IDEAS home Printed from
   My bibliography  Save this paper

A Jump Telegraph Model for Option Pricing


  • Nikita Ratanov



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.

Suggested Citation

  • Nikita Ratanov, 2004. "A Jump Telegraph Model for Option Pricing," BORRADORES DE INVESTIGACIÓN 001919, UNIVERSIDAD DEL ROSARIO.
  • Handle: RePEc:col:000091:001919

    Download full text from publisher

    File URL:
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    1. Elisa Nicolato & Emmanouil Venardos, 2003. "Option Pricing in Stochastic Volatility Models of the Ornstein-Uhlenbeck type," Mathematical Finance, Wiley Blackwell, vol. 13(4), pages 445-466.
    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.
    3. Nikita Ratanov, 2004. "Option Pricing Model Based on Telegraph Processes with Jumps," BORRADORES DE INVESTIGACIÓN 004330, UNIVERSIDAD DEL ROSARIO.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Alessandro De Gregorio & Stefano M. Iacus, 2007. "Change point estimation for the telegraph process observed at discrete times," Papers 0705.0503,
    2. 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.
    3. Ratanov, Nikita, 2014. "On piecewise linear processes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 60-67.
    4. López, Oscar & Ratanov, Nikita, 2012. "Kac’s rescaling for jump-telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1768-1776.
    5. Igor G. Pospelov & Stanislav A. Radionov, 2015. "Optimal Dividend Policy When Cash Surplus Follows The Telegraph Process," HSE Working papers WP BRP 48/FE/2015, National Research University Higher School of Economics.
    6. Ratanov, Nikita, 2015. "Hypo-exponential distributions and compound Poisson processes with alternating parameters," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 71-78.
    7. De Gregorio, Alessandro & Macci, Claudio, 2012. "Large deviation principles for telegraph processes," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1874-1882.
    8. 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.
    9. 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.

    More about this item

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:col:000091:001919. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Facultad de Economía). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.