The price of a stock is currently $60. Suppose the movement of the stock during each six-month period for the next twelve months is given in the following figure. The risk-free rate of interest with continuous compounding is 12% per annum. (a) Let p denote the risk-neutral probability (of an upward movement). Calculate p. (b) What is the expected return rate of the stock with continuous compounding in a risk-neutral world? (c) Use the two-step tree to calculate the value of a derivative that pays off Max(70 - S1, 2), where Sy is the stock price in twelve months. (d) If the derivative in (c) is American-style, calculate the price of the derivative. + 86.4 72 D B 60 A 64.8 E 54 48.6 F