Consider the following discrete time one-period market model. The savings account is $1 at time 0 and $β at time 1. The stock price is given by S0 = 1 and S1 = ξ where ξ is a random variable taking two possible values u and d, each with positive probability. Moreover, assume that 0
(a) Define what is meant by an equivalent martingale measure (EMM). Find, with proof, the EMM of this model. Does this model have arbitrage opportunities?
(b) Consider a contract which pays D1 = 1/S1 at time 1. Prove that the time 0 price of this contract is given by: D0 = (u + d − β) / (udβ) .
(c) Find the replicating portfolio for this contract.