Question

Find the one-year forward exchange rate if 1-year European call option for £1 with strike price of 1.8 $/£ is selling for 0.1$ while 1-year European put option with strike price of 1.8 $/£ is selling for 0.12$. U.S. interest rate is 10%.

Answer 1

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As per put-call parity

P+ S = present value of X + C

P= value of put option.
S= current price of the share
X= strike price
C= value of call option.
Present value of X = X/e^r
r = risk free rate.

Given:
P= value of put option = 0.12
S= current price of share=?
X= strike price = 1.80
Present value of X = 1.80/(1+0.1)
r = risk free rate. 10%
C= value of call option = 0.1

0.12+S = (1.80/(1+0.10))+0.1
S= 1.616

1 year forward rate is = 1.616(1+0.1)
= 1.778

The answer is: $1.78/pound.