IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i3p423-d1328156.html
   My bibliography  Save this article

Regime Tracking in Markets with Markov Switching

Author

Listed:
  • Andrey Borisov

    (Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44/2 Vavilova Str., 119333 Moscow, Russia)

Abstract

The object of the investigation is a model of the incomplete financial market. It includes a bank deposit with a known interest rate and basic risky securities. The instant interest rate and volatility are governed by a hidden market regime, represented by some finite-state Markov jump process. The paper presents a solution to two problems. The first one consists of the characterization of the derivatives based on the existing market securities, which are valid to complete the considered market. It is determined that for the market completion, it is sufficient to add the number of derivatives equal to the number of possible market regimes. A generalization of the classic Black–Scholes equation, describing the evolution of the fair derivative price, is obtained along with the structure of a self-financing portfolio, replicating an arbitrary contingent claim in the market. The second problem consists of the online estimation of the market regime, given the observations of both the underlying and derivative prices. The available observations are either a combination of the time-discretized risky security prices or some high-frequency multivariate point processes associated with these prices. The paper presents the numerical algorithms of the market regime tracking for both observation types. The comparative numerical experiments illustrate the high quality of the proposed estimates.

Suggested Citation

  • Andrey Borisov, 2024. "Regime Tracking in Markets with Markov Switching," Mathematics, MDPI, vol. 12(3), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:423-:d:1328156
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/3/423/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/3/423/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. David Criens, 2018. "No Arbitrage in Continuous Financial Markets," Papers 1809.09588, arXiv.org, revised Feb 2020.
    2. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    3. Hamilton, J.D., 2016. "Macroeconomic Regimes and Regime Shifts," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 163-201, Elsevier.
    4. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    5. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
    6. Jakv{s}a Cvitani'c & Robert Liptser & Boris Rozovskii, 2006. "A filtering approach to tracking volatility from prices observed at random times," Papers math/0612212, arXiv.org.
    7. Gibson, Rajna & Lhabitant, Francois-Serge & Talay, Denis, 2010. "Modeling the Term Structure of Interest Rates: A Review of the Literature," Foundations and Trends(R) in Finance, now publishers, vol. 5(1–2), pages 1-156, December.
    8. Mesias Alfeus & Ludger Overbeck & Erik Schlögl, 2019. "Regime switching rough Heston model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 39(5), pages 538-552, 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. Tatyana Averina, 2024. "Conditional Optimization of Algorithms for Estimating Distributions of Solutions to Stochastic Differential Equations," Mathematics, MDPI, vol. 12(4), pages 1-16, February.

    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. Elisa Alòs & Maria Elvira Mancino & Tai-Ho Wang, 2019. "Volatility and volatility-linked derivatives: estimation, modeling, and pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 42(2), pages 321-349, December.
    2. Cavicchioli, Maddalena, 2024. "A matrix unified framework for deriving various impulse responses in Markov switching VAR: Evidence from oil and gas markets," The Journal of Economic Asymmetries, Elsevier, vol. 29(C).
    3. Bansal, Ravi & Miller, Shane & Song, Dongho & Yaron, Amir, 2021. "The term structure of equity risk premia," Journal of Financial Economics, Elsevier, vol. 142(3), pages 1209-1228.
    4. Motta, Anderson C. O. & Hotta, Luiz K., 2003. "Exact Maximum Likelihood and Bayesian Estimation of the Stochastic Volatility Model," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 23(2), November.
    5. Prosper Dovonon, 2013. "Conditionally Heteroskedastic Factor Models With Skewness And Leverage Effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 28(7), pages 1110-1137, November.
    6. Masaru Chiba, 2023. "Robust and efficient specification tests in Markov-switching autoregressive models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 99-137, April.
    7. E. Ramos-P'erez & P. J. Alonso-Gonz'alez & J. J. N'u~nez-Vel'azquez, 2020. "Forecasting volatility with a stacked model based on a hybridized Artificial Neural Network," Papers 2006.16383, arXiv.org, revised Aug 2020.
    8. Josh Stillwagon & Peter Sullivan, 2020. "Markov switching in exchange rate models: will more regimes help?," Empirical Economics, Springer, vol. 59(1), pages 413-436, July.
    9. Alfred A. Haug & Syed Abul Basher, 2019. "Exchange rates of oil exporting countries and global oil price shocks: a nonlinear smooth-transition approach," Applied Economics, Taylor & Francis Journals, vol. 51(48), pages 5282-5296, October.
    10. Bernardo D'Auria & Jos'e Antonio Salmer'on, 2017. "Optimal portfolios with anticipating information on the stochastic interest rate," Papers 1711.03642, arXiv.org, revised Jul 2024.
    11. Jackson, Laura E. & Owyang, Michael T. & Soques, Daniel, 2018. "Nonlinearities, smoothing and countercyclical monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 95(C), pages 136-154.
    12. Shaw, Charles, 2018. "Regime-Switching And Levy Jump Dynamics In Option-Adjusted Spreads," MPRA Paper 94154, University Library of Munich, Germany, revised 27 May 2019.
    13. Berdin, Elia, 2016. "Interest rate risk, longevity risk and the solvency of life insurers," ICIR Working Paper Series 23/16, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    14. Liang Wang & Weixuan Xia, 2022. "Power‐type derivatives for rough volatility with jumps," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(7), pages 1369-1406, July.
    15. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    16. Beum-Jo Park, 2011. "Forecasting Volatility in Financial Markets Using a Bivariate Stochastic Volatility Model with Surprising Information," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 37-58, September.
    17. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    18. repec:bla:jecsur:v:22:y:2008:i:4:p:711-751 is not listed on IDEAS
    19. Aycan HEPSAG, 2016. "Asymmetric stochastic volatility in central and eastern European stock markets," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania / Editura Economica, vol. 0(2(607), S), pages 135-144, Summer.
    20. Virbickaitė, Audronė & Frey, Christoph & Macedo, Demian N., 2020. "Bayesian sequential stock return prediction through copulas," The Journal of Economic Asymmetries, Elsevier, vol. 22(C).
    21. Alfeus, Mesias & Nikitopoulos, Christina Sklibosios, 2022. "Forecasting volatility in commodity markets with long-memory models," Journal of Commodity Markets, Elsevier, vol. 28(C).

    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:gam:jmathe:v:12:y:2024:i:3:p:423-:d:1328156. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.