Answer: USD3.22

The correct answer is B: USD 3.22. The Black-Scholes-Merton (BSM) model is used to price European-style call options, and it requires several inputs to calculate the option's price. In this case, the inputs are the current stock price (So), stock price volatility (σ), risk-free rate (r), and the call option exercise price (k). Additionally, the model uses the cumulative standard normal distribution function (N) to account for the probability of the option being in-the-money at expiration. The formula for pricing a European call option without dividends is: \[ \text{Call option price} = So \cdot N(d_1) - Ke^{-rT} \cdot N(d_2) \] where \( N(d_1) \) and \( N(d_2) \) are the cumulative probabilities from the standard normal distribution, \( K \) is the exercise price, \( r \) is the risk-free rate, and \( T \) is the time to expiration. However, in this scenario, there is an upcoming dividend payment, which affects the stock price. The present value of the dividend is calculated and subtracted from the current stock price to adjust for the expected drop in price on the ex-dividend date. The present value of the dividend is given by: \[ \text{Present value of dividends} = \text{Dividend amount} \cdot e^{-r \cdot (T_{\text{div}})} \] where \( T_{\text{div}} \) is the time until the dividend is paid. In this case, the dividend amount is USD 1.25, and it will be paid 1 month from now. The risk-free rate is 3.5% per year, so the present value of the dividend is: \[ 1.25 \cdot e^{-0.035 \cdot \frac{1}{12}} = 1.2464 \] Subtracting the present value of the dividend from the current stock price gives us the adjusted stock price: \[ So = 60 - 1.2464 = 58.7536 \] Now, we can plug the adjusted stock price into the BSM formula along with the given values for \( N(d_1) \) and \( N(d_2) \): \[ \text{Call option price} = 58.7536 \cdot 0.570143 - 60 \cdot e^{-0.035 \cdot 1} \cdot 0.522623 \] \[ \text{Call option price} = 33.4978 - 30.2787 = 3.2191 \] Rounded to two decimal places, the price of the 1-year call option on the stock is USD 3.22, which corresponds to option B.

Author: LeetQuiz Editorial Team