On financial markets based on telegraph processes Academic Article

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.

publication date

  • 2008/4/1

keywords

  • Analogue
  • Arbitrage
  • Black-Scholes
  • Black-Scholes Model
  • Class
  • Correspondence
  • Differential equation
  • Differential equations
  • European Options
  • Explicit Formula
  • Financial Markets
  • Financial markets
  • Hedging
  • Interest Rates
  • Jump
  • Market
  • Market Model
  • Markov Process
  • Markov processes
  • Model
  • Quantile
  • Stock Prices
  • Telegraph

International Standard Serial Number (ISSN)

  • 1744-2508

number of pages

  • 22

start page

  • 247

end page

  • 268