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Jump Telegraph Processes and Financial Markets with Memory

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  • Nikita Ratanov

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.

Suggested Citation

  • Nikita Ratanov, 2007. "Jump Telegraph Processes and Financial Markets with Memory," International Journal of Stochastic Analysis, Hindawi, vol. 2007, pages 1-19, October.
    • Handle: RePEc:hin:jnijsa:072326
    DOI: 10.1155/2007/72326
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    Cited by:

    1. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(C).

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