Explanation:
The correct answer is A (£6.79). This is derived using the put-call forward parity for European options, which states:
P₀ - C₀ = [X - F₀(T)](1 + r)^(-T)
P₀ - C₀ = [X - F₀(T)](1 + r)^(-T)
Where:
Rearranging for C₀ (call option price):
C₀ = P₀ - [X - F₀(T)](1 + r)^(-T)
C₀ = P₀ - [X - F₀(T)](1 + r)^(-T)
Substituting the values:
C₀ = £4 - [£47 - £50](1.10)^(-0.75) = £6.79
C₀ = £4 - [£47 - £50](1.10)^(-0.75) = £6.79
Option B (£7.22) is incorrect due to a miscalculation of the exponent, and Option C (£7.30) is incorrect as it omits the exponent entirely.
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An investor holds a long position in a risk-free bond and a forward contract on a non-dividend-paying stock priced at £50. The annual risk-free rate is 10%. A nine-month put option on the stock with an exercise price of £47 trades at £4. The price of a nine-month call option on the stock with an exercise price of £47 is closest to:
A
£6.79
B
£7.22
C
£7.30