On financial markets based on telegraph processes

Nikita Ratanov, Alexander Melnikov

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 generalised 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.

Original languageEnglish (US)
Pages (from-to)247-268
Number of pages22
JournalStochastics
Volume80
Issue number2-3
DOIs
StatePublished - Apr 2008

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation

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