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.