<>Rendleman and Bartter Model

<> preface

Rendleman-Bartter Model is one of the short-term interest rate models , The model holds that the interest rate follows the geometric Brownian motion . However, the interest rate level simulated by the model lacks the attribute of mean regression , That is, the interest rate cannot return to the long-term average level .

<> one ,Rendleman and Bartter Analytical formula of model

among ,u Is the instantaneous drift value .

<> two ,python quantification
import math import numpy as np def rendleman_bartter(r0,theta,sigma,T=1,N=10
,seed=777): np.random.seed(seed) dt=T/float(N) rates=[r0] for i in range(N): dr=
theta*rates[-1]*dt+sigma*rates[-1]*math.sqrt(dt)*np.random.normal() rates.append
(rates[-1]+dr) return range(N+1),rates import matplotlib.pyplot as plt
plt.figure(figsize=(12,10)) for theta in [0.01, 0.05, 0.1]: x, y =
rendleman_bartter(0.005, theta, 0.05, T=10, N=200) plt.plot(x,y, label=
'theta=%s'%theta) plt.legend(loc='upper left') plt.xlabel('Rendleman and
Bartter model');

<> summary

This chapter is about Rendleman-Bartter The model is introduced , The model lacks the feature of returning to the long-term mean .