PDE Boundary Conditions for Vasicek and CIR Interest Rate Models by Wujiang Lou :: SSRN

Specifying PDE boundary conditions in mathematical finance has largely drawn from the expected boundary value or intuitive hedging activity of the financial instruments being priced. Unlike equity derivatives, interest rate derivatives are different in that underlying rates are not tradable, thus not hedgeable. In this paper, we propose an upper and lower boundary conditions for the Vasicek model and its variants (such as Hull-White model). An upper boundary condition for Cox-Ingersoll-Ross (CIR) model is also derived. We provide stability heat map, implementations, and examples of zero-coupon bond pricing and examples involving both lognormal asset and stochastic rate processes in the structural credit model.