In: Finance
8. (Put-Call Parity) XYZ stock is trading at $40. The effective annual interest rate is 5%, so that 100 dollars lent for 1 year will return 105 dollars. One year call premiums are 9, 4, and 2 for strike prices of 35, 40, and 45, respectively. Draw a profit graph (or make a table) for the following strategy: buy one 45 strike call, sell one 40 strike put.
Solution:
The put option premium of the strike price $40 can be calculated using Put-call parity formula
C = $4
S= $40
X = $40
Interest rate = 5% , T =1 Year
Using the put-call parity formula
C + X / exp(rT) = P + S
4 + 40 / exp(5% *1) = P + 40
4 + 40 / 1.05127 = P +40
42.05 = P +40
P = 2.05
The table and graph is provided in the below excel diagram.