In this paper we overcome a lacks of Black-Scholes model, i.e. the infinite propagation velocity, the infinitely large asset prices etc. The proposed model is based on the telegraph process with jumps. The option price formula is derived.

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and with jumps occurring when the velocity switches. If jump directions are in the certain correspondence with the velocity directions of the underlying random motion...

In this paper we develop a financial market model based on continuous time random motions with alternating constant velocities and with jumps occurrng when the velocity switches. If jump directions are in the certain correspondence with the velocity directions of the underlyig random motion with...

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps occurring when the velocities are switching. This model is free of arbitrage if jump directions are in a certain correspondence with the velocities of the...

The paper develops a new class of financial market models. These models are based on generalized telegraph processes: Markov random flows with alternating velocities and jumps occurring when the velocities are switching. While such markets may admit an arbitrage opportunity, the model under...

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...

The paper develops a class of Financial market models with jumps based on a Brownian motion, and inhomogeneous telegraph processes: random motions with alternating velocities. We assume that jumps occur when the velocities are switching. The distribution of such a process is described in detail....

The letter concerns piecewise deterministic processes controlled by a Markov flow with exponentially, Exp(λn), distributed interarrival times Tn. Assuming all rates λn to be different, we study the distribution of a piecewise linear process with jumps.

We present limit theorems for an asymmetric telegraph process with drift and jumps under different rescaling conditions. The explicit formulae for the related characteristic functions are derived by solving a Cauchy problem for the respective hyperbolic system.

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps, which occur with velocity switches. Given that jump directions match velocity directions of the underlying random motion properly in relation to interest...