Page 21 - FINAL CFA II SLIDES JUNE 2019 DAY 9

LOS 34.k: Describe modern term structure READING 34: THE TERM STRUCTURE AND
models and how they are used. INTEREST RATE DYNAMICS
MODULE 34.6: INTEREST RATE MODELS

Illustrative example: Assume that the current short-term rate is r = 3% and the long-run value for the short-term rate is b = 8%.
Also assume that the speed of the adjustment factor is a = 0.40 and the annual volatility is σ = 20%. Using CIR model as above,
we have developed the formula for the change in short-term interest rates,

dr: dr = 0.40 (8% − r) dt + (20%) √rdz

And that a random number generator produced standard normal random error terms, dz, of 0.50, –0.10, 0.50, and –0.30.

How would you apply the CIR model to assess the evolution of interest rates?

The simulation of interest rates starts with
an interest rate of 3%, which is well below
the long-run value of 8%.

Interest rates generated by the model
The bottom half of quickly move toward this long-run (mean-
the exhibit shows reverting, via the drift term a(b – r)dt, even
the pricing of after exceeding at t=3, drift term brings it
back down!
bonds consistent
with the evolution Volatility increases with the level of
of the short-term interest rates:
interest rate.
• dz = 0.50 at t = 0/t = 2 but the volatility
term(σ√rdz) is much higher in t = 2
than in t = 0

This example is stylized and intended for
illustrative purposes only. The parameters
used in practice typically vary significantly
from these.