Python金融大数据分析-BSM、Term Struc、Ho-Lee 与Vasicek模型路径仿真

# -*- coding: utf-8 -*-
import numpy as np  
import pandas as pd  
import matplotlib.pyplot as plt  
import scipy.stats as scs  
'''
#initial parameters and introductions
created by luyixiao 2016/12/29
S0 = 100#initial stock price or other value 
r = 0.05#risk-free rate
sigma = 0.25#standard devitaion 
T = 2.0#simulation time
I = 10#the number of path you wanna simluate
M = 50#the step you wanna simulate
'''

def modelSimulation(modelType,S0 = 100,r = 0.05,sigma = 0.25,T = 2.0,I = 10,M = 50,lamda = 0.05,k = 0.1,theta = 102):
    dt = T/M  
    S = np.zeros((M + 1,I))  
    S[0] = S0  
    print S[0]  
    if modelType == 'BSM':
        for t in range(1,M+1):  
            S[t] = S[t-1]*np.exp((r-0.5*sigma**2)*dt+sigma*np.sqrt(dt)*np.random.standard_normal(I))  
    if modelType == 'TSnD':
        for t in range(1,M+1):       
            S[t] = S[t-1]+np.sign(np.random.uniform(-1,1,I))*sigma*np.sqrt(dt)*np.random.standard_normal(I)  
    if modelType == 'TSwD':
        for t in range(1,M+1):       
            S[t] = S[t-1]+lamda*np.sqrt(dt)+np.sign(np.random.uniform(-1,1,I))*sigma*np.sqrt(dt)*np.random.standard_normal(I)  
    if modelType == 'HoLee':
        for t in range(1,M+1):       
            lamdan = np.random.uniform(0.01,0.09)            
            S[t] = S[t-1]+lamdan*np.sqrt(dt)+np.sign(np.random.uniform(-1,1,I))*sigma*np.sqrt(dt)*np.random.standard_normal(I)  
    if modelType == 'Vasicek':
        for t in range(1,M+1):       
            S[t] = S[t-1]+k*(theta-S[t-1])+sigma*np.sqrt(dt)*np.random.standard_normal(I)  
    plt.plot(S[:,:],lw = 1.5)  
    plt.xlabel('time')  
    plt.ylabel('price')
    plt.title(modelType)
    plt.show()  
modelSimulation('TSnD')   
modelSimulation('TSwD')   
modelSimulation('HoLee')    
modelSimulation('Vasicek')

for i in range(0,5):
    modelSimulation('Vasicek',k = 0.1*i,theta=100)