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Python for Finance. - Second Edition

You're reading from  Python for Finance. - Second Edition

Product type Book
Published in Jun 2017
Publisher
ISBN-13 9781787125698
Pages 586 pages
Edition 2nd Edition
Languages

Table of Contents (23) Chapters

Python for Finance Second Edition
Credits
About the Author
About the Reviewers
www.PacktPub.com
Customer Feedback
Preface
1. Python Basics 2. Introduction to Python Modules 3. Time Value of Money 4. Sources of Data 5. Bond and Stock Valuation 6. Capital Asset Pricing Model 7. Multifactor Models and Performance Measures 8. Time-Series Analysis 9. Portfolio Theory 10. Options and Futures 11. Value at Risk 12. Monte Carlo Simulation 13. Credit Risk Analysis 14. Exotic Options 15. Volatility, Implied Volatility, ARCH, and GARCH Index

Replicating a Black-Scholes-Merton call using simulation


After knowing the terminal prices, we can estimate the payoff for a call if the exercise price is given. The mean of those discounted payoffs using the risk-free rate as our discount rate will be our call price. The following code helps us estimate the call price:

import scipy as sp 
from scipy import zeros, sqrt, shape 
#
S0 = 40.              # stock price at time zero 
X= 40.                # exercise price 
T =0.5                # years 
r =0.05               # risk-free rate 
sigma = 0.2           # annualized volatility 
n_steps=100          # number of steps 
#
sp.random.seed(12345) # fix those random numbers 
n_simulation = 5000   # number of simulation 
dt =T/n_steps 
call = sp.zeros([n_simulation], dtype=float) 
x = range(0, int(n_steps), 1) 
for j in range(0, n_simulation): 
    sT=S0 
    for i in x[:-1]: 
        e=sp.random.normal() 
        sT*=sp.exp((r-0.5*sigma*sigma)*dt+sigma*e*sqrt(dt)) 
        call[j]=max(sT-X...
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