Impulse control of interest rates

This paper examines the effect that a central bank's interventions have on longer term interest rate securities by examining a stochastic short rate process that can be controlled by the central bank. Rather than investigate the motivations for the intervention, we assume that the bank is able to quantify its preferences and tolerances for various rates. We allow for a very general class of stochastic processes for the short rate, and most of the popular models in literature fall within this class. Interventions are best modeled as impulse controls, which are very difficult to handle, even computationally, except in very special cases. Allowing interventions to be modeled by impulse controls, we develop a computational method and provide relevant convergence results. We also derive error bounds for intermediate iterations. Using this method, we solve for the central bank's optimal control policy and also study the effect of this on longer term interest rate securities using a change of measure. The method developed here can easily be applied to a very wide range of impulse control problems beyond the realm of interest rate models.