python Barrier Option Pricing Formula
- 2021-07-22 10:24:25
- OfStack
The pricing script of python barrier option written in the early stage is for your reference. The specific contents are as follows
#coding:utf-8
'''
Barrier option
q=x/s
H = h/x H Barrier price
[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'): # Get code from code table
codes = pd.read_excel(path)
codes = codes.iloc[:,1]
return codes
def get_datas(code,N=1,path='D:\\data\\'): # Get data N=1 Data of the day
datas = pd.read_csv(path+eval(code)+'.csv',encoding='gbk',skiprows=2,header=None,skipfooter=N,engine='python').dropna() # Read CSV Documents The name is stock code Solution gbk skiprows Skip the first two lines of text No. 1 1 Rows are not used as headers
date_c = datas.iloc[:,[0,4,5]] # Only use the number 0 Column code data and column 4 Column closing price data
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)