Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

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:

The current stock price of ARA is SGD 82.

The option's strike price is SGD 85.

The option has an expiration period of 6 months.

The risk-free interest rate, compounded continuously, is 2.5% per annum.

The value of N(-d1) is 0.5205.

The value of N(-d2) is 0.6040.

Based on the given information, what is the BSM model's calculated price for the put option on ARA's stock?

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