A Theory of the Term Structure with an Official Short Rate

Many of the larger movements in market interest rates are associated with changes in official interest rate policy. This applies especially in the UK, where the Bank of England effectively controls very short term rates and moves its key dealing rate in multiples of a discrete unit. We present a theory of the term structure, with the short rate following a pure jump process with stochastic intensities depending on the short rate and a diffusion state variable. An illustrative model mimics empirical regularities of UK rates. We suggest how to extend our approach to other countries, most readily the US