Parametric

Nelson and Siegel (1987)
Svensson, L (1994)

Spline Interpolation

FNZ (Fisher Nychka Zervos) (1995) - smoothing
Anderson and Sleath (2001)

Cubic-Spline Interpolation

McCulloch (1971)
Anderson and Sleath (2001)

A basis spline is a spline function that has minimual support with respect to a given degree, smoothness and domain partition.

One Factor

just use the short rate for everything

No-Arbitrage

also called relative value
use observed market prices

No-Arbitrage - Normal

assumes interest rate volatility is independent (not related to) the level of the interest rate

Ho and Lee (1986)
No mean reversion

Hull and White (HW) (1990)
This model extends the Vasicek Model and Cox-Ingersoll-Ross models and allows for mean reversion.

No-Arbitrage - Lognormal

assumes interest rate volatility depends on the level of the interest rate

Black (1976)

Heath-Jarrow-Morton (HJM) (1987)

Black-Derman-Toy (BDT) (1990)
Allows for mean reversion which is determined by market conditions

Black-Karasinski (BK)
Allows for mean reversion

Kalotay-Williams-Fabozzi (KWF)
No mean reversion. For pricing bonds with embedded options

Equilibrium

Vasicek (1977)

Brennan-Schwartz (1979, 1982)

Cox-Ingersoll-Rox (CIR) (1981, 1985)
This is a square root process

Multi Factor

one factor for short rate
another factor for long rate

No-Arbitrage

Hull and White (HW) (1987) - Two Factor

Heath-Jarrow-Morton (HJM) (1992)
This model is for predicting forward rates

Equilibrium

Longstaff-Schwartz (1989)

Others ??

Merton (1973)
Geometric Brownian Motion
Dothan (1978)
Courtadon (1982)
Langetieg (1980)
Richard (1979)
Black Scholes (1973)
Jarrow and Rudd (1982)
Boyle (1977) - monte carlo simulation

Pure Expectations Theory

Term structure reflects the markets current expectation of the future rates. A rising yield curve is explained by investors expecting short-term interest rates to go up.
This says that the only factor that affects the shape of a yield curve is the markets expectation about future interest rates.

Liquidity Preference Theory

Investors prefer liquidity, upward sloping yield curve. Intuitively long-term investments are more risky than short-term so long dated yields should be higher than short-term yields.

Market Segmentation Hypothesis

Shape is determined by the supply and demand of the securities within each maturity sector. Shape is best explained by a combination of all 3 theories.