Explanation:
Using the put-call parity formula for European options with annual compounding:
C + PV(K) = P + S0
where:
C = Call option price = $4.50
K = Strike price = $75
T = Time to maturity = 3 months = 0.25 years
r = Risk-free rate = 8%
S0 = Current stock price = $76.50
First, find the present value of the strike price: PV(K) = 75 / (1 + 0.08)^0.25 = 75 / 1.0194265 = 73.5707
Now rearrange put-call parity to solve for Put (P): P = C + PV(K) - S0 P = 4.5 + 73.5707 - 76.50 = 1.5707
The estimated price of the 3-month put option is approximately $1.57. Option A is correct.
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Q.21 An investment manager is looking to price a 3-month put option on the stock of AWWE, but there's insufficient trading data on put options linked to the stock. Luckily, he's managed to get pricing information of a 3-month call option on the stock. The call option - with an exercise price of $75 - is priced at $4.5. The current price of the stock is $76.5. Estimate the price of the 3-month put option if the risk-free rate is 8% per annum compounded annually.
A
$1.57.
B
$2.78.
C
$1.52.
D
$1.43.
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