
Explanation:
For the Black-Scholes-Merton model and in the absence of arbitrage opportunities, the put-call parity satisfies:
For the market prices, put-call parity holds when arbitrage opportunities are absent such that:
The difference between the two equations is:
From the question we have:
Thus:
0.05`01 - 0.0317 = 0.0249 - C_{\text{MKT}} \ \Rightarrow C_{\text{MKT}} = 0.0065
Where, $P_{\text{BS}} =$ put price calculated by the Black-Scholes-Merton model. $C_{\text{BS}} =$ call price calculated by the Black-Scholes-Merton model. $C_{\text{MKT}} =$ market call price. $P_{\text{MKT}} =$ market put price.Ultimate access to all questions.
Q.2862 Suppose that a small-cap stock is priced at $0.6560. Suppose further that the price of European call and put options computed by the Black-Scholes-Merton model are $0.0249 and $0.0501, respectively. Calculate the market price of a call option if the market price of a put option on the same stock is $0.0317.
A
$0.0065
B
$0.0025
C
$0.0337
D
$0.0654
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