Ítem
Acceso Abierto
On Financial Markets Based on Telegraph Processes, Quantitative Finance Papers
Título de la revista
Autores
Ratanov, Nikita
Melnikov, Alexander
Archivos
Fecha
2007-01-01
Directores
ISSN de la revista
Título del volumen
Editor
Cornell UNiversity
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Resumen
Abstract
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.
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Keywords
Option Pricing , Jump Telegraph Process , Hedging
