Estimation of Bond Risks using Minimax

  • Irina Yurievna VYGODCHIKOVA Saratov State University, Saratov, Russian Federation
  • Anna Alexandrovna FIRSOVA Saratov State University, Saratov, Russian Federation
  • Alla Vladimirovna VAVILINA RUDN University, Moscow, Russian Federation
  • Oksana Yurievna KIRILLOVA Independent non-comercial institution of higher education, Institute ofInternational Economic Relations, Moscow, Russian Federation
  • Olga Sergeevna GORLOVA RUDN University, Moscow, Russian Federation

Abstract

The alarmist sentiment pertaining to extremely rare events in the financial markets – ‘the black swan events’ – place a particular focus on the issue of risk assessment, since most of the methods of classical statistics tend to underestimate their influence. The present paper aims to apply the new instruments of mathematical data analysis to obtain information on the quality of the regression model for indicators associated with corporate security investment. The authors suggest mathematical tools that can be applied to analyze heterogeneous noise phenomena using the following indicators – the absolute and the relative approximation errors arising from the deviations obtained through the Minimax model, and the indicators of bond price elasticity based on the problem of best uniform approximation of functions by polynomials of specified degree. According to computational experiments, the suggested methodology can be applied in practice, and mathematical apparatus should be developed to explore this dynamic process in detail, mainly for the bonds and other securities threatened by risks that cannot be efficiently assessed by employing conventional valuation techniques.

References

[1] Awrejcewicz, J. et al. 2015. On the methods of critical load estimation of spherical circle axially symmetrical shells. Thin-Walled Structures, 94: 293-301.
[2] Awrejcewicz, J. et al. 2015. Quantifying chaos of curvilinear beam via exponents. Communications in Non-linear Science and Numerical Simulation, 27(1–3): 81–92
[3] Box, G.P., and Jenkins, G.M. 1970. Time Series Analysis Forecasting and Control. San Francisco: Holden-Day.
[4] Dem’yanov, V.F., and Malozemov, V.N. 1972. Introduction in to minimax. Moscow: Science Publ., p. 13.
[5] Derunova, et al. 2014. The study of the dynamics of innovative development of economy on the endogenous growth through multi-sector extension of the Solow model. Biosci., Biotech. Res. Asia, 11(3): 1581-1589
[6] Derunova, et al. 2016. The Mechanisms of Formation of Demand in the High-Tech Products Market. International Journal of Economics and Financial Issues, 6(1): 96-102.
[7] Dickey, D.A., and Fuller, W.A. 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association, 74: 427– 431.
[8] Dubovikov, M.M., and Starchenko, N.S. 2003. Variation index and its applications to analysis of fractal structures. Sci. Almanac Gordon, 1: 1-30.
[9] Firsova, A., Balash, O., and Nosov, V. 2014. Sustainability of Economic System in the Chaos. Chaos, Complexity and Leadership. Springer Proceedings in Complexity, 299-304: 2213-8684.
[10] Granger, C.W. 1980. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14: 227–238.
[11] Johansen, S. 1994. The Role of the Constant Term in Cointegration Analysis of Nonstationary Variables. Econometric Reviews, 13, 205-219.
[12] Kashyap, R.L., and Rao, A.R. 1976. Dynamic Stochastic Models from Empirical Data. New York, San Francisco. London: Academic Press.
[13] Lo, A.W. 1991. Long-term memory in stock market prices. Econometrica, 59: 1279–1313.
[14] Mandelbrot, B. 1972. Statistical methodology for non-periodic cycles: From the covariance to R/S analysis. Annals of Economic and Social Measurement, 1: 259–290.
[15] Markowitz, H.M. 1972. Investment for the long run. Philadelphia: Univ. of Pennsylvania
[16] Markowitz, H.M. 1990. Normative Portfolio Analysis: Past, Present and Future. Journal of Economics and Business. Special Issue on Portfolio Theory, 42 (2): 99-103.
[17] Sendov, B. K. 1979. Hausdorff approximations. Sofia: BAN, p. 372.
[18] Sharpe, W.F., and Alexander, G.J. 1990. Investments (4-Th ed). Prentice-Hall International Inc.
[19] Taleb, N. N. 2007. The Black Swan: The Impact of the Highly Improbable. New York: Random House.
[20] Vygodchikova, I.Y. 2013. An estimate of the risk of formation of complex operations. Bulletin of Saratov State Technical University, 4-1 (73): 7-11.
Published
2017-03-06
How to Cite
VYGODCHIKOVA, Irina Yurievna et al. Estimation of Bond Risks using Minimax. Journal of Advanced Research in Law and Economics, [S.l.], v. 7, n. 7, p. 1899-1907, mar. 2017. ISSN 2068-696X. Available at: <https://journals.aserspublishing.eu/jarle/article/view/784>. Date accessed: 20 apr. 2024.