1. (Pricing of derivatives in a Binomial tree, risk-neutral probability) Consider a binomial model with 3...

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1. (Pricing of derivatives in a Binomial tree, risk-neutral probability) Consider a binomial model with 3 periods, in which r = 1%, u = 1.07, d = and the initial price So = 1. (a) Find the risk-neutral probability of the first two moves being up. (b) Find the risk-neutral probability that exactly two of the first three moves are up. (c) Consider a derivative security, whose final payoff is min(S, 1), in which S3 is the final stock price. Calculate the no-arbitrage price of this derivative at each node in the binomial tree. (d) For the derivative in (c), find its initial price by directly calculating (1+)3E [V3]. (1+r) 1. (Pricing of derivatives in a Binomial tree, risk-neutral probability) Consider a binomial model with 3 periods, in which r = 1%, u = 1.07, d = and the initial price So = 1. (a) Find the risk-neutral probability of the first two moves being up. (b) Find the risk-neutral probability that exactly two of the first three moves are up. (c) Consider a derivative security, whose final payoff is min(S, 1), in which S3 is the final stock price. Calculate the no-arbitrage price of this derivative at each node in the binomial tree. (d) For the derivative in (c), find its initial price by directly calculating (1+)3E [V3]. (1+r)