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)

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