On financial markets based on telegraph processes

Nikita Ratanov, Alexander Melnikov

Resultado de la investigación: Contribución a RevistaArtículo

8 Citas (Scopus)

Resumen

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.
Idioma originalEnglish (US)
Páginas (desde-hasta)247-268
Número de páginas22
PublicaciónStochastics
DOI
EstadoPublished - abr 1 2008

Huella dactilar

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

Citar esto

Ratanov, Nikita ; Melnikov, Alexander. / On financial markets based on telegraph processes. En: Stochastics. 2008 ; pp. 247-268.
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On financial markets based on telegraph processes. / Ratanov, Nikita; Melnikov, Alexander.

En: Stochastics, 01.04.2008, p. 247-268.

Resultado de la investigación: Contribución a RevistaArtículo

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