I. Module 2 Homework 2 [final]: Meet the Binomial Model

Due No due date
Points 4
Questions 4
Time Limit None

Instructions

The binomial model is really useful in asset pricing. Suppose that there are two states tomorrow,"up" and "down," and each can happen with probability 1/2. Consumption is $LaTeX: c_{t}=1$ today, $LaTeX: c_{t+1}(u)=2$ in the up state and $LaTeX: c_{t+1}(d)=1/2$ in the down state. Assume $LaTeX: \gamma=1$ , $LaTeX: \beta=1$ and power utility $LaTeX: u'(c)=c^{-\gamma}$ .

This assignment introduces the binomial setup. I set it up so the payoffs are very symmetric, yet the model generates very asymmetric prices and expected returns. Ponder why.

Start by writing down a general asset pricing formula. If a payoff is LaTeX: x(u) and LaTeX: x(d) in the up and down states at time LaTeX: t+1 , write a formula for its price at time . Then you can do the examples that follow.

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