# 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 ...*