Financial signal processing: a self calibrating model

Previous work on multifactor term structure models has proposed that the short rate process is a function of some unobserved diffusion process. We consider a model in which the short rate process is a function of a Markov chain which represents the 'state of the world'. This enables us to obtain explicit expressions for the prices of zero-coupon bonds and other securities. Discretizing our model allows the use of signal processing techniques from Hidden Markov Models. This means we can estimate not only the unobserved Markov chain but also the parameters of the model, so the model is self-calibrating. The estimation procedure is tested on a selection of U.S. Treasury bills and bonds.