Question

Problem 1.4.2. (Long put vs short forward) You are given: (6) The current price of a 100-strike 9-month European put option is 12. (ii) A 9-month forward has a forward price of 105 (iii) The continuously compounded risk-free interest rate is 3% Caleulate the stock price after 9 months such that the long put option and the short forward contract have the same profit.

Answer 1

Present value of Long put profit=MAX(100-S,0)*e^(-3%*9/12)-12

Present value of short forward=(105-S)*e^(-3%*9/12)

Hence,

MAX(100-S,0)-12*e^(3%*9/12)=(105-S)

If S<100 no solution exists

Hence S<100

-12*e^(3%*9/12)=105-S

S=105+12*e^(3%*9/12)=117.27