# Rendleman-Bartter model

The Rendleman-Bartter model in finance is a short rate model describing the evolution of interest ratess. It is a type of "one factor model" as describes interest rate movements as driven by only one source of market risk. It can be used in the valuation of interest rate derivatives.

The model specifies that the instantaneous interest rate follows a geometric Brownian motion:

where Wt is a Wiener process 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. 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).

## References

• Hull, John C. (2003). Options, Futures and Other Derivatives. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-009056-5.
• Rendleman, R. and B. Bartter (1980). "The Pricing of Options on Debt Securities". Journal of Financial and Quantitative Analysis 15: 11-24.
Mathematical finance is the branch of applied mathematics concerned with the financial markets.

The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory.
In the context of interest rate derivatives, a short rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate.
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Market risk is the risk that the value of an investment will decrease due to moves in market factors. The four standard market risk factors are:
• Equity risk, or the risk that stock prices will change.

An interest rate derivative is a derivative where the underlying asset is the right to pay or receive a (usually notional) amount of money at a given interest rate.

The interest rate derivatives market is the largest derivatives market in the world.
A geometric Brownian motion (GBM) (occasionally, exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion, or a Wiener process.
Wiener process is a continuous-time stochastic process named in honor of Norbert Wiener. It is often called Brownian motion, after Robert Brown. It is one of the best known Lévy processes (càdlàg stochastic processes with stationary independent increments) and occurs
In probability and statistics, the standard deviation of a probability distribution, random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma).
Volatility is the measure of the state of instability.
• Volatility (finance) frequently refers to the standard deviation of the change in value of a financial instrument with a specific time horizon.