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On Financial Markets Based on Telegraph Processes

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Author Info
Nikita Ratanov
Alexander Melnikov

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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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File URL: http://arxiv.org/abs/0712.3428
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File URL: http://arxiv.org/pdf/0712.3428
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Publisher Info
Paper provided by arXiv.org in its series Quantitative Finance Papers with number 0712.3428.

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Date of creation: Dec 2007
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Handle: RePEc:arx:papers:0712.3428

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  1. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June. [Downloadable!] (restricted)
  2. Tomas Björk & Henrik Hult, 2005. "A note on Wick products and the fractional Black-Scholes model," Finance and Stochastics, Springer, vol. 9(2), pages 197-209, 04. [Downloadable!] (restricted)
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This page was last updated on 2009-12-17.

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