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Information-Based Asset Pricing

Author

Listed:
  • DORJE C. BRODY

    (Department of Mathematics, Imperial College London, London SW7 2AZ, UK)

  • LANE P. HUGHSTON

    (Department of Mathematics, King's College London, London WC2R 2LS, UK)

  • ANDREA MACRINA

    (Department of Mathematics, King's College London, London WC2R 2LS, UK)

Abstract

A new framework for asset price dynamics is introduced in which the concept of noisy information about future cash flows is used to derive the corresponding price processes. In this framework an asset is defined by its cash-flow structure. Each cash flow is modelled by a random variable that can be expressed as a function of a collection of independent random variables called market factors. With each such "X-factor" we associate a market information process, the values of which we assume are accessible to market participants. Each information process consists of a sum of two terms; one contains true information about the value of the associated market factor, and the other represents "noise". The noise term is modelled by an independent Brownian bridge that spans the interval from the present to the time at which the value of the factor is revealed. The market filtration is assumed to be that generated by the aggregate of the independent information processes. The price of an asset is given by the expectation of the discounted cash flows in the risk-neutral measure, conditional on the information provided by the market filtration. In the case where the cash flows are the dividend payments associated with equities, an explicit model is obtained for the share-price process. Dividend growth is taken into account by introducing appropriate structure on the market factors. The prices of options on dividend-paying assets are derived. Remarkably, the resulting formula for the price of a European-style call option is of the Black–Scholes–Merton type. We consider the case where the rate at which information is revealed to the market is constant, and the case where the information rate varies in time. Option pricing formulae are obtained for both cases. The information-based framework generates a natural explanation for the origin of stochastic volatility in financial markets, without the need for specifying on an ad hoc basis the dynamics of the volatility.

Suggested Citation

  • Dorje C. Brody & Lane P. Hughston & Andrea Macrina, 2008. "Information-Based Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 107-142.
    • Handle: RePEc:wsi:ijtafx:v:11:y:2008:i:01:n:s0219024908004749
    DOI: 10.1142/S0219024908004749
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    Citations

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    Cited by:

    1. Edward Hoyle & Levent Ali Menguturk, 2020. "Generalised Liouville Processes and their Properties," Papers 2003.11312, arXiv.org, revised May 2020.
    2. George Bouzianis & Lane P. Hughston & Leandro S'anchez-Betancourt, 2022. "Information-Based Trading," Papers 2201.08875, arXiv.org, revised Jan 2024.
    3. Andrea Macrina, 2012. "Heat Kernel Framework for Asset Pricing in Finite Time," Papers 1211.0856, arXiv.org, revised Sep 2013.
    4. Edward Hoyle & Andrea Macrina & Levent A. Menguturk, 2017. "Modulated Information Flows in Financial Markets," Papers 1708.06948, arXiv.org, revised May 2020.
    5. Tim Leung & Jiao Li & Xin Li, 2018. "Optimal Timing to Trade along a Randomized Brownian Bridge," IJFS, MDPI, vol. 6(3), pages 1-23, August.
    6. Miles B. Gietzmann & Adam J. Ostaszewski, 2016. "The Sound of Silence: equilibrium filtering and optimal censoring in financial markets," Papers 1606.04039, arXiv.org.
    7. Pavel V. Gapeev & Monique Jeanblanc, 2019. "Defaultable Claims In Switching Models With Partial Information," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-18, June.
    8. Hoyle, Edward & Hughston, Lane P. & Macrina, Andrea, 2011. "Lévy random bridges and the modelling of financial information," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 856-884, April.
    9. William T. Shaw, 2008. "A model of returns for the post-credit-crunch reality: Hybrid Brownian motion with price feedback," Papers 0811.0182, arXiv.org, revised Aug 2009.
    10. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    11. Ulrich Horst & Michael Kupper & Andrea Macrina & Christoph Mainberger, 2013. "Continuous equilibrium in affine and information-based capital asset pricing models," Annals of Finance, Springer, vol. 9(4), pages 725-755, November.
    12. Mengütürk, Levent Ali, 2018. "Gaussian random bridges and a geometric model for information equilibrium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 465-483.
    13. Levent Ali Mengütürk, 2023. "From Irrevocably Modulated Filtrations to Dynamical Equations Over Random Networks," Journal of Theoretical Probability, Springer, vol. 36(2), pages 845-875, June.
    14. Lane P. Hughston & Leandro S'anchez-Betancourt, 2020. "Pricing with Variance Gamma Information," Papers 2003.07967, arXiv.org, revised Sep 2020.
    15. William T. Shaw & Marcus Schofield, 2015. "A model of returns for the post-credit-crunch reality: hybrid Brownian motion with price feedback," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 975-998, June.

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