The stock of a New York based company AFF is trading at $53. The volatility of the stock is 38% and the risk-free rate is 4.2%. The company has just paid its regular semiannual dividend of $1.25 per share, but informed its investors that it will skip the next dividend (six months from now) due to a planned expansion. The missed dividend will be made up 12 months from now with a total dividend of $2.5 per share, and another one of $1.25 per share 15 months from now. After that, the company will resume its regular semi-annual dividend payments. An option written on the stock has a time to maturity of 16 months and an exercise price of $50. a. Price the option if it is a European put. b. Price the option if it is a European call. c. Please determine if there is an early exercise possibility at all the ex-dividend dates if the option is an American call. d. Please use Black's approximation to estimate the value of the option if it is an American call. (Hint: if there is an early exercise possibility at all dividend dates, you may still use the Black's approximation, except that you may want to calculate more option prices.)