屏障選項程式碼說明

我想知道是否有人可以解釋障礙選項定價背後的程式碼（特別是 def(up_and_out_call) 部分。我發現循環概念中的循環非常混亂。謝謝。

import numpy as np
from scipy import stats
from math import log,exp,sqrt

s0=30. # today stock price
K=30 # exercise price
barrier=32 # barrier level
T=6./12. # maturity in years
r=0.05 # risk-free rate
sig=0.2 # volatility (annualized)
n_sim=100 # number of simulations
np.random.seed(12) # fix a seed

#
def bsCall(s0,K,T,r,sig):
d1=(log(s0/K)+(r+sig*sig/2.)*T)/(sig*sqrt(T))
d2= d1-sig*sqrt(T)
return s0*stats.norm.cdf(d1)-K*exp(-r*T)*stats.norm.cdf(d2)
#
def up_and_out_call(s0,K,T,r,sig,n_sim,barrier):
   n_steps=100 # for each simulation there are 100 steps
   dt=T/n_steps #time increment 
   total=0 
   for j in np.arange(0, n_sim):
       x=s0 #sT=s0
       out=False
       for i in range(0,int(n_steps)):
           n=np.random.normal()
           x*=exp((r-0.5*sig*sig)*dt+sig*n*sqrt(dt))
           if x>barrier: #for all paths greater than the barrier level, they expire worthless
               out=True
       if out==False:
           total+=bsCall(s0,K,T,r,sig)
   return total/n_sim 

#
result=up_and_out_call(s0,K,T,r,sig,n_sim,barrier)
print('up-and-out-call = ', round(result,5)) #prints 'up-and-out-call = result up to 5 decimal places.

引用自：https://quant.stackexchange.com/questions/69302