I. Module 4 Quiz 1: States and Complete Markets

Due No due date
Points 12
Questions 12
Time Limit None
Allowed Attempts 3

Instructions

In lecture, I claimed that one could synthesize contingent claims when there were fewer securities than states, by dynamic trading. Let's work out an example. There are two dates. There are two securities: 1) A stock has price 1 and either rises or declines $LaTeX: \{u,d\}=\{1.2, 0.9\}$ in each state. 2) A one-period risk-free rate with 0% return, i.e. payoff $LaTeX: \{1,1\}$ and price 1.

(This is a "nonrecombining binomial tree.")

Find the dynamic trading strategy that creates a contingent claim to the first of the final states, that is, if the "up" move occurs twice in a row. This means, find the investment in stock and bond $LaTeX: \{h_0, k_0\}$ at the first node, and the investment $LaTeX: \{h_{1u}, k_{1u}, h_{1d}, k_{1d}\}$ in each of the two nodes at time 1 that produces the final payoff $LaTeX: \{1,0,0,0\}$ . Find also the time-0 price of this contingent claim, LaTeX: p(uu).

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