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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

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    1. Min Dai & Yifei Zhong & Yue Kuen Kwok, 2011. "Optimal arbitrage strategies on stock index futures under position limits," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 31(4), pages 394-406, April.
    2. Tim Leung & Jiao Li & Xin Li & Zheng Wang, 2016. "Speculative Futures Trading under Mean Reversion," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 23(4), pages 281-304, December.
    3. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
    4. Brennan, Michael J & Schwartz, Eduardo S, 1990. "Arbitrage in Stock Index Futures," The Journal of Business, University of Chicago Press, vol. 63(1), pages 7-31, January.
    5. Tim Leung & Peng Liu, 2012. "Risk Premia And Optimal Liquidation Of Credit Derivatives," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(08), pages 1-34.
    6. 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..
    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. Tim Leung & Yoshihiro Shirai, 2015. "Optimal derivative liquidation timing under path-dependent risk penalties," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(01), pages 1-32.
    9. Álvaro Cartea & Sebastian Jaimungal & Damir Kinzebulatov, 2016. "Algorithmic Trading With Learning," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(04), pages 1-30, June.
    10. Guo, Kevin & Leung, Tim, 2017. "Understanding the non-convergence of agricultural futures via stochastic storage costs and timing options," Journal of Commodity Markets, Elsevier, vol. 6(C), pages 32-49.
    11. Andrea Macrina, 2014. "Heat Kernel Models For Asset Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(07), pages 1-34.
    12. S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
    13. 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..
    14. 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.
    15. 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.
    16. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893.
    17. Tim Leung & Michael Ludkovski, 2010. "Optimal Timing to Purchase Options," Papers 1008.3650, arXiv.org, revised Apr 2011.
    18. Baurdoux, Erik J. & Chen, Nan & Surya, Budhi & Yamazak, Kazutoshi, 2015. "Optimal double stopping of a Brownian bridge," LSE Research Online Documents on Economics 61618, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. 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.
    2. Abel Azze & Bernardo D'Auria & Eduardo Garc'ia-Portugu'es, 2022. "Optimal stopping of Gauss-Markov bridges," Papers 2211.05835, arXiv.org, revised Dec 2023.
    3. 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.
    4. Tiziano De Angelis & Alessandro Milazzo, 2019. "Optimal stopping for the exponential of a Brownian bridge," Papers 1904.00075, arXiv.org, revised Nov 2019.
    5. Bahman Angoshtari & Tim Leung, 2019. "Optimal dynamic basis trading," Annals of Finance, Springer, vol. 15(3), pages 307-335, September.
    6. D'Auria, Bernardo & García Portugués, Eduardo & 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.
    7. 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.
    8. Leunglung Chan, 2018. "Editorial for Special Issue “Finance, Financial Risk Management and their Applications”," IJFS, MDPI, vol. 6(4), pages 1-3, October.

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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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