Jump Telegraph Processes and Financial Markets with Memory

Nikita Ratanov ()

International Journal of Stochastic Analysis, 2007, vol. 2007, 1-19

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.

Date: 2007
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:072326

DOI: 10.1155/2007/72326

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