Problem 1 A stock price is currently $40. It is known that at the end of six months it will be either $48 or $32. The risk-free rate of interest with continuous compounding is 8% per annum. Calculate the value of a six-month European call option on the stock with an exercise price of $38. Verify that no-arbitrage arguments and risk-neutral valuation arguments give the same answers.

Problem 2 A stock price is currently $50. Over each of the next two three-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 six-month European put option with a strike price of $52? b. What is the value of a six-month American put option with a strike price of $52?