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Conditional Density Models For Asset Pricing

Author

Listed:
  • DAMIR FILIPOVIĆ

    (Swiss Finance Institute, Ecole Polytechnique Fédérale de Lausanne, Switzerland)

  • LANE P. HUGHSTON

    (Department of Mathematics, University College London, London WC1E 6BT, United Kingdom;
    Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom)

  • ANDREA MACRINA

    (Department of Mathematics, King's College London, London WC2R 2LS, United Kingdom;
    Institute of Economic Research, Kyoto University, Kyoto 606-8501, Japan)

Abstract

We model the dynamics of asset prices and associated derivatives by consideration of the dynamics of the conditional probability density process for the value of an asset at some specified time in the future. In the case where the price process is driven by Brownian motion, an associated "master equation" for the dynamics of the conditional probability density is derived and expressed in integral form. By a "model" for the conditional density process we mean a solution to the master equation along with the specification of (a) the initial density, and (b) the volatility structure of the density. The volatility structure is assumed at any time and for each value of the argument of the density to be a functional of the history of the density up to that time. In practice one specifies the functional modulo sufficient parametric freedom to allow for the input of additional option data apart from that implicit in the initial density. The scheme is sufficiently flexible to allow for the input of various types of data depending on the nature of the options market and the class of valuation problem being undertaken. Various examples are studied in detail, with exact solutions provided in some cases.

Suggested Citation

  • 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.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:01:n:s0219024912500021
    DOI: 10.1142/S0219024912500021
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    Citations

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    Cited by:

    1. Andrea Macrina & Priyanka A. Parbhoo, 2011. "Randomised Mixture Models for Pricing Kernels," Papers 1112.2059, arXiv.org.
    2. Lane P. Hughston & Leandro Sánchez-Betancourt, 2020. "Pricing with Variance Gamma Information," Risks, MDPI, vol. 8(4), pages 1-22, October.
    3. Xixuan Han & Boyu Wei & Hailiang Yang, 2018. "Index Options And Volatility Derivatives In A Gaussian Random Field Risk-Neutral Density Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-41, June.
    4. Rene Carmona & Yi Ma & Sergey Nadtochiy, 2015. "Simulation of Implied Volatility Surfaces via Tangent Levy Models," Papers 1504.00334, arXiv.org.
    5. George Bouzianis & Lane P. Hughston & Leandro S'anchez-Betancourt, 2022. "Information-Based Trading," Papers 2201.08875, arXiv.org, revised Jan 2024.
    6. 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.
    7. Thomas Mazzoni, 2018. "Asymptotic Expansion of Risk-Neutral Pricing Density," IJFS, MDPI, vol. 6(1), pages 1-26, March.
    8. Henrik Hult & Filip Lindskog & Johan Nykvist, 2013. "A simple time-consistent model for the forward density process," Papers 1301.4869, arXiv.org.
    9. Lane P. Hughston & Leandro S'anchez-Betancourt, 2020. "Pricing with Variance Gamma Information," Papers 2003.07967, arXiv.org, revised Sep 2020.

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