Estimation of Bond Risks using Minimax
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.
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