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Pricing Options under Telegraph Processes

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  • Nikita Ratanov

Abstract

In this paper we introduce a financial market model based on continuous time random motions with alternating constant velocities and jumps, which occur with velocity switches. Given that jump directions match velocity directions of the underlying random motion properly in relation to interest rates, in this setting will be free of arbitrage. Additionally, we suppose also the interest rate depending on the market state. The replicating strategies for options are constructed in detail, and closed form formulas for option prices are obtained.

Suggested Citation

  • Nikita Ratanov, 2005. "Pricing Options under Telegraph Processes," Revista de Economía del Rosario, Universidad del Rosario, December.
    • Handle: RePEc:col:000151:003373
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    File URL: http://revistas.urosario.edu.co/index.php/economia/article/view/1031/930
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    More about this item

    Keywords

    jump telegraph process; European option pricing; perfect hedging; selffinancing strategy; fundamental equation;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

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