Rendleman-Bartter model

The Rendleman-Bartter model in finance is a short rate model describing the evolution of interest rates. 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:

:$dr\_t\; =\; heta\; r\_t,dt\; +\; sigma\; r\_t,dW\_t$

where "W_t" is a Wiener process modelling the random market risk factor. The drift parameter, $heta$, 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).

References

*cite book | author=Hull, John C. | title=Options, Futures and Other Derivatives| year=2003 | publisher = Upper Saddle River, NJ: Prentice Hall | id = ISBN 0-13-009056-5
*cite journal | author=Rendleman, R. and B. Bartter | title=The Pricing of Options on Debt Securities | journal=Journal of Financial and Quantitative Analysis| year=1980 | volume=15 | pages=11–24 | doi=10.2307/2979016