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Fixed Income Securities, 4th Edition
book

Fixed Income Securities, 4th Edition

by Bruce Tuckman, Angel Serrat
September 2022
Beginner content levelBeginner
560 pages
17h 36m
English
Wiley
Content preview from Fixed Income Securities, 4th Edition

APPENDIX TO CHAPTER 9The Vasicek and Gauss+ Models

A9.1 THE VASICEK MODEL IN A BINOMIAL TREE

This section illustrates the implementation of the Vasicek model in a binomial tree. The parameters are r 0 equals 2 percent-sign; theta equals 11 percent-sign; k equals 0.0165; and sigma equals 0.95 percent-sign. The step size is one year. The first stages of construction are shown in Figure A9.1. The starting short‐term rate, by definition is 2%. By a discrete time approximation to the dynamics of the risk‐neutral process in Equation (9.1) of the text, the expected short‐term rate after one year is,

Note that, if the time step were one month, instead of one year, the d t factor would be 1 slash 12 instead of 1. In any case, adding a volatility of 0.95% up and down around the expectation from (A9.1) gives the date‐1 up‐ and down‐states in Figure A9.1.

Because of the mean reversion in the Vasicek ...

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