Answer:
$ 0.000912 / pound
Explanation:
Current spot rate : 100 pound / $ or 0.01 $ / pound
In the next period the $ value of the pound can either increase or decrease by 15%
$ Risk-free rate = 5% and
pound Risk-free rate = 1%
Net Risk- free Rate = 5 - 1
= 4%
Risk-Neutral Probability of price Rise (p) = (0.04 - 0.085) / (1.15 - 0.85)
= 0.653
$ price of pound if price rises = 1.15 x 0.01 =$ 0.0115 / pound
$ price of pound if price falls = 0.85 x 0.01 = $ 0.0085 / pound
Strike price = current spot rate (as option is at the money) = 0.01 $ / pound
Therefore, pay offs one period later
if price is $ 0.0115 / pound, pay off (p₁)= 0.0115 - 0.01
= 0.0015$/ Pound
If price is 0.0085 $ / pound, pay off (p₂) = $0
Hence, Expecyed pay off = p₁ x p + p₂ x (1-p)
= 0.0015 x 0.633 + 0 x ( 1 - 0.633)
= $ 0.00095 / pound
Call price = Present value of Expected pay off at Net Risk-free risk
= 0.00095 exp (0.04)
= $ 0.000912 / pound
