# Chapter 1. Financial Markets, Prices and Risk (in MATLAB/Python)

Copyright 2011 - 2022 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: https://www.gnu.org/licenses/.

##### Listing 1.1/1.2: Download S&P 500 data in MATLAB Last updated July 2020

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 Last updated July 2020

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 Last updated July 2020

mean(y)
std(y)
min(y)
max(y)
skewness(y)
kurtosis(y)
[h,pValue,stat]=jbtest(y);
%% NOTE: in MATLAB some functions require name-value pairs
%% e.g. [h,pValue,stat]=jbtest(y);

##### Listing 1.3/1.4: Sample statistics in Python Last updated July 2020

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 Last updated July 2020

%% subplots here are just for ease of visualization
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 Last updated July 2020

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 Last updated 2011

%% subplots here are just for ease of visualization
subplot(1,2,1)
qqplot(y)
subplot(1,2,2)
qqplot(y, fitdist(y,'tLocationScale'))

##### Listing 1.7/1.8: QQ plots in Python Last updated June 2018

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()