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Jarrow-Rudd树.py
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Jarrow-Rudd树.py
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# -*- coding: utf-8 -*-
"""
Created on Tue May 16 11:28:36 2017
一个基本的二叉树机构由以下三个参数决定:
up 标的资产价格向上跳升的比例, up必然大于1
down 标的资产价格向下跳升的比例, down必然小于1
upProbability 标的资产价格向上跳升的概率
@author: Unknow
"""
import numpy as np
import seaborn as sns
import math
from matplotlib import pylab
# 解决图像中文不输出问题
from matplotlib.font_manager import FontProperties
font = FontProperties(fname=r"c:\windows\font\simsun.tcc",size=14)
# 设置基本参数
ttm = 3.0 # 到期时间,单位年
tSteps = 25 # 时间方向步数
r = 0.03 # 无风险利率
d = 0.02 # 标的股息率
sigma = 0.2 # 波动率
strike = 100.0 # 期权行权价
spot = 100.0 # 标的现价
# Jarrow - Rudd 树
# 这个树的深度为16层(时间节点数+1)
dt = ttm/tSteps
up = math.exp((r-d-0.5*sigma*sigma)*dt+sigma*math.sqrt(dt))
down = math.exp((r-d-0.5*sigma*sigma)*dt-sigma*math.sqrt(dt))
discount = math.exp(-r*dt)
lattice = np.zeros((tSteps+1,tSteps+1))
lattice[0][0] = spot
for i in range(tSteps):
for j in range(i+1):
lattice[i+1][j+1] = up*lattice[i][j]
lattice[i+1][0] = down*lattice[i][0]
pylab.figure(figsize=(12,8))
pylab.plot(lattice[tSteps])
pylab.title(u"二叉树到期时刻标的价格分布",fontproperties='SimHei')
def call_payoff(spot):
global strike
return max(spot-strike,0.0)
"""
pylab.figure(figsize=(12,8))
pylab.plot(map(call_payoff,lattice[tSteps]))
pylab.title(u"二叉树到期时刻标的Pay off分布",fontproperties='SimHei')
"""
for i in range(tSteps,0,-1):
for j in range(i,0,-1):
if i == tSteps:
lattice[i-1][j-1] = 0.5 * discount * (call_payoff(lattice[i][j]) + call_payoff(lattice[i][j-1]))
else:
lattice[i-1][j-1] = 0.5 * discount * (lattice[i][j] + lattice[i][j-1])
print( u'二叉树价格: %.4f' % lattice[0][0])