The current price of one share of the ABC stock is 40 dollars. The stock is expected to pay acontinuously compounded dividend yield of10%per year. The current interest rate is2%per year.The volatility of the stock return is assumed to be30%per year.SuuSuSudS0= 40SduSdSdd1. Consider a European option with strike price38dollars per share and a maturity of sixmonths. Use McDonalds formula to find outuanddand draw a binomial tree of stock pricemovement.2. Calculate the price of the call option at node0. You may use the replicating portfolio or therisk-neutral probability method.3. Consider an otherwise identical American option (That is, you are now allowed to exercisethe option at nodeuandd). Do you want to exercise the American option at nodeu? Doyou want to exercise the American option at noded? Explain why.

1 An American Call Option The current price of one share of the ABC stock is 40 dollars. The stock is expected to pay a continuously compounded dividend yield of 10% per year. The current interest rate is 2% per year. The volatility of the stock return is assumed to be 30% per year. Suu Su Sud So = 40 Sdu Sa Sda 1. Consider a European option with strike price 38 dollars per share and a maturity of six months. Use McDonald's formula to find out u and d and draw a binomial tree of stock price movement. 2. Calculate the price of the call option at node 0. You may use the replicating portfolio or the risk-neutral probability method. 3. Consider an otherwise identical American option (That is, you are now allowed to exercise the option at node u and d). Do you want to exercise the American option at node u? Do you want to exercise the American option at node d? Explain why