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Quantitative Finance > Trading and Market Microstructure

arXiv:0712.3428 (q-fin)
[Submitted on 20 Dec 2007]

Title:On Financial Markets Based on Telegraph Processes

Authors: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.
Comments: To appear in a Special Volume of Stochastics: An International Journal of Probability and Stochastic Processes (this http URL) edited by N.H. Bingham and I.V. Evstigneev which will be reprinted as Volume 57 of the IMS Lecture Notes Monograph Series (this http URL)
Subjects: Trading and Market Microstructure (q-fin.TR); Probability (math.PR)
MSC classes: 91B28, 60J75
Cite as: arXiv:0712.3428 [q-fin.TR]
  (or arXiv:0712.3428v1 [q-fin.TR] for this version)
  https://doi.org/10.48550/arXiv.0712.3428

Submission history

From: Alexander Melnikov [view email] [via VTEX proxy]
[v1] Thu, 20 Dec 2007 14:05:41 UTC (80 KB)
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