#### Overview of this book

Python for Finance
Credits
Acknowledgments
www.PacktPub.com
Preface
Free Chapter
Introduction and Installation of Python
13 Lines of Python to Price a Call Option
Introduction to Modules
Statistical Analysis of Time Series
Index

## Barrier in-and-out parity

If we buy an up-and-out European call and an up-and-in European call, then the following parity should hold good:

The logic is very simple—if the stock price reaches the barrier, then the first call is worthless and the second call will be activated. If the stock price never touches the barrier, the first call will remain active, while the second one is never activated. Either way, one of them is active. The following Python program illustrates such scenarios:

```def up_call(s0,x,T,r,sigma,n_simulation,barrier):
import scipy as sp
import p4f
n_steps=100.
dt=T/n_steps
inTotal=0
outTotal=0
for j in range(0, n_simulation):
sT=s0
inStatus=False
outStatus=True
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:
outStatus=False
inStatus=True
#print 'sT=',sT
#print 'j='...```