Answer to Question #96126 in Financial Math for Frank

Question

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 d < β < u.
(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 = S^2 1 at time 1. Prove that the time 0
price of this contract is given by D0 = u + d − ud/β
(c) If we assume d = β < u instead, would the EMM from part (a) still be a
valid probability measure? Is it still a valid EMM?
(d) In the case of d = β < u, find an arbitrage strategy

Answer 1

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