Assuming the short rate process of Exercise 2 and risk-neutral probabilities of .5 , consider a zero-coupon

Question:

Assuming the short rate process of Exercise 2 and risk-neutral probabilities of .5 , consider a zero-coupon bond that pays $\$ 1$ at time $t=2$. Find the value at time $t=0$ of this bond in two ways:

(a) Using the short rate lattice and equation (19.1).

(b) Using the tree for $R_{0 s}$ and equation (19.2).

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Exercises 2

Consider a short rate binomial lattice where the risk-free rate at $t=0$ is $10 \%$. At $t=1$ the rate is either $10 \%$ (for the upper node) or $0 \%$ (for the lower node). Trace out the growth of $\$ 1$ invested risk free at $t=0$ and rolled over at $t=1$ for one more period. The values obtained at $t=1$ and $t=2$ correspond to $R_{01}$ and $R_{02}$. Show that these factors cannot be represented on a binomial lattice, but rather a full tree is required. Draw the tree.