Python for Finance

The relationship between input values and
option values
When the volatility of an underlying stock increases, both its call and put values
increase. The logic is that when a stock becomes more volatile, we have a better
chance to observe extreme values, that is, we have a better chance to exercise our
option. The following Python program shows this relationship:
Chapter 10
import numpy as np
import p4f as pf
import matplotlib.pyplot as plt
s0=30
T0=0.5
sigma0=0.2
r0=0.05
x0=30
sigma=np.arange(0.05,0.8,0.05)
T=np.arange(0.5,2.0,0.5)
call_0=pf.bs_call(s0,x0,T0,r0,sigma0)
call_sigma=pf.bs_call(s0,x0,T0,r0,sigma)
call_T=pf.bs_call(s0,x0,T,r0,sigma0)
plt.title("Relationship between sigma and call, T and call")
plt.plot(sigma,call_sigma,'b')
plt.plot(T,call_T,'r')
plt.annotate('x=Sigma, y=call price', xy=(0.6,5), xytext=(1,6), arrowp
rops=dict(facecolor='blue',shrink=0.01),)
plt.annotate('x=T(maturity), y=call price', xy=(1,3), xytext=(0.8,1),
arrowprops=dict(facecolor='red',shrink=0.01),)
plt.ylabel("Call premium")
plt.xlabel("Sigma (volatility) or T(maturity) ")
plt.show()
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