a. A stock price is currently traded at $50. It is known that next year it will be either $60 or $42. The yield curve is flat, and the risk-free rate of interest with annual compounding is 10% per annum. Using the binomial model, calculate the value of a one-year European call option on the stock with an exercise price of $48. b. A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or reduce by 10%. The yield curve is flat, and the risk-free interest rate is 5% per annum, continuously compounded. (b1) Use a two-step tree to calculate the value of a European-style derivative, which is called "power option", that pays off [max(30ST,0)]2, where ST is the stock price in four months. (b2) If the derivative is American style, should it be exercised early