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Optimal Timing to Trade along a Randomized Brownian Bridge

Author

Listed:
  • Tim Leung

    (Department of Applied Mathematics, University of Washington, Seattle, WA 98195, USA)

  • Jiao Li

    (APAM Department, Columbia University, New York, NY 10027, USA)

  • Xin Li

    (Bank of America Merrill Lynch, One Bryant Park, New York, NY 10036, USA)

Abstract

This paper studies an optimal trading problem that incorporates the trader’s market view on the terminal asset price distribution and uninformative noise embedded in the asset price dynamics. We model the underlying asset price evolution by an exponential randomized Brownian bridge (rBb) and consider various prior distributions for the random endpoint. We solve for the optimal strategies to sell a stock, call, or put, and analyze the associated delayed liquidation premia. We solve for the optimal trading strategies numerically and compare them across different prior beliefs. Among our results, we find that disconnected continuation/exercise regions arise when the trader prescribe a two-point discrete distribution and double exponential distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jijfss:v:6:y:2018:i:3:p:75-:d:166614
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    References listed on IDEAS

    as
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    11. 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.
    12. 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.
    13. Tim Leung & Xin Li, 2016. "Futures Trading Under Mean Reversion," World Scientific Book Chapters, in: Optimal Mean Reversion Trading Mathematical Analysis and Practical Applications, chapter 5, pages 105-127, World Scientific Publishing Co. Pte. Ltd..
    14. 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.
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    Citations

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    Cited by:

    1. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Jul 2024.
    2. Azze, A. & D’Auria, B. & García-Portugués, E., 2024. "Optimal stopping of an Ornstein–Uhlenbeck bridge," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    3. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    4. D'Auria, Bernardo & Guada Azze, Abel, 2021. "Optimal stopping of an Ornstein-Uhlenbeck bridge," DES - Working Papers. Statistics and Econometrics. WS 33508, Universidad Carlos III de Madrid. Departamento de Estadística.
    5. Leunglung Chan, 2018. "Editorial for Special Issue “Finance, Financial Risk Management and their Applications”," IJFS, MDPI, vol. 6(4), pages 1-3, October.
    6. Glover, Kristoffer, 2022. "Optimally stopping a Brownian bridge with an unknown pinning time: A Bayesian approach," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 919-937.
    7. Xiaodong Chen & Tim Leung & Yang Zhou, 2022. "Constrained dynamic futures portfolios with stochastic basis," Annals of Finance, Springer, vol. 18(1), pages 1-33, March.
    8. Tiziano De Angelis & Alessandro Milazzo, 2019. "Optimal stopping for the exponential of a Brownian bridge," Papers 1904.00075, arXiv.org, revised Nov 2019.
    9. Bernardo D’Auria & Eduardo García-Portugués & Abel Guada, 2020. "Discounted Optimal Stopping of a Brownian Bridge, with Application to American Options under Pinning," Mathematics, MDPI, vol. 8(7), pages 1-27, July.

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    More about this item

    Keywords

    speculative trading; Brownian bridge; optimal stopping; variational inequality;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • F42 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Policy Coordination and Transmission

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