  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 consideration is
arbitrage-free and complete if directions of jumps in stock prices are in a
certain correspondence with their velocity and interest rate behaviour. An
analog of the Black-Scholes fundamental differential equation is derived, but,
in contrast with the Black-Scholes model, this equation is hyperbolic. Explicit
formulas for prices of European options are obtained using perfect and quantile
hedging.
