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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
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    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. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
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    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.

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