IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v407y2014icp350-359.html
   My bibliography  Save this article

New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models

Author

Listed:
  • Preda, Vasile
  • Dedu, Silvia
  • Sheraz, Muhammad

Abstract

In this paper we construct the minimal entropy martingale for semi-Markov regime switching interest rate models using some general entropy measures. We prove that, for the one-period model, the minimal entropy martingale for semi-Markov processes in the case of the Tsallis and Kaniadakis entropies are the same as in the case of Shannon entropy.

Suggested Citation

  • Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    • Handle: RePEc:eee:phsmap:v:407:y:2014:i:c:p:350-359
    DOI: 10.1016/j.physa.2014.04.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711400315X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2014.04.011?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. D’Amico, Guglielmo & Manca, Raimondo & Salvi, Giovanni, 2013. "A semi-Markov modulated interest rate model," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2094-2102.
    2. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    3. Hunt, Julien & Devolder, Pierre, 2011. "Semi Markov regime switching interest rate models and minimal entropy measure," LIDAM Discussion Papers ISBA 2011010, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    5. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    6. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.
    7. Hunt, Julien & Devolder, Pierre, 2011. "Semi-Markov regime switching interest rate models and minimal entropy measure," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3767-3781.
    8. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    9. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    10. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
    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. Gzyl, Henryk & Mayoral, Silvia, 2016. "Determination of zero-coupon and spot rates from treasury data by maximum entropy methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 456(C), pages 38-50.
    2. Patrick Assonken & G. S. Ladde, 2015. "Option Pricing With A Levy-Type Stochastic Dynamic Model For Stock Price Process Under Semi-Markovian Structural Perturbations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(08), pages 1-72, December.
    3. Sfetcu, Răzvan-Cornel, 2016. "Tsallis and Rényi divergences of generalized Jacobi polynomials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 131-138.
    4. Aida Toma & Samuela Leoni-Aubin, 2015. "Robust Portfolio Optimization Using Pseudodistances," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-26, October.
    5. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    6. Florentin ŞERBAN & Anca-Teodora ŞERBAN-OPRESCU & George-Laurenţiu ŞERBAN-OPRESCU, 2017. "Appraisal of Scientific Research in European Countries. An Entropy-Based Analysis," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 51(1), pages 103-116.
    7. Muhammad Sheraz & Imran Nasir, 2021. "Information-Theoretic Measures and Modeling Stock Market Volatility: A Comparative Approach," Risks, MDPI, vol. 9(5), pages 1-20, May.
    8. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    9. Răzvan-Cornel Sfetcu & Sorina-Cezarina Sfetcu & Vasile Preda, 2021. "Ordering Awad–Varma Entropy and Applications to Some Stochastic Models," Mathematics, MDPI, vol. 9(3), pages 1-15, January.

    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. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    2. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    3. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    4. Meyer-Gohde, Alexander, 2019. "Generalized entropy and model uncertainty," Journal of Economic Theory, Elsevier, vol. 183(C), pages 312-343.
    5. Stavroyiannis, S. & Makris, I. & Nikolaidis, V., 2010. "Non-extensive properties, multifractality, and inefficiency degree of the Athens Stock Exchange General Index," International Review of Financial Analysis, Elsevier, vol. 19(1), pages 19-24, January.
    6. Preda, Vasile & Dedu, Silvia & Gheorghe, Carmen, 2015. "New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 925-932.
    7. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    8. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    9. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    10. Leitner, Johannes, 2000. "Convergence of Arbitrage-free Discrete Time Markovian Market Models," CoFE Discussion Papers 00/07, University of Konstanz, Center of Finance and Econometrics (CoFE).
    11. Qin, Guyue & Shang, Pengjian, 2021. "Analysis of time series using a new entropy plane based on past entropy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    12. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    13. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    14. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.
    15. Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    16. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    17. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    18. 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.
    19. D’Amico, Guglielmo & Manca, Raimondo & Salvi, Giovanni, 2013. "A semi-Markov modulated interest rate model," Statistics & Probability Letters, Elsevier, vol. 83(9), pages 2094-2102.
    20. Jos'e Cl'audio do Nascimento, 2019. "Rational hyperbolic discounting," Papers 1910.05209, arXiv.org, revised Feb 2020.

    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:eee:phsmap:v:407:y:2014:i:c:p:350-359. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.