IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v20y2018i1d10.1007_s11009-017-9558-3.html
   My bibliography  Save this article

A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models

Author

Listed:
  • Yue Liu

    (Jiangsu University)

  • Nicolas Privault

    (Nanyang Technological University)

Abstract

We propose a recursive algorithm for the numerical computation of the optimal value function inf t ≤ τ ≤ T 𝔼 sup 0 ≤ s ≤ T Y s / Y τ F t $\inf _{t\le \tau \le T} \mathbb {E} \left [\sup _{0\le s\le T } Y_{s} / Y_{\tau } \left | {\mathcal F}_{t}\right .\right ] $ over the stopping times τ with respect to the filtration of a geometric Brownian motion Y t with Markovian regime switching. This method allows us to determine the boundary functions of the optimal stopping set when no associated Volterra integral equation is available. It applies in particular when regime-switching drifts have mixed signs, in which case the boundary functions may not be monotone.

Suggested Citation

  • Yue Liu & Nicolas Privault, 2018. "A Recursive Algorithm for Selling at the Ultimate Maximum in Regime-Switching Models," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 369-384, March.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9558-3
    DOI: 10.1007/s11009-017-9558-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-017-9558-3
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-017-9558-3?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Goran Peskir & Farman Samee, 2013. "The British call option," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 95-109, January.
    2. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
    3. David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    4. Goran Peskir & Farman Samee, 2011. "The British Put Option," Applied Mathematical Finance, Taylor & Francis Journals, vol. 18(6), pages 537-563, April.
    5. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    6. Yue Liu & Nicolas Privault, 2017. "Selling At The Ultimate Maximum In A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-27, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Yue & Sun, Huaping & Meng, Bo & Jin, Shunlin & Chen, Bin, 2023. "How to purchase carbon emission right optimally for energy-consuming enterprises? Analysis based on optimal stopping model," Energy Economics, Elsevier, vol. 124(C).
    2. Yue Liu & Nicolas Privault, 2017. "Selling At The Ultimate Maximum In A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-27, May.
    3. Yue Liu & Jijian Zhang & Xuhui Ding & Xiling Zhang, 2023. "Intervene in advance or passively? Analysis and application on congestion control of smart grid," Annals of Operations Research, Springer, vol. 320(2), pages 887-899, January.
    4. Yue Liu & Lixin Tian & Zhuyun Xie & Zaili Zhen & Huaping Sun, 2021. "Option to survive or surrender: carbon asset management and optimization in thermal power enterprises from China," Papers 2104.04729, arXiv.org.
    5. Yue Liu & Aijun Yang & Jijian Zhang & Jingjing Yao, 2020. "An Optimal Stopping Problem of Detecting Entry Points for Trading Modeled by Geometric Brownian Motion," Computational Economics, Springer;Society for Computational Economics, vol. 55(3), pages 827-843, March.
    6. Lesław Gajek & Marcin Rudź, 2020. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1507-1528, December.
    7. Liu, Yue & Tian, Lixin & Sun, Huaping & Zhang, Xiling & Kong, Chuimin, 2022. "Option pricing of carbon asset and its application in digital decision-making of carbon asset," Applied Energy, Elsevier, vol. 310(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Yue & Sun, Huaping & Zhang, Jijian & Taghizadeh-Hesary, Farhad, 2020. "Detection of volatility regime-switching for crude oil price modeling and forecasting," Resources Policy, Elsevier, vol. 69(C).
    2. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    3. Alessandro Ramponi, 2011. "Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 349-368, June.
    4. Yang, Aijun & Liu, Yue & Xiang, Ju & Yang, Hongqiang, 2016. "Optimal buying at the global minimum in a regime switching model," Mathematical Social Sciences, Elsevier, vol. 84(C), pages 50-55.
    5. Yue Liu & Nicolas Privault, 2017. "Selling At The Ultimate Maximum In A Regime-Switching Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(03), pages 1-27, May.
    6. Emilio Russo, 2020. "A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model," Risks, MDPI, vol. 8(1), pages 1-22, January.
    7. Jang, Bong-Gyu & Tae, Hyeon-Wuk, 2018. "Option pricing under regime switching: Integration over simplexes method," Finance Research Letters, Elsevier, vol. 24(C), pages 301-312.
    8. Chun-Hung Chiu & Shui-Hung Hou & Xun Li & Wei Liu, 2017. "Real options approach for fashionable and perishable products using stock loan with regime switching," Annals of Operations Research, Springer, vol. 257(1), pages 357-377, October.
    9. Massimo Costabile & Arturo Leccadito & Ivar Massabó & Emilio Russo, 2014. "A reduced lattice model for option pricing under regime-switching," Review of Quantitative Finance and Accounting, Springer, vol. 42(4), pages 667-690, May.
    10. John Driffill & Turalay Kenc & Martin Sola, 2013. "Real Options With Priced Regime-Switching Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-30.
    11. Hainaut, Donatien, 2012. "Multidimensional Lee–Carter model with switching mortality processes," Insurance: Mathematics and Economics, Elsevier, vol. 50(2), pages 236-246.
    12. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    13. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    14. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.
    15. Mehrdoust, Farshid & Noorani, Idin & Hamdi, Abdelouahed, 2023. "Two-factor Heston model equipped with regime-switching: American option pricing and model calibration by Levenberg–Marquardt optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 660-678.
    16. Chinonso I. Nwankwo & Weizhong Dai & Ruihua Liu, 2023. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 817-854, October.
    17. Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    18. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    19. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    20. Chen, Ping & Yam, S.C.P., 2013. "Optimal proportional reinsurance and investment with regime-switching for mean–variance insurers," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 871-883.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metcap:v:20:y:2018:i:1:d:10.1007_s11009-017-9558-3. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.