  The paper proposes a class of financial market models which are based on
inhomogeneous telegraph processes and jump diffusions with alternating
volatilities. It is assumed that the jumps occur when the tendencies and
volatilities are switching. We argue that such a model captures well the stock
price dynamics under periodic financial cycles. The distribution of this
process is described in detail. For this model we obtain the structure of the
set of martingale measures. This incomplete model can be completed by adding
another asset based on the same sources of randomness. Explicit closed-form
formulae for prices of the standard European options are obtained for the
completed market model.
