Let S0 = $100, the risk-free rate equal 5%, and the volatility equal 35%. Answer the following, assuming continuous compounding.
(a) Use the three discrete-time approaches to value a European call option with a two time-period tree with an exercise price equal to $105 and T = 18 months. To maintain a riskless hedge, how many shares of stock should be held long today and in nine months?
(b) Value a European put option assuming the underlying asset with K = $100,7 = 1 year, and use a four time-period tree.
(c) Value an American put option with the same attributes as in part b.