A stock's price is $100. Over each of the next two three month periods it is expected to go up or down by 15% or down by 10%. The risk free rate is 4% p.a. The stock pays a dividend of $1 per quarter. Assume the option expires the day after the second period dividend is paid.
a. What should be the current price of a 6-month European style put option with a strike price of $95?
b. What should be the current price of a 6-month American style put option with a strike price of $95?
c. What should be the current price of a 6-month European style call option with a strike price of $95?
d. What should be the current price of a 6-month American style call option with a strike price of $95?