Option pricing model based on a Markov-modulated diffusion with jumps

Abstract

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. Such a model captures well the stock price dynamics under periodic financial cycles. The distribution of this process is described in detail. We also provide a closed form of the structure of risk-neutral measures. This incomplete model can be completed by adding another asset based on the same sources of randomness. For completed market model we obtain explicit formulae for call prices.