Handbook of Asset and Liability Management: From models to optimal return strategies

35

The Basis of Interest Rate Modelling

Bonne semence fait bon grain.

This chapter will describe yield curve evolution modelling in order to propose a practical implementation.

First, A/L managers do not speak about the yield curve model but about the modelS of the yield curveS. There is not only one model and of course, there is not only one yield curve.

Interest rate models are developed in order to:

• price and hedge (and delta hedge);
• compute economic values and economic value sensitivities;
• simulate interest rates and diffuse interest rate trajectories.

35.1 YIELD CURVE RECONSTITUTION

In this section, we will reconstitute the initial zero-coupon yield curve, i.e. we will model the market information in order to get a zero-coupon yield curve. Interest rate models will try to simulate the evolution of this curve as time passes.

To begin with, let us recall that the zero-coupon rates TZC introduced in Section 19.3 allowing for the computation of a fixed rate bond price V as the sum of its discounted cash flows :

There are indeed three major types of zero-coupon yield curves:

• The government bond yield curve or risk free yield curve built from the quotations of the government bonds (i.e. usually G7 countries not exposed to default).
• The Interbank yield curve (or swap yield ...