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<>Rendleman and Bartter模型
<>前言
Rendleman-Bartter模型是短期利率模型中的一种，模型认为利率变得遵循几何布朗运动过程。但是模型模拟出的利率水平缺乏均值回归的属性，即利率不能回归到长期均值水平。
<>一、Rendleman and Bartter模型解析式
其中，u是瞬时飘移值。
<>二、python量化
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');
<>总结
本章对Rendleman-Bartter模型进行了介绍，模型缺乏回复到长期均值的特征。
