The CARMA Interest Rate Model

Abstract

In this paper we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This models is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provide closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.