python障礙式期權(quán)定價(jià)公式

#coding:utf-8
'''
障礙期權(quán)
q=x/s
H = h/x H 障礙價(jià)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'):     #從代碼表格從獲取代碼
 codes = pd.read_excel(path)
 codes = codes.iloc[:,1]    
 return codes

def get_datas(code,N=1,path='D:\\data\\'):        #獲取數(shù)據(jù)N=1當(dāng)天數(shù)據(jù)
 datas = pd.read_csv(path+eval(code)+'.csv',encoding='gbk',skiprows=2,header=None,skipfooter=N,engine='python').dropna() #讀取CSV文件 名稱為股票代碼 解gbk skiprows跳過(guò)前兩行文字 第一行不做為表頭
 date_c = datas.iloc[:,[0,4,5]]     #只用第0 列代碼數(shù)據(jù)和第4列收盤(pán)價(jià)數(shù)據(jù)
 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)