Jump telegraph processes and financial markets with memory

Nikita Ratanov

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

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.

Original languageEnglish (US)
Article number72326
JournalJournal of Applied Mathematics and Stochastic Analysis
Volume2007
DOIs
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics

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