Python障碍式期权定价脚本实现与解析

核心代码实现与逻辑解析

#coding:utf-8
'''
障碍期权
q=x/s
H = h/x H 障碍价格
[1] Down-and-in call cdi
[2] Up-and-in call cui
[3] Down-and-in put pdi
[4] Up-and-in put pui
[5] Down-and-out call cdo
[6] Up-and-out call cuo
[7] Down-and-out put pdo
[8] Up-and-out put puo

'''
from math import log,sqrt,exp,ceil
from scipy import stats
import datetime
import tushare as ts
import pandas as pd
import numpy as np
import random
import time as timess
import os

def get_codes(path='D:\\code\\20180313.xlsx'):     #从代码表格从获取代码
 codes = pd.read_excel(path)
 codes = codes.iloc[:,1]    
 return codes

def get_datas(code,N=1,path='D:\\data\\'):        #获取数据N=1当天数据
 datas = pd.read_csv(path+eval(code)+'.csv',encoding='gbk',skiprows=2,header=None,skipfooter=N,engine='python').dropna() #读取CSV文件 名称为股票代码 解gbk skiprows跳过前两行文字 第一行不做为表头
 date_c = datas.iloc[:,[0,4,5]]     #只用第0 列代码数据和第4列收盘价数据
 date_c.index = datas[0]
 return date_c

def get_sigma(close,std_th):
 x_i = np.log(close/close.shift(1)).dropna()
 sigma = x_i.rolling(window=std_th).std().dropna()*sqrt(244)
 return sigma

def get_mu(sigma,r):
 mu = (r-pow(sigma,2)/2)/pow(sigma,2)
 return mu

def get_lambda(mu,r,sigma):
 lam = sqrt(mu*mu+2*r/pow(sigma,2))
 return lam

def x_y(sigma,T,mu,H,lam,q=1):
 x1 = log(1/q)/(sigma*sqrt(T))+(1+mu)*sigma*sqrt(T)
 x2 = log(1/(q*H))/(sigma*sqrt(T))+(1+mu)*sigma*sqrt(T)
 y1 = log(H*H/q)/(sigma*sqrt(T))+(1+mu)*sigma*sqrt(T)
 y2 = log(q*H)/(sigma*sqrt(T))+(1+mu)*sigma*sqrt(T)
 z = log(q*H)/(sigma*sqrt(T))+lam*sigma*sqrt(T)
 return x1,x2,y1,y2,z

def get_standardBarrier(eta,phi,mu,sigma,r,T,H,lam,x1,x2,y1,y2,z,q=1):
 f1 = phi*1*stats.norm.cdf(phi*x1,0.0,1.0)-phi*q*exp(-r*T)*stats.norm.cdf(phi*x1-phi*sigma*sqrt(T),0.0,1.0)
 f2 = phi*1*stats.norm.cdf(phi*x2,0.0,1.0)-phi*q*exp(-r*T)*stats.norm.cdf(phi*x2-phi*sigma*sqrt(T),0.0,1.0)
 f3 = phi*1*pow(H*q,2*(mu+1))*stats.norm.cdf(eta*y1,0.0,1.0)-phi*q*exp(-r*T)*pow(H*q,2*mu)*stats.norm.cdf(eta*y1-eta*sigma*sqrt(T),0.0,1.0)
 f4 = phi*1*pow(H*q,2*(mu+1))*stats.norm.cdf(eta*y2,0.0,1.0)-phi*q*exp(-r*T)*pow(H*q,2*mu)*stats.norm.cdf(eta*y2-eta*sigma*sqrt(T),0.0,1.0)
 f5 = (H-1)*exp(-r*T)*(stats.norm.cdf(eta*x2-eta*sigma*sqrt(T),0.0,1.0)-pow(H*q,2*mu)*stats.norm.cdf(eta*y2-eta*sigma*sqrt(T),0.0,1.0))
 f6 = (H-1)*(pow(H*q,(mu+lam))*stats.norm.cdf(eta*z,0.0,1.0)+pow(H*q,(mu-lam))*stats.norm.cdf(eta*z-2*eta*lam*sigma*sqrt(T),0.0,1.0))
 return f1,f2,f3,f4,f5,f6

def main(param,t,r=0.065):
 typeflag = ['cdi','cdo','cui','cuo','pdi','pdo','pui','puo']
 r = log(1+r)
 T = t/365
 codes = get_codes()
 H = 1.2
 for i in range(len(codes)):
 sdbs = []
 for j in typeflag:
 code = codes.iloc[i]
 datas = get_datas(code)
 close = datas[4]
 sigma = get_sigma(close,40)[-1]
 mu = get_mu(sigma,r)
 lam = get_lambda(mu,r,sigma)
 x1,x2,y1,y2,z = x_y(sigma,T,mu,H,lam)
 eta = param[j]['eta']
 phi = param[j]['phi']
 f1,f2,f3,f4,f5,f6 = get_standardBarrier(eta,phi,mu,sigma,r,T,H,lam,x1,x2,y1,y2,z)
 if j=='cdi':
 sdb = f1-f2+f4+f5
 if j=='cui':
 sdb = f2-f3+f4+f5
 if j=='pdi':
 sdb = f1+f5
 if j=='pui':
 sdb = f3+f5
 if j=='cdo':
 sdb = f2+f6-f4
 if j=='cuo':
 sdb = f1-f2+f3-f4+f6
 if j=='pdo':
 sdb = f6
 if j=='puo':
 sdb = f1-f3+f6
 sdbs.append(sdb)
 print(T,r,sigma,H,sdbs)
if __name__ == '__main__':
 param = {'cdi':{'eta':1,'phi':1},'cdo':{'eta':1,'phi':1},'cui':{'eta':-1,'phi':1},'cuo':{'eta':-1,'phi':1},
 'pdi':{'eta':1,'phi':-1},'pdo':{'eta':1,'phi':-1},'pui':{'eta':-1,'phi':-1},'puo':{'eta':-1,'phi':-1}}
 t = 30
 main(param,t)