Fixed Income and Interest Rate Derivative Analysis

STATE PRICES, FORWARD INDUCTION, AND TREE-FITTING 103

The drift will be matched by setting the up and down probabilities equal.

Call this probability p, then the middle probability must be 1- 2p, since

probabilities must sum to one. The variance is then given by

2p22~2cr2 -- 2per 2

Setting this equal to the required variance of 4a2/12 then gives the appro-

priate probability p of

1

p-g

With the initial step accounted for in this way, an interest rate tree can be

constructed. This is easily done in a spreadsheet package by copying and

pasting cells for up-branches ...