Python and Julia Chapter 1. Financial Markets, Prices and Risk

# Chapter 1. Financial Markets, Prices and Risk

### Python and Julia

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
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 1.1/1.2
using CSV
using DataFrames;
y = diff(log.(price[:,1]))
using Plots;
plot(y, title = "S&P500 returns", legend = false)


##### 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))

##### Sample statistics in Julia
using Statistics, StatsBase;
println("Standard deviation: ", std(y), "\n")
println("Minimum value: ", minimum(y), "\n")
println("Maximum value: ", maximum(y), "\n")
println("Skewness: ", skewness(y), "\n")
println("Kurtosis: ", kurtosis(y), "\n")
println("Autocorrelation of returns:", "\n", autocor(y, 1:20), "\n")
println("Autocorrelation of returns squared:", "\n", autocor(y.^2, 1:20), "\n")
using HypothesisTests;
println(JarqueBeraTest(y))
println(LjungBoxTest(y,20))
println(LjungBoxTest(y.^2, 20))


##### 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))

##### ACF plots and the Ljung-Box test in Julia
q1 = autocor(y, 1:20)
q2 = autocor(y.^2, 1:20)
plot(bar(q1, title = "ACF of returns"),
bar(q2, title = "ACF of returns squared"), legend = false)


##### 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()

##### QQ plots in Julia
using StatsPlots, Distributions;
plot(qqplot(Normal,float(y),qqline=:quantile, title = "QQPlot vs Normal"),
qqplot(TDist(5),float(y),qqline=:quantile, title = "QQPlot vs Student-t(5)"),
qqplot(TDist(4),float(y),qqline=:quantile, title = "QQPlot vs Student-t(4)"),
qqplot(TDist(3),float(y),qqline=:quantile, title = "QQPlot vs Student-t(3)"))


##### Listing 1.9/1.10
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

##### Listing 1.9/1.10
price = CSV.read("stocks.csv", DataFrame)