ANSWER 13 14

(13, 14, 15, 16)[5 points each] BINOMIAL MODEL: Let's assume the current price of gold is S(0) = $50/gram. Next Monday (time t=1) the Freeport McMoran company will release the results on the new gold-based catalyst for sunlight-based hydrolysis. Industry analysts expect the price either to rise to $100 if the experiments are promising, or to sink to $25 if they aren't. But no one knows what the situation actually is! Let the probability that S(1) = 100 be p and that S(1)=25 be q=(1-p). (13) For what value of p is the expectation of S(1) equal to S(O) = 50 ? Suppose you are an options dealer interested in knowing the price of call and put options with exercise price X=75. Calculate (but you don't have to tell me) the payoffs if S(1)=100 and if S(1)=25 ? (14) Use the foregoing probabilities and payoffs to calculate the expectation P of the payoff for a put. (15) Use the foregoing probabilities and payoffs to calculate the expectation C of the payoff for a call. (16) The Put Call Parity Theorem says that S(0) + P =X+C (neglecting interest). Check that the PCPT is true using the quantities you calculated in (14, 15). What is the value of S(0)+P and X+C