Chapter 5: Langetieg s Multi-Factor Equilibrium Framework

The term structure of interest rates is embedded in the macro-economic system and is related to various economic factors. For this reason, Langetieg [ 36 ] proposes a model that can accommodate an arbitrary number of economic variables . The model is essentially an extension of Vasicek's term structure model [ 50 ], studied in Chapter 1, with multiple sources of uncertainty.

5.1 Underlying assumptions

Langetieg makes certain assumptions which allow for a mathematically tractable, intuitively sound model:

Assumption 1

The set of stochastic economic factors which are related to the interest rate term structure follow a joint elastic random walk.

 

Assumption 2

The instantaneous risk-free rate of interest may be expressed as a linear combination of these factors.

 

Assumption 3

The market prices of risk of the factors are deterministic, that is, they are either constants or function of time only.

 

The assumption of an elastic random walk means that the Vasicek model, which incorporates a univariate elastic random walk, is extended to a multivariate elastic random walk. Vasicek does not assume the functional form of the bond price, but derives it from the following assumptions (which apply to Langetieg's model as well):

• Bond prices are functionally related to certain stochastic factors.

• These underlying factors follow a specific stochastic process.

• The markets are sufficiently perfect to allow for a no arbitrage equilibrium to be reached.