*MAX(55-S,0)+MAX(60-S,0)-2+2*4-7
=difference between highest & center strike prices minus net cost
=60-55-(2+7-2*4)
=4

2.
=net cost
=2+7-2*4
=1

3.
Upper breakeven =highest strike price - cost=60-1=59
Lower breakeven =lowest strike price + cost=50+1=51