On Financial Markets Based on Telegraph Processes

Details On Financial Markets Based on Telegraph Processes On Financial Markets Based on Telegraph Processes

2007-12-20

arxiv.org/abs/0712.3428v1

Economy

Quantitative Finance

Trading and Market Microstructure

To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (http://www.i

Scientific paper

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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