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  3. consider the following discrete time oneperiod market model the savings...

Question: consider the following discrete time oneperiod market model the savings...

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  1. 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 < d < β < u.

    1. (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?

    2. (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+dβ)/udβ

    3. (c)  Find the replicating portfolio for this contract.

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