Rendleman–Bartter model

The Rendleman–Bartter model (Richard J. Rendleman, Jr. and Brit J. Bartter) in

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 W_t 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

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

underlyings. ("Two-State Option Pricing". Journal of Finance 24: 1093-1110

.)

References

Hull, John C. (2003). Options, Futures and Other Derivatives. Upper Saddle River, NJ:
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 (1): 11–24.
S2CID 154495945
.