NAME: 1. (20 points) True or False? (a) For a random variable X # 0 with E [ex]

NAME: 1. (20 points) me or False? (a) For a random variable X 0 with E [ex < DC, we have E [eon x O.IE[XI TRUE/FALSE (b) Let with So O, be a symmetric random walk process. (i.e. Sn = X" where Xi are i.i.d. random variables with P (Xi 1) P (Xi 1 Then, minosjsn} Sj } is a Markov process. TRUE/FALSE (c) A long call is the same a short put. TRUE/FALSE (d) In the N-period BAPM with r 41, u 1 2, So 4, risk-neutral probabilities 2 actual probabilities p = 1 q, the stochastic process is a martingale under both risk-neutral and actual probability measure. TRUE/FALSE (e) Suppose that the process {M } is a martingale and let q5(x) be a convex function. Then {+(M )} is a super-martingale under the same probability measure. TRUE/FALSE (f) The random walk process of part (b) is a martingale under the probabilities p = = TRUE/FALSE (g) The random walk process of part (b) is a Markov process. TRUE/FALSE (h) In the model of part measure. Then {M } TRUE/FALSE (d), a process {M } is a martingale under the actual is also a martingale under risk-neutral measure. 1