Regime Tracking in Markets with Markov Switching

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

Mathematics, 2024, vol. 12, issue 3, 1-27

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.

Keywords: Markov jump process; fair derivative price; optimal filtering problem; multivariate point process; central limit theorem; generalized regenerative process (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/3/423/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/3/423/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:3:p:423-:d:1328156

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().