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A Jump Telegraph Model for Option Pricing

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  • Nikita Ratanov

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Abstract

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and with jumps occurring when the velocity switches. If jump directions are in the certain correspondence with the velocity directions of the underlying random motion with respect to the interest rate, the model is free of arbitrage. The replicating strategies for options are constructed in details. Closed form formulas for the option prices are obtained. En este trabajo se presenta un modelo de mercado financiero basado en movimientos aleatorios de tiempo continuo con velocidades constantes alternantes que ocurren cuando cambia la velocidad. Si las direcciones de los saltos se encuentran en determinada correspondencia con las direcciones de velocidad de los movimientos aleatorios subyacentes con respecto a la tasa de interés, entonces el modelo está libre de arbitraje. Las réplicas de estrategias para opciones se construyen en detalle. Se obtienen fórmulas de forma cerrada para los precios de las opciones.

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Bibliographic Info

Paper provided by UNIVERSIDAD DEL ROSARIO in its series BORRADORES DE INVESTIGACIÓN with number 001919.

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Length: 19
Date of creation: 01 Nov 2004
Date of revision:
Handle: RePEc:col:000091:001919

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  1. Nikita Ratanov, 2004. "Option Pricing Model Based on Telegraph Processes with Jumps," BORRADORES DE INVESTIGACIÓN 004330, UNIVERSIDAD DEL ROSARIO.
  2. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
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Cited by:
  1. Alessandro Gregorio & Stefano Iacus, 2008. "Parametric estimation for the standard and geometric telegraph process observed at discrete times," Statistical Inference for Stochastic Processes, Springer, vol. 11(3), pages 249-263, October.
  2. Alessandro De Gregorio & Stefano M. Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," Papers 0705.0503, arXiv.org.
  3. López, Oscar & Ratanov, Nikita, 2012. "Kac’s rescaling for jump-telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1768-1776.
  4. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
  5. Nikita Ratanov, 2005. "Quantil Hedging for telegraph markets and its applications to a pricing of equity-linked life insurance contracts," BORRADORES DE INVESTIGACIÓN 003410, UNIVERSIDAD DEL ROSARIO.
  6. Bogachev, Leonid & Ratanov, Nikita, 2011. "Occupation time distributions for the telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1816-1844, August.

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