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Awriter needs to determine a rational value for a derivative premium. The underlying asset of the derivative has current value $S(O). When the derivative expires the underlying asset will have one of two values, either $S(1,T) or $S(1,.L), with $S(1,T) > $S(1,.L). When the asset's value is $S(1,T) the derivative value is $W(1,T), and when the asset's value is $S(1.J,) the derivative value is $W[1,.L). The return on $1 from now until the derivative's expiry is R. The writer wants to use a replicating portfolio to nd the derivative premium. (a) A replicating portfolio for the derivative at the current time consists of H1 of the underlying asset and a bank investment worth $Ho. Write an equation for this replicating portfolio at the current time in terms of H0 and H1. (b) What are the two possible values of the replicating portfolio when the derivative expires? Express your answer in terms of H0 and H1. (c) Assume that at the expiry the replicating portfolio is equal to the derivative portfolio. Determine the values of Ho and H1 in terms of underlying asset values $S(1,T) and $S(1,.|,), derivative values $W(1,T) and $W[1,J,), and the return R. (d) Assuming that the replicating portfolio is currently equal to the derivative portfolio, substitute the H0 and H1 equations found in (c) into the equation found in (a) to show that the premium of the derivative is (Eq.1) W(0) = [W(1,T) + (1 7r)W(1,)] where _ w [Eq. 2) 7T 5(1,T)S(1,~l) and (Eq. 3) 1 7r sumR510) _ sumsun (e) When attempting to calculate the derivative premium using equations (Eq. 1), (Eq. 2) and (Eq. 3), the writer nds that the risk neutral probability 71' has a negative value. The writer knows that a probability cannot be negative. The writer correctly concludes than an assumption made when deriving equations (Eq. 1), (Eq. 2) and (Eq. 3) must have failed. Which assumption must have failed? What limits must be placed on the underlying asset values to ensure this assumption does not fail? (f) When the risk neutral probability is negative, describe one way an investor can make a guaranteed prot