***This is from Investment and Financial Mathematics (IFM) course for Actuaries. Please give handwritten solution with all steps shown. I will give "thumbs-up" for clear and correct solution. Thanks in advance!***

Question 4 (10 marks] The current price of a stock is 10 and it is expected to increase or decrease in price by 10% over each of the next two 6-month periods. The annual risk free rate with continuous compounding is 6%. The stock pays no dividends. a) Determine the value of an American put option with a strike price of 10.50 maturing in one year. b) Determine the number of shares of stock, A, and the amount of bonds earning the risk-free rate, B, to be held at time 0) in the replicating portfolio for the put option