• A stock is trading for $80 in the spot market and at-the-money options on this stock are currently trading at an implied volatility of 50%. The options expire in 1.5 years. The continuously compounded risk-free interest rate is equal to 1% per annum. Using a 5-date binomial lattice, calculate the price of plain vanilla call options on this stock in the following situations:
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• (a) The stock will pay dividends at a continuous rate of 3% per annum during the option's life and the option is of American style. Calculate the value of the option's early exercise privilege.
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•  (b) The stock's current dividend yield is equal to 3% and the dividend will be paid in one installment in exactly one year. The option is of American style. Calculate the value of the option's early exercise privilege.