On Financial Markets Based on Telegraph Processes

Nikita Ratanov () and Alexander Melnikov

Papers from arXiv.org

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.

Date: 2007-12
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:0712.3428

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