5. (*) A stock price is currently 100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk free interest rate is 8% per annum with continuous compounding (a) What is the value of a one-year European call option with a strike price of $100? (b) What is the value of a one-year European put option with a strike price of 100? (c) Verify that the European call and European put prices satisfy put-call parity. (d) What is the value of a one-year American call option with a strike price of $100? (e) Calculate the delta of the stock option at each time-step in (a). 5. (*) A stock price is currently 100. Over each of the next two six-month periods it is expected to go up by 10% or down by 10%. The risk free interest rate is 8% per annum with continuous compounding (a) What is the value of a one-year European call option with a strike price of $100? (b) What is the value of a one-year European put option with a strike price of 100? (c) Verify that the European call and European put prices satisfy put-call parity. (d) What is the value of a one-year American call option with a strike price of $100? (e) Calculate the delta of the stock option at each time-step in (a)