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

Chapter 1. Financial Markets, Prices and Risk

Matlab 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
% 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&P 500 data in Julia
using CSV
using DataFrames;
price = CSV.read("index.csv",DataFrame)
y = diff(log.(price[:,1]))
using Plots;
plot(y, title = "S&P500 returns", legend = false)
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 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))
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 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)
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 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
% 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 Julia
price = CSV.read("stocks.csv", DataFrame)
y1 = diff(log.(price[:,1]))
y2 = diff(log.(price[:,2]))
y3 = diff(log.(price[:,3]))
y = hcat(y1,y2,y3)
println(cor(y)) # correlation matrix
Financial Risk Forecasting
Market risk forecasting with R, Julia, Python and Matlab. Code, lecture slides, implementation notes, seminar assignments and questions.
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