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Pricing with Variance Gamma Information

Author

Listed:
  • Lane P. Hughston

    (Department of Computing, Goldsmiths University of London, New Cross, London SE14 6NW, UK)

  • Leandro Sánchez-Betancourt

    (Mathematical Institute, University of Oxford, Oxford OX2 6GG, UK)

Abstract

In the information-based pricing framework of Brody, Hughston & Macrina, the market filtration { F t } t ≥ 0 is generated by an information process { ξ t } t ≥ 0 defined in such a way that at some fixed time T an F T -measurable random variable X T is “revealed”. A cash flow H T is taken to depend on the market factor X T , and one considers the valuation of a financial asset that delivers H T at time T . The value of the asset S t at any time t ∈ [ 0 , T ) is the discounted conditional expectation of H T with respect to F t , where the expectation is under the risk neutral measure and the interest rate is constant. Then S T − = H T , and S t = 0 for t ≥ T . In the general situation one has a countable number of cash flows, and each cash flow can depend on a vector of market factors, each associated with an information process. In the present work we introduce a new process, which we call the normalized variance-gamma bridge. We show that the normalized variance-gamma bridge and the associated gamma bridge are jointly Markovian. From these processes, together with the specification of a market factor X T , we construct a so-called variance-gamma information process. The filtration is then taken to be generated by the information process together with the gamma bridge. We show that the resulting extended information process has the Markov property and hence can be used to develop pricing models for a variety of different financial assets, several examples of which are discussed in detail.

Suggested Citation

  • Lane P. Hughston & Leandro Sánchez-Betancourt, 2020. "Pricing with Variance Gamma Information," Risks, MDPI, vol. 8(4), pages 1-22, October.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:4:p:105-:d:425852
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    References listed on IDEAS

    as
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Marek Rutkowski & Nannan Yu, 2007. "An Extension Of The Brody–Hughston–Macrina Approach To Modeling Of Defaultable Bonds," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(03), pages 557-589.
    3. George Bouzianis & Lane P. Hughston, 2019. "Determination Of The Lévy Exponent In Asset Pricing Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(01), pages 1-18, February.
    4. Damir Filipović & Lane P. Hughston & Andrea Macrina, 2012. "Conditional Density Models For Asset Pricing," World Scientific Book Chapters, in: Matheus R Grasselli & Lane P Hughston (ed.), Finance at Fields, chapter 9, pages 225-248, World Scientific Publishing Co. Pte. Ltd..
    5. Lane P. Hughston & Andrea Macrina, 2012. "Pricing Fixed-Income Securities in an Information-Based Framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(4), pages 361-379, September.
    6. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    7. Damir Filipović & Lane P. Hughston & Andrea Macrina, 2012. "Conditional Density Models For Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(01), pages 1-24.
    8. George Bouzianis & Lane Hughston, 2018. "Determination of the L\'evy Exponent in Asset Pricing Models," Papers 1811.07220, arXiv.org, revised Feb 2019.
    9. Edward Hoyle, 2010. "Information-based models for finance and insurance," Papers 1010.0829, arXiv.org.
    10. Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2010. "Credit Risk, Market Sentiment and Randomly-Timed Default," Papers 1006.2909, arXiv.org.
    11. Edward Hoyle & Andrea Macrina & Levent A. Menguturk, 2017. "Modulated Information Flows in Financial Markets," Papers 1708.06948, arXiv.org, revised May 2020.
    12. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    Cited by:

    1. George Bouzianis & Lane P. Hughston & Leandro S'anchez-Betancourt, 2022. "Information-Based Trading," Papers 2201.08875, arXiv.org, revised Jan 2024.
    2. Kazi Wahadul Hasan & Maliha Binte Hanif, 2022. "A pricing model for real-estate business in Bangladesh incorporating the uncertainty in buyer’s readiness: considerations during COVID-19 pandemic," SN Business & Economics, Springer, vol. 2(10), pages 1-16, October.

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