I. Module 4 Homework [final]: Three Ways to Price an Option

Due No due date
Points 17
Questions 9
Time Limit None

Instructions

We don't always use consumption growth to find a discount factor. In option pricing, we find a discount factor that prices the stock and bond ("what must consumption growth have been to make the stock and bond price what they are?") and use that discount factor to price an option. In this problem you get to see this approach, and compare it with arbitrage pricing and risk neutral pricing.

A stock right now ( LaTeX: t=0 ) has price $LaTeX: S_{0}$ . At time LaTeX: t=1 it will either rise to $LaTeX: S_{1}=S_{u}=u\ S_{0}$ or decline to $LaTeX: S_{1}=S_{d}=d\ S_{0}$ with equal probability. ( LaTeX: u and LaTeX: d are numbers, like 1.2 and 0.90. Assume LaTeX: u>d and LaTeX: u>1, d<1 .) There is also a bond that pays $LaTeX: R^{f}$ .

For all numerical answer questions, use $LaTeX: R^{f}=1$ , LaTeX: u=1.2 , LaTeX: d=0.9 , and $LaTeX: S_{0}=100$ .

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