Abstract
In this paper we develop a stochastic model incorporating a double-Markov modulated mean-reversion model. Unlike a price process the basis process X can take positive or negative values. This model is based on an explicit discretisation of the corresponding continuous time dynamics. The new feature in our model is that we suppose the mean reverting level in our dynamics as well as the noise coefficient can change according to the states of some finite-state Markov processes which could be the economy and some other unseen random phenomenon.