The stock of Timmins Mining Inc. is trading at $25. The volatility of the stock is 35% and the risk-free rate is 2%. The stock usually pays semi-annual dividends of $0.5 each and the last one was paid four months ago. Shortly after the last dividend payment, Timmins Mining announced that it will miss the next dividend due to cash requirement for a major equipment upgrading. However, it will double the usual amount in the following payment (i.e., $1.0 per share eight months from now). An option written on the stock has a time to maturity of 16 months and an exercise price of $23.
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 either of the two exdividend 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 both dividend dates, you may still use the Black’s approximation, except that you may want to calculate three option prices.)