The exact discretisation of CARMA models with applications in finance

Abstract

The problem of estimating a continuous time model using discretely observed data is common in empirical finance. This paper uses recently developed methods of deriving the exact discrete representation for a continuous time ARMA (autoregressive moving average) system of order p, q to consider three popular models in finance. Our results for two benchmark term structure models show that higher order ARMA processes provide a significantly better fit than standard Ornstein–Uhlenbeck processes. We then explore present value models linking stock prices and dividends in the presence of cointegration. Our methods enable us to take account of the fact that the two variables are observed in fundamentally different ways by explicitly modelling the data as mixed stock–flow type, which we then compare with the (more common, but incorrect) treatment of dividends as a stock variable.