In this article we discuss fundamentals of the debt securities pricing. We begin with a generalization of the present value concept. Though the present value is the base valuation method in the modern finance we will illustrate that this concept does not sufficiently accurate in producing instrument pricing. The incompleteness of the unique present value approach stems from variability of the interest rates. Admitting variability of the interest rates we define two present values one for buyer other for seller. Therefore future buyer and seller cash payments can be described by the correspondent present values. Usually used assumption that future interest on investment over a specified time period would be the same as before specified period is a theoretical simplification that might be admitted or not. Admitting such assumption leads to eliminating an important component of the market risk. Recall that the assumption that a future payment can be invested with the same constant interest rate equal to the one used in the past is a component of the group conditions that specify frictionless of the market. We use this new concept that splits present value within two counterparties to outline details of the new valuation method of the fixed income securities. The primary goal of this paper is a credit derivative pricing method of the risky debt instruments. First we introduce a formal definition of the default. It somewhat close but does not coincide with the reduced form of the default setting.
