Python for Finance

Chapter 14
x=40. # exercise price
T=6./12 # maturity date ii years
tao=1/12 # when to choose
r=0.05 # risk-free rate
sigma=0.2 # volatility
n=1000 # number of steps
#
price=binomialCallAmerican(s,x,T,r,sigma,n)
print("American call =", price)
('American call =', 2.7549263174936502)
The price of this American call is $2.75. The key for modifying the previous program
to satisfy only a few exercise prices is the following two lines:
v2=max(v[i][j]-x,0)
v[i][j]=max(v1,v2)
# early exercise
Here is the Python program for a Bermudan call option. The key different is the
variable called T2, which contains the dates when the Bermudan option could
be exercised:
def callBermudan(s,x,T,r,sigma,T2,n=100):
from math import exp,sqrt
import numpy as np
n2=len(T2)
deltaT = T /n
u = exp(sigma * sqrt(deltaT))
d = 1.0 / u
a = exp(r * deltaT)
p = (a - d) / (u - d)
v =[[0.0 for j in np.arange(i + 1)] for i in np.arange(n + 1)]
for j in np.arange(n+1):
v[n][j] = max(s * u**j * d**(n - j) - x, 0.0)
for i in np.arange(n-1, -1, -1):
for j in np.arange(i + 1):
v1=exp(-r*deltaT)*(p*v[i+1][j+1]+(1.0-p)*v[i+1][j])
for k in np.arange(n2):
if abs(j*deltaT-T2[k])<0.01:
v2=max(v[i][j]-x,0) # potential early exercise
else:
v2=0
v[i][j]=max(v1,v2)
return v[0][0]
#
s=40.
# stock price today
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