"""
Name : c14_25_up_and_out_call.py
Book : Python for Finance (2nd ed.)
Publisher: Packt Publishing Ltd.
Author : Yuxing Yan
Date : 6/6/2017
email : yany@canisius.edu
paulyxy@hotmail.com
"""
import scipy as sp
from scipy import log,exp,sqrt,stats
#
def bsCall(S,X,T,r,sigma):
d1=(log(S/X)+(r+sigma*sigma/2.)*T)/(sigma*sqrt(T))
d2 = d1-sigma*sqrt(T)
return S*stats.norm.cdf(d1)-X*exp(-r*T)*stats.norm.cdf(d2)
#
def up_and_out_call(s0,x,T,r,sigma,n_simulation,barrier):
n_steps=100.
dt=T/n_steps
total=0
for j in sp.arange(0, n_simulation):
sT=s0
out=False
for i in range(0,int(n_steps)):
e=sp.random.normal()
sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sp.sqrt(dt))
if sT>barrier:
out=True
if out==False:
total+=bsCall(s0,x,T,r,sigma)
return total/n_simulation
#
s0=30. # today stock price
x=30. # exercise price
barrier=32 # barrier level
T=6./12. # maturity in years
r=0.05 # risk-free rate
sigma=0.2 # volatility (annualized)
n_simulation=100 # number of simulations
sp.random.seed(12) # fix a seed
#
result=up_and_out_call(s0,x,T,r,sigma,n_simulation,barrier)
print('up-and-out-call = ', round(result,3))
