Journal of Applied Mathematics and Decision Sciences
Volume 8 (2004), Issue 1, Pages 1-14
Three ways to solve for bond prices in the Vasicek model
Department of Statistics, University of British Columbia Vancouver, V6T 1Z2, BC, Canada
Copyright © 2004 Rogemar S. Mamon. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Three approaches in obtaining the closed-form solution of the Vasicek bond
pricing problem are discussed in this exposition. A derivation based solely on the distribution
of the short rate process is reviewed. Solving the bond price partial differential
equation (PDE) is another method. In this paper, this PDE is derived via a martingale
approach and the bond price is determined by integrating ordinary differential equations.
The bond pricing problem is further considered within the Heath-Jarrow-Morton (HJM)
framework in which the analytic solution follows directly from the short rate dynamics
under the forward measure.