On financial markets based on telegraph processes
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 consider...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2008
- Institución:
- Universidad del Rosario
- Repositorio:
- Repositorio EdocUR - U. Rosario
- Idioma:
- eng
- OAI Identifier:
- oai:repository.urosario.edu.co:10336/23339
- Acceso en línea:
- https://doi.org/10.1080/17442500701841156
https://repository.urosario.edu.co/handle/10336/23339
- Palabra clave:
- Black-Scholes model
Hedging
Jump telegraph process
Option pricing
- Rights
- License
- Abierto (Texto Completo)
| Summary: | 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. |
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