Overview of Rendleman-Bartter Model
In the context of finance the Rendleman-Bartter Model is a very important theory. The Rendleman-Bartter Model could be called a short rate model. This model deals with rates of interest. To be more specific, the Rendleman-Bartter Model tries to explain the growth of rates of interest.
The Rendleman-Bartter model is among the earliest models that dealt with rates of interest for a shorter period of time. It applied the random process that had been used to explain the movements of the basic prices of stock options.
According to the Rendleman-Bartter model the instantaneous rate of interest changes in accordance with the geometric Brownian motion, which is also called the exponential Brownian motion. The geometric Brownian motion is an uninterrupted random process.
Description of Rendleman-Bartter Model
According to the Rendleman-Bartter Model market risk is the sole factor that is responsible for the changes in the rates of interest. This is why the Rendleman-Bartter Model could also be called a kind of "one factor model".
Equational Representation of Rendleman-Bartter Model
The equational presentation of the Rendleman-Bartter Model is as follows:
drt = φrtdt + σrtdWt
In this model Wt is nothing but a Wiener process. It models the risk factor involved in random markets. σ is the drift parameter of the Rendleman-Bartter model. φ is the standard deviation parameter of the Rendleman-Bartter model.
The drift parameter of the Rendleman-Bartter model stands for the extent of fluctuation in the rate of interest. This rate is normally fixed, anticipated and instantaneous. The standard deviation parameter of the Rendleman-Bartter model ascertains the unpredictability of rates of interest.
Use of Rendleman-Bartter Model
The Rendleman-Bartter model is mainly used to determine the value of the interest rate derivatives.