Problem
Consider a 6-month European call option on a stock that pays dividends. There are two ex-dividend dates: the first in 1 month and the second in 4 months. The expected dividend in 1 month is $0.60 and the expected dividend in 4 months is $0.65. The current share price is $45, the exercise price is $45, the risk-free interest rate is 8% per annum, and the stock-price volatility is 35% per annum.
1. Calculate the value of d1 MANUALLY to four decimal places. Use the BSM model to calculate the price of the call option MANUALLY. Do not use the BSM spreadsheet here. Use N(d1) = 0.5689; N(d2) = 0.4705.
2. Now, assume that the call price is higher than the value you calculated in part a). Would the implied volatility be greater than or lower than the value of 35% you used in part 1)? Explain concisely.