Ítem
Solo Metadatos
On financial markets based on telegraph processes
Título de la revista
Autores
Ratanov, Nikita
Melnikov, Alexander
Resumen
Abstract
The paper develops a new class of financial market models. These models are based on generalised 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.
Palabras clave
Keywords
Black-Scholes model , Hedging , Jump telegraph process , Option pricing
