Evaluation of obligation

The evaluation of a obligation amounts finding what it should be worth in theory under the current conditions of the market by a mathematical operation known as of Actualisation, by determining the theoretical Current value of the whole of flows which compose it. The selected Rates up-dating for this operation are determined by the observation of those already applied to the market to comparable obligations by the duration, the liquidity and the credit risk presented.

The theoretical value of a obligation' , just as its price on the market, change permanently under the effect:

of the market evolution of the Interest rate
of the flow of time.

Case of the obligations withfluctuating rate

Case of the obligations withfixed rate

The general principle is that, mechanically, the prices of the obligations withfixed rate evolve/move contrary to interest rate: if the rates go up, the prices drop, and conversely. A simplification often used of the reasoning is the following one:

If market rate passes from 6% to 6,10% the old obligations withfixed rate emitted to 6% undergo the competition of the emitted news with 6.10%. To restore balance, their value drops so that, on the basis of this lower value, their interests remaining to be run bear them also 6,10%. That is checked by observing that them Cours drops under the influence of the arbitration (purchase-sales of the operators).
Of course, if on the contrary market rate passes from 6% to 5,90%, the commercial value of these obligations increases.

General principles of pricing of the rates

Directing markets of interest rates

In the United States and in the euro area, like, to a lesser extent, in Japan and in the United Kingdom, there exist permanently two gone of reference of interest rates from 0 to 30, even 50 years, of a very large Liquidité:

that of principal the Government loans;
that of the swap S against IBOR.

For interest rates of the other currencies, that is certainly a little less true, but the principles remain the same ones.

The market of the Government loans provides the curve of interest rates without risk ; that of the swaps , that of interbank interest rates .

The rates of the Government loans are formed according to supply and instantaneous demand concentrated on the future .

Case of the obligations involving a credit risk

The valorization of an instrument of comprising rate, contrary to the credit risk, Government loans, like an obligation emitted by an local government agency, a company, a foreign State, etc, is carried out in theory in:

bringing up to date the bill book of financial flows of the instrument with the discount coefficients applicable to the Government loans;
by adding a to him premium of liquidity , i.e. an estimate of the cost of negotiation of the instrument;
and finally by adding an estimate of the expectation of the risk of defect of the borrower throughout loan, corrected by the rate of average covering anticipated for this borrower in the event of defect.

The amount, expressed in basic points, of which it would be necessary to move in parallel, generally to the top, the whole of the curve of the rates zero-coupon of the Government loans so that the actualization of flows of obligation on this new curve corresponds at its price actually noted on the market, is called the Spread of credit of the obligation.

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