article
An option pricing model based on jump telegraph processes
Autor
Ratanov, Nikita
Institución
Resumen
A new class of ?nancial market models is developed. These models are based on generalized telegraph processes: Markovrandom ?ows with alternating velocities and jumps occurring when the velocities are switching. While such markets mayadmit an arbitrage opportunity, the model under consideration is arbitrage-free and complete if directions of jumps in stockprices are in a certain correspondence with their velocity and interest rate behaviour. An analog of the Black-Scholes funda-mental differential equation is derived, but, in contrast with the Black-Scholes model, this equation is hyperbolic. Explicitformulas for prices of European options are obtained using perfect and quantile hedging