The Mathematics of Financial Modelingand Investment Management

20-Term Structure Page 646 Wednesday, February 4, 2004 1:33 PM

646 The Mathematics of Financial Modeling and Investment Management

EXHIBIT 20.5 (Continued)

Hull-White model:

L(t) = 1 + 0.002t, T(t) = cost. = 200, CIR model:

σ = 0.01 L = 1, T = 200, σ = 0.005

Black-Karasinski model:

Kalotay-Williams-Fabozzi model: θ(t) = 0.005exp(–0.005t),

θ(t) = 0.005exp(–0.005t), σ = 0.01 φ(t) = 0.001, σ = 0.01

SUMMARY

■ There are different types of interest rates.

■ The term structure of interest rates is a curve that associates to each

future date the yield of an hypothetical risk-free zero-coupon bond

maturing exactly at that date.

■ The term structure of interest rates can be recovered from empirical

data using the no-arbitrage principle and curve smoothing techniques.

■ The term structure of interest rates is not fixed but might change with

time.