The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in
finance is a
short-rate model
A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,.
The short rate
Under a sho ...
describing the evolution of
interest rates. It is a "one factor model" as it describes interest rate movements as driven by only one source of
market risk
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility.
There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the mos ...
. It can be used in the valuation of
interest rate derivative
In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of dif ...
s. It is a
stochastic asset model
A stochastic investment model tries to forecast how returns and prices on different assets or asset classes, (e. g. equities or bonds) vary over time. Stochastic models are not applied for making point estimation rather interval estimation and ...
.
The model specifies that the instantaneous interest rate follows a
geometric Brownian motion
A geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift. ...
:
:
where ''W
t'' is a
Wiener process
In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It i ...
modelling the random market risk factor. The drift parameter,
, represents a constant expected instantaneous rate of change in the interest rate, while the
standard deviation parameter,
, determines the
volatility of the interest rate.
This is one of the early models of the short-term interest rates, using the same
stochastic process as the one already used to describe the dynamics of the underlying price in
stock options
In finance, an option is a contract which conveys to its owner, the ''holder'', the right, but not the obligation, to buy or sell a specific quantity of an underlying asset or instrument at a specified strike price on or before a specified d ...
. Its main disadvantage is that it does not capture the
mean reversion of interest rates (their tendency to revert toward some value or range of values rather than wander without bounds in either direction).
Note that in 1979 Rendleman-Bartter also published a version of the
Binomial options pricing model for equity
underlying
In finance, a derivative is a contract that ''derives'' its value from the performance of an underlying entity. This underlying entity can be an asset, index, or interest rate, and is often simply called the "underlying". Derivatives can be us ...
s.
"Two-State Option Pricing". ''Journal of Finance'' 24: 1093-1110)
References
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{{DEFAULTSORT:Rendleman-Bartter model
Interest rates
Short-rate models
Financial models