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Lévy random bridges and the modelling of financial information

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  • Hoyle, Edward
  • Hughston, Lane P.
  • Macrina, Andrea

Abstract

The information-based asset-pricing framework of Brody-Hughston-Macrina (BHM) is extended to include a wider class of models for market information. To model the information flow, we introduce a class of processes called Lévy random bridges (LRBs), generalising the Brownian bridge and gamma bridge information processes of BHM. Given its terminal value at T, an LRB has the law of a Lévy bridge. We consider an asset that generates a cash-flow XT at T. The information about XT is modelled by an LRB with terminal value XT. The price process of the asset is worked out, along with the prices of options.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:4:p:856-884
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    References listed on IDEAS

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    Cited by:

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    3. Hoyle, Edward & Mengütürk, Levent Ali, 2013. "Archimedean survival processes," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 1-15.
    4. Mohammed Louriki, 2019. "Brownian bridge with random length and pinning point for modelling of financial information," Papers 1907.08047, arXiv.org, revised Dec 2021.
    5. 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.
    6. Boonen, Tim J. & Tsanakas, Andreas & Wüthrich, Mario V., 2017. "Capital allocation for portfolios with non-linear risk aggregation," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 95-106.
    7. 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.
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    9. Giovanni Conforti & Tetiana Kosenkova & Sylvie Rœlly, 2019. "Conditioned Point Processes with Application to Lévy Bridges," Journal of Theoretical Probability, Springer, vol. 32(4), pages 2111-2134, December.

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