The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in
finance
Finance refers to monetary resources and to the study and Academic discipline, discipline of money, currency, assets and Liability (financial accounting), liabilities. As a subject of study, is a field of Business administration, Business Admin ...
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 sh ...
describing the evolution of
interest rates
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...
. 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 m ...
. 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.
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. It ...
:
:
where ''W
t'' is a
Wiener process
In mathematics, the Wiener process (or Brownian motion, due to its historical connection with Brownian motion, the physical process of the same name) is a real-valued continuous-time stochastic process discovered by Norbert Wiener. It is one o ...
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
In statistics, the standard deviation is a measure of the amount of variation of the values of a variable about its Expected value, mean. A low standard Deviation (statistics), deviation indicates that the values tend to be close to the mean ( ...
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
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Sto ...
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 dat ...
. 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
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. Essentially, the model uses a "discrete-time" ( lattice based) model of the varying price over time of the underlying fin ...
for equity
underlying
In finance, a derivative is a contract between a buyer and a seller. The derivative can take various forms, depending on the transaction, but every derivative has the following four elements:
# an item (the "underlier") that can or must be bou ...
s.
"Two-State Option Pricing". ''Journal of Finance'' 24: 1093-1110)
References
*
*
{{DEFAULTSORT:Rendleman-Bartter model
Interest rates
Short-rate models
Financial models