Financial Risk Manager Part 1
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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?
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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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: where is the current stock price, is the strike price, is the time to maturity in years, and is the continuously compounded risk-free interest rate. Therefore:
- A is incorrect. This switches and in the equation above.
- B is incorrect. This uses the incorrect equation .
- 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.