Jump Telegraph Processes and Financial Markets with Memory

Ratanov, Nikita

doi:https://doi.org/10.1155/2007/72326

International Journal of Stochastic Analysis

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Research Article | Open Access

Volume 2007 | Article ID 072326 | https://doi.org/10.1155/2007/72326

Jump Telegraph Processes and Financial Markets with Memory

Nikita Ratanov¹

Received21 Nov 2006

Revised22 Apr 2007

Accepted09 Aug 2007

Published25 Oct 2007

Abstract

The paper develops a new class of financial market models. These models are based on generalized telegraph processes with alternating velocities and jumps occurring at switching velocities. The model under consideration is arbitrage-free and complete if the directions of jumps in stock prices are in a certain correspondence with their velocity and with the behaviour of the interest rate. A risk-neutral measure and arbitrage-free formulae for a standard call option are constructed. This model has some features of models with memory, but it is more simple.

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Copyright

Copyright © 2007 Nikita Ratanov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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