Financial Implications of the Interest Rate Positivity Assumption

The conception of non-negativity of nominal interest rate was the undoubted axiom in the financial world for a long time. However, frequent recent violations of this conception can be interpreted as a signal for reconsideration of established views on existence and justification of zero lower bound on nominal interest rates. In this paper we will analyzе the empirical evidence of negative interest rates and their explanation, theoretical justification and disproof of zero lower bound (ZLB) on nominal interest rates concept in the existing literature. We will also examine the examples of the elimination and the mathematical modelling of ZLB. Moreover the shadow rate term-structure model method of valuation of lower bound on nominal interest rates is proposed in this paper. Application of this method using real data of the German government bonds prices confirmed the presumption of the negative lower bound on nominal interest rates.