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<>短期利率模型之Cox-Ingersoll-Ross模型
<>前言
上篇文章对Vasicek模型进行了简单的介绍，本偏文章则要对短期利率模型中的Cox-Ingersoll-Ross模型进行介绍
<>一、Cox-Ingersoll-Ross模型
Cox-Ingersoll-Ross模型是用于解决Vasicek模型出现负利率问题的单因素模型。
Cox-Ingersoll-Ross模型计算公式为（The equation for the CIR model is expressed as
follows:）
其中：
rt=Instantaneous interest rate at time t（t时刻的瞬时利率）
a=Rate of mean reversion（回归速度）
b=Mean of the interest rate（长期平均水平。在长期水平下产生一系列r的轨道值）
Wt =Wiener process (random variable modeling the market risk
factor/风险中性框架下的维纳过程)
σ=Standard deviation of the interest rate (measure of volatility/标准差参数)
<>二、Cox-Ingersoll-Ross模型的python量化
# CIR模型 # CIR模型是用于解决Vasicek模型负利率的问题 import math import numpy as np def CIR(
r0,K,theta,sigma,T=1,N=10,seed=777): np.random.seed(seed) df=T/float(N) rates=[
r0] for i in range(N): dr=K*(theta-rates[-1])*dt+sigma*math.sqrt(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 K in [
0.002,0.02,0.2]: x,y=CIR(0.005,K,0.15,sigma,T=10,N=200,seed=777) plt.plot(
x,y,label='K=%s'%K) plt.legend(loc=0) plt.xlabel('CRR model')
<>总结
本章介绍了Cox-Ingersoll-Ross模型，Cox-Ingersoll-Ross模型是用于解决Vasicek模型出现负利率问题的单因素模型。
