Question

Suppose the prices of 3-month European call options with strike prices of $40, $45 and $50 are
$6.08, $2.70, and $0.86, respectively. 
a) Explain how a trader can create a butterfly spread using these options.
b) What is the profit when the price of the underlying asset in three months is $40
c) What is the profit when the price of the underlying asset in three months is $43
d) What is the profit when the price of the underlying asset in three months is $49
e) For what range of prices of the underlying asset does a trader make a profit?

Answer 1

a) A trader can create a butterfly spread by buying one call option with a strike price of $40, selling two call options with a strike price of $45, and buying one call option with a strike price of $50. This creates a spread where the trader profits if the price of the underlying asset is near the middle strike price of $45. b) If the price of the underlying asset in three months is $40, the trader will not make a profit. This is because the option with a strike price of $40 will expire worthless, while the options with strike prices of $45 and $50 will also expire worthless since they are out of the money. c) If the price of the underlying asset in three months is $43, the trader will make a profit of $1.70. This is because the option with a strike price of $40 will expire in the money and have a value of $3, while the options with strike prices of $45 and $50 will expire out of the money and have a value of $0. d) If the price of the underlying asset in three months is $49, the trader will make a profit of $3.14. This is because the option with a strike price of $50 will expire in the money and have a value of $9, while the options with strike prices of $40 and $45 will expire out of the money and have a value of $0. e) A trader makes a profit when the price of the underlying asset is between $41.30 and $48.70. Outside of this range, the trader will not make a profit. In summary, the trader creates a butterfly spread with options of different strike prices and then makes a profit when the price of the underlying asset is at certain range, in this case between $41.30 and $48.70