September 2022
Beginner
560 pages
17h 36m
English
Content preview from Fixed Income Securities, 4th Edition
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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 
; 
; 
; and 
. 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 
factor would be 
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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