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Answer: SGD8.45
C is correct. The value of a European put option on a stock paying a continuous dividend yield at an annual rate q is found using the equation: \[ p = Ke^{-rT}N(-d2) - S_0e^{-qT}N(-d1) \] where \( S_0 \) is the current stock price, \( K \) is the strike price, \( T \) is the time to maturity in years, and \( r \) is the continuously compounded risk-free interest rate. Therefore: - A is incorrect. This switches \( K \) and \( S \) in the equation above. - B is incorrect. This uses the incorrect equation \( p = S_0N(-d2) - Ke^{-qT}N(-d1) \). - D is incorrect. This treats the dividend as discrete, in the amount of the current stock price multiplied by the dividend yield, and then discounted by the 6 months to the option's expiration.
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A trader is using the Black-Scholes-Merton (BSM) model to estimate the price of a European put option on the shares of company ARA, which pays a continuous annual dividend of 2%. The relevant details for the calculation are as follows:
Based on the given information, what is the BSM model's calculated price for the put option on ARA's stock?
A
SGD 5.11
B
SGD 5.73
C
SGD8.45
D
SGD8.86
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