Forward interest rate curves in discrete time settings driven by random fields

In this paper, we study the term structure of forward interest rates in discrete time settings. We introduce a generalisation of the classical Heath-Jarrow-Morton type models. The forward rates corresponding to different time to maturity values will be equipped with different driving processes. In this way, we use a discrete time random field to drive the forward rates instead of a single process. We assume the existence of a general stochastic (market) discount factor process, which involves market price of risk factors. This way of building the model is motivated by statistical problems, which is the aim of our further studies. Since we are interested only in arbitrage free markets, we derive several sufficient conditions to exclude arbitrage opportunities in the models and we also present examples for the structure of the driving field, in particular, we use Gaussian autoregression fields.