Chapter 1. Financial Markets, Prices and Risk
Matlab and Python
Copyright 2011 - 2023 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: www.gnu.org/licenses.
Listing 1.1/1.2
% Download S&P 500 data in MATLAB
price = csvread('index.csv', 1, 0);
y=diff(log(price)); % calculate returns
plot(y) % plot returns
title("S&P500 returns")
Listing 1.1/1.2
Download S&P500 data in Python
import numpy as np
import matplotlib.pyplot as plt
price = np.loadtxt('index.csv', delimiter = ',', skiprows = 1)
y = np.diff(np.log(price), n=1, axis=0)
plt.plot(y)
plt.title("S&P500 Returns")
plt.show()
plt.close()
Listing 1.3/1.4
% Sample statistics in MATLAB
mean(y)
std(y)
min(y)
max(y)
skewness(y)
kurtosis(y)
[h,pValue,stat]=jbtest(y);
Listing 1.3/1.4
Sample statistics in Python
from scipy import stats
print (np.mean(y))
print (np.std(y, ddof=1))
print (np.min(y))
print (np.max(y))
print (stats.skew(y))
print (stats.kurtosis(y, fisher = False))
print (stats.jarque_bera(y))
Listing 1.5/1.6
% ACF plots and the Ljung-Box test in MATLAB
subplot(1,2,1)
autocorr(y, 20)
subplot(1,2,2)
autocorr(y.^2, 20)
[h,pValue,stat]=lbqtest(y,'lags',20);
[h,pValue,stat]=lbqtest(y.^2,'lags',20);
Listing 1.5/1.6
ACF plots and the Ljung-Box test in Python
import statsmodels.api as sm
import matplotlib.pyplot as plt
from statsmodels.stats.diagnostic import acorr_ljungbox
q = sm.tsa.stattools.acf(y, nlags=20)
plt.bar(x = np.arange(1,len(q)), height = q[1:])
plt.title("Autocorrelation of returns")
plt.show()
plt.close()
q = sm.tsa.stattools.acf(np.square(y), nlags=20)
plt.bar(x = np.arange(1,len(q)), height = q[1:])
plt.title("Autocorrelation of returns squared")
plt.show()
plt.close()
print (acorr_ljungbox(y, lags=20))
print (acorr_ljungbox(np.square(y), lags=20))
Listing 1.7/1.8
% QQ plots in MATLAB
subplot(1,2,1)
qqplot(y)
subplot(1,2,2)
qqplot(y, fitdist(y,'tLocationScale'))
Listing 1.7/1.8
QQ plots in Python
from statsmodels.graphics.gofplots import qqplot
fig1 = qqplot(y, line='q', dist = stats.norm, fit = True)
plt.show()
plt.close()
fig2 = qqplot(y, line='q', dist = stats.t, distargs=(5,), fit = True)
plt.show()
plt.close()
Listing 1.9/1.10
% Download stock prices in MATLAB
price = csvread('stocks.csv', 1, 0);
y=diff(log(price));
corr(y) % correlation matrix
Listing 1.9/1.10
Download stock prices in Python
p = np.loadtxt('stocks.csv',delimiter=',',skiprows = 1)
y = np.diff(np.log(p), n=1, axis=0)
print(np.corrcoef(y, rowvar=False)) # correlation matrix
Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.© All rights reserved, Jon Danielsson,