# Rendleman–Bartter model

The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in finance is a short rate model 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. It can be used in the valuation of interest rate derivatives. It is a stochastic asset model.

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

$dr_t = \theta r_t\,dt + \sigma r_t\,dW_t$

where Wt is a Wiener process modelling the random market risk factor. The drift parameter, $\theta$, represents a constant expected instantaneous rate of change in the interest rate, while the standard deviation parameter, $\sigma$, 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).

Note that in 1979 Rendleman-Bartter also published a version of the Binomial options pricing model . ("Two-State Option Pricing". Journal of Finance 24: 1093-1110.)

## 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. doi:10.2307/2979016.
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Last modified on 20 April 2013, at 15:58