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Derivatives pricing with marked point processes using Tick-by-tick data

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  • Cartea, Álvaro

Abstract

I propose to model stock price tick-by-tick data via a non-explosive marked point process. The arrival of trades is driven by a counting process in which the waiting-time between trades possesses a Mittag-Leffler survival function and price revisions have an infinitely divisible distribution. I show that the partial-integro-differential equation satisfied by the value of European-style derivatives contains a non-local operator in time-to-maturity known as the Caputo fractional derivative. Numerical examples are provided for a marked point process with conditionally Gaussian and with conditionally CGMY price innovations. Furthermore, the infinitesimal generator of the marked point process derived to price derivatives coincides with that of a Lévy process of either finite or infinite activity.

Suggested Citation

  • Cartea, Álvaro, 2010. "Derivatives pricing with marked point processes using Tick-by-tick data," DEE - Working Papers. Business Economics. WB wb101604, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    • Handle: RePEc:cte:wbrepe:wb101604
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    Cited by:

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    3. Scalas, Enrico & Politi, Mauro, 2012. "A parsimonious model for intraday European option pricing," Economics Discussion Papers 2012-14, Kiel Institute for the World Economy (IfW Kiel).
    4. S. Banihashemi & A. Ghasemifard & A. Babaei, 2024. "On the Numerical Option Pricing Methods: Fractional Black-Scholes Equations with CEV Assets," Computational Economics, Springer;Society for Computational Economics, vol. 64(3), pages 1463-1488, September.
    5. Yuanda Chen & Zailei Cheng & Haixu Wang, 2023. "Option Pricing for the Variance Gamma Model: A New Perspective," Papers 2306.10659, arXiv.org.
    6. Zhang, Meihui & Jia, Jinhong & Zheng, Xiangcheng, 2023. "Numerical approximation and fast implementation to a generalized distributed-order time-fractional option pricing model," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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    More about this item

    Keywords

    Tick-by-tick data;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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