Search Advanced

AIMS Mathematics

2020, Volume 5, Issue 1: 300-310. doi: 10.3934/math.2020020
Previous Article Next Article
Research article

Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling

  • 1.
    Department of Mathematical Sciences, Institute of Business Administration Karachi, Pakistan
  • 2.
    University of Bucharest, Romania
  • 3.
    "Gh. Mihoc-C. Iacob" Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy
  • 4.
    National Institute for Economic Research "Costin C. Kiritescu", Bucharest, Romania
  • 5.
    Bucharest University of Economic Studies, Bucharest, Romania
  • Received: 15 August 2019 Accepted: 04 November 2019 Published: 13 November 2019

  • MSC : 60Gxx, 60Jxx, 90Bxx

  • A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt & Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho & Lee model in the semi-Markov regime-switching framework [1]. We formulate and solve the optimization problem of Hunt & Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [2]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques.

    Citation: Muhammad Sheraz, Vasile Preda, Silvia Dedu. Non-extensive minimal entropy martingale measures and semi-Markov regime switching interest rate modeling[J]. AIMS Mathematics, 2020, 5(1): 300-310. doi: 10.3934/math.2020020

    Related Papers:

  • A minimal entropy martingale measure problem is studied to investigate risk-neutral densities and interest rate modelling. Hunt & Devolder focused on the method of Shannon minimal entropy martingale measure to select the best measure among all the equivalent martingale measures and, proposed a generalization of the Ho & Lee model in the semi-Markov regime-switching framework [1]. We formulate and solve the optimization problem of Hunt & Devolder for deriving risk-neutral densities using a new non-extensive entropy measure [2]. We use the Lambert function and a new type of approach to obtain results without depending on stochastic calculus techniques.


    加载中


    [1] J. Hunt, P. Devolder, semi-Markov regime switching interest rate models and minimal entropy measure, Phys. A Stat. Mech. Appl., 390 (2011), 3767-3778.
    [2] F. Shafee, Lambert function and a new non-extensive form of entropy, J. App. Math., 72 (2007), 785-800.
    [3] C. E. Shannon, W. Weaver, The Mathematical Theory of Communication, Urbana: The University of Illinois Press, 1998.
    [4] G. Kaniadakis, Non-linear kinetics underlying generalized statistics, Phys. A Stat. Mech. Appl., 296 (2001), 405-425.
    [5] A. Renyi, On measures of entropy and information, In: Proceed. 4th. Berkely. Symp. Math Stat. Prob., 1 (1961), 547-561.
    [6] C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52 (1988), 479-487.
    [7] M. R. Ubriaco, Entropies based on fractional calculus, Phys. Lett. A Stat. Mech. Appl., 373 (2009), 2516-2519.
    [8] T. S. Y. Ho, S. B. Lee, Term structure movements and pricing interest rate contingent claims, J. Financ., 41 (1986), 1011-1029.
    [9] J. C. Cox, J. E. Ingersoll, S. A. Ross, A theory of the term structure of interest rates, Econometrica, 53 (1985), 385-408.
    [10] J. Hull, A. White, Pricing interest-rate derivative securities, Rev. Financ. Stud., 3 (1990), 573-592.
    [11] O. Vasicek, An equilibrium characterization of the term structure, J. Financ. Econ., 5 (1977), 177-188.
    [12] P. J. Hunt, J. E. Kennedy, Financial Derivatives in Theory and Practice, John Wiley and Sons, 2004.
    [13] G. C. Philippatos, C. J. Wilson, Entropy, market risks and the selection of efficient portfolios, Appl. Econ., 4 (1972), 209-220.
    [14] L. Gulko, The entropy theory of stock option pricing, Int. J. Theo. Appl. Financ., 2 (1999), 331-355.
    [15] B. Trivellato, Deformed exponentials and applications to finance, Entropy, 15 (2013), 3471-3489.
    [16] B. Trivellato, The minimal k-entropy martingale measure, Int. J. Theo. Appl. Financ., 15 (2012), 1250038.
    [17] V. Preda, S. Dedu, M. Sheraz, New measure selection for Hunt and Devolder semi-Markov regime switching interest rate model, Phys. A Stat. Mech. Appl., 407 (2014), 350-359.
    [18] V. Preda, S. Dedu, C. Gheorghe, New classes of Lorenz curves by maximizing Tsallis entropy under mean and Gini equality and inequality constraints, Phys. A Stat. Mech. Appl., 436 (2015), 925-932.
    [19] V. Preda, M. Sheraz, Risk-neutral densities in entropy theory of stock options using Lambert function and a new approach, P. Romanian Acad. A, 4 (2015), 20-27.
    [20] M. Sheraz, V. Preda, S. Dedu, Tsallis and Kaniadakis entropy measures for risk neutral densities, International Conference on Computer Aided Systems Theory, Springer, 2017.
    [21] T. Bjö rk, Arbitrage Theory in Continuous Time, New York: Oxford University Press, 2009.
    [22] J. C. Cox, S. A. Ross, M. Rubinstein, Option pricing: A simplified approach, J. Financ. Econ., 7 (1979), 229-263.
    [23] S. R. Valluri, R. M. Corrless, D. J. Jeffrey, Some applications of Lambert W function to physics, Canadian J. Phys., 78 (2000), 823-831.
    [24] J. Borwein, R. Choksi, P. Maréchal, Probability distributions of assets inferred from option prices via the principle of maximum entropy, SIAM J. Optimiz., 14 (2003), 464-478.
    [25] D. G. Luenberger, Optimization by Vector Space Methods, New York: Wiely, 1969.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(3928) PDF downloads(433) Cited by(2)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog