几何布朗运动模拟 MATLAB实现

time = data.date;%抽取年份
close = data.close; %抽取收盘价
pos = time.Year == 2019;%选择2019年打标签
close_2019 = close(pos);%选择2019年收盘价[ret,vol] = RetVolCaculation(data);
simup = MCSimulation(ret,vol,time,close);
resultplot(close_2019,simup);

function [ret,vol] = RetVolCaculation(data)
ret = zeros(14,1);
vol = zeros(14,1);
time_2005 = table2array(data(timerange...('2005-01-04','2005-12-30'),'close'));
time_2006 = table2array(data(timerange...('2006-01-04','2006-12-29'),'close'));
time_2007 = table2array(data(timerange...('2007-01-04','2007-12-28'),'close'));
time_2008 = table2array(data(timerange...('2008-01-04','2008-12-29'),'close'));
time_2009 = table2array(data(timerange...('2009-01-05','2009-12-11'),'close'));
time_2010 = table2array(data(timerange...('2010-01-04','2010-12-30'),'close'));
time_2011 = table2array(data(timerange...('2011-01-04','2011-12-30'),'close'));
time_2012 = table2array(data(timerange...('2012-01-04','2012-12-28'),'close'));
time_2013 = table2array(data(timerange...('2013-01-04','2013-12-30'),'close'));
time_2014 = table2array(data(timerange...('2014-01-02','2014-12-30'),'close'));
time_2015 = table2array(data(timerange...('2015-01-05','2015-12-30'),'close'));
time_2016 = table2array(data(timerange...('2016-01-05','2016-12-29'),'close'));
time_2017 = table2array(data(timerange...('2017-01-03','2017-12-29'),'close'));
time_2018 = table2array(data(timerange...('2018-01-02','2018-12-28'),'close'));ret(1) = log(table2array(data({'2005-01-04'},'close')))...- log(table2array(data({'2005-12-30'},'close')));
ret(2) = log(table2array(data({'2006-01-04'},'close')))...- log(table2array(data({'2006-12-29'},'close')));
ret(3) = log(table2array(data({'2007-01-04'},'close')))...- log(table2array(data({'2007-12-28'},'close')));
ret(4) = log(table2array(data({'2008-01-04'},'close')))...- log(table2array(data({'2008-12-29'},'close')));
ret(5) =log(table2array(data({'2009-01-05'},'close')))...- log(table2array(data({'2009-12-11'},'close')));
ret(6) = log(table2array(data({'2010-01-04'},'close')))...- log(table2array(data({'2010-12-30'},'close')));
ret(7) = log(table2array(data({'2011-01-04'},'close')))...- log(table2array(data({'2011-12-30'},'close')));
ret(8) = log(table2array(data({'2012-01-04'},'close')))...- log(table2array(data({'2012-12-28'},'close')));
ret(9) =  log(table2array(data({'2013-01-04'},'close')))...- log(table2array(data({'2013-12-30'},'close')));
ret(10) =  log(table2array(data({'2014-01-02'},'close')))...- log(table2array(data({'2014-12-30'},'close')));
ret(11) =  log(table2array(data({'2015-01-05'},'close')))...- log(table2array(data({'2015-12-30'},'close')));
ret(12) =  log(table2array(data({'2016-01-05'},'close')))...- log(table2array(data({'2016-12-29'},'close')));
ret(13) =  log(table2array(data({'2017-01-03'},'close')))...- log(table2array(data({'2017-12-29'},'close')));
ret(14) =  log(table2array(data({'2018-01-02'},'close')))...- log(table2array(data({'2018-12-28'},'close')));m = length(time_2005);
vol(1) = 0;
for i = 1:m-1vol(1) = vol(1) + (log(time_2005(i+1)) - log(time_2005(i)))^2;
end
vol(1) = sqrt(vol(1));m = length(time_2006);
vol(2) = 0;
for i = 1:m-1vol(2) = vol(2) + (log(time_2006(i+1)) - log(time_2006(i)))^2;
end
vol(2) = sqrt(vol(2));m = length(time_2007);
vol(3) = 0;
for i = 1:m-1vol(3) = vol(3) + (log(time_2007(i+1)) - log(time_2007(i)))^2;
end
vol(3) = sqrt(vol(3));m = length(time_2008);
vol(4) = 0;
for i = 1:m-1vol(4) = vol(4)+(log(time_2008(i+1)) - log(time_2008(i)))^2;
end
vol(4) = sqrt(vol(4));m = length(time_2009);
vol(5) = 0;
for i = 1:m-1vol(5) = vol(5) + (log(time_2009(i+1)) - log(time_2009(i)))^2;
end
vol(5) = sqrt(vol(5));m = length(time_2010);
vol(6) = 0;
for i = 1:m-1vol(6) = vol(6)+(log(time_2010(i+1)) - log(time_2010(i)))^2;
end
vol(6) = sqrt(vol(6));m = length(time_2011);
vol(7) = 0;
for i = 1:m-1vol(7) =vol(7)+ (log(time_2011(i+1)) - log(time_2011(i)))^2;
end
vol(7) = sqrt(vol(7));m = length(time_2012);
vol(8) = 0;
for i = 1:m-1vol(8) = vol(8) + (log(time_2012(i+1)) - log(time_2012(i)))^2;
end
vol(8) = sqrt(vol(8));m = length(time_2013);
vol(9) = 0;
for i = 1:m-1vol(9) = vol(9) +  (log(time_2013(i+1)) - log(time_2013(i)))^2;
end
vol(9) = sqrt(vol(9));m = length(time_2014);
vol(10) = 0;
for i = 1:m-1vol(10) = vol(10) + (log(time_2014(i+1)) - log(time_2014(i)))^2;
end
vol(10) = sqrt(vol(10));m = length(time_2015);
vol(11) = 0;
for i = 1:m-1vol(11) = vol(11) +(log(time_2015(i+1)) - log(time_2015(i)))^2;
end
vol(11) = sqrt(vol(11));m = length(time_2016);
vol(12) = 0;
for i = 1:m-1vol(12) = vol(12)+(log(time_2016(i+1)) - log(time_2016(i)))^2;
end
vol(12) = sqrt(vol(12));m = length(time_2017);
vol(13) = 0;
for i = 1:m-1vol(13) = vol(13) +(log(time_2017(i+1)) - log(time_2017(i)))^2;
end
vol(13) = sqrt(vol(13));m = length(time_2018);
vol(14) = 0;
for i = 1:m-1vol(14) = vol(14) + (log(time_2018(i+1)) - log(time_2018(i)))^2;
end
vol(14) = sqrt(vol(14));fprintf('2005, Yearly Return: %f, Yearly Volatility: %f \n',ret(1),vol(1));
fprintf('2006, Yearly Return: %f, Yearly Volatility: %f \n',ret(2),vol(2));
fprintf('2007, Yearly Return: %f, Yearly Volatility: %f \n',ret(3),vol(3));
fprintf('2008, Yearly Return: %f, Yearly Volatility: %f \n',ret(4),vol(4));
fprintf('2009, Yearly Return: %f, Yearly Volatility: %f \n',ret(5),vol(5));
fprintf('2010, Yearly Return: %f, Yearly Volatility: %f \n',ret(6),vol(6));
fprintf('2011, Yearly Return: %f, Yearly Volatility: %f \n',ret(7),vol(7));
fprintf('2012, Yearly Return: %f, Yearly Volatility: %f \n',ret(8),vol(8));
fprintf('2013, Yearly Return: %f, Yearly Volatility: %f \n',ret(9),vol(9));
fprintf('2014, Yearly Return: %f, Yearly Volatility: %f \n',ret(10),vol(10));
fprintf('2015, Yearly Return: %f, Yearly Volatility: %f \n',ret(11),vol(11));
fprintf('2016, Yearly Return: %f, Yearly Volatility: %f \n',ret(12),vol(12));
fprintf('2017, Yearly Return: %f, Yearly Volatility: %f \n',ret(13),vol(13));
fprintf('2018, Yearly Return: %f, Yearly Volatility: %f \n',ret(14),vol(14));

function [simup] = MCSimulation(ret,vol,time,close)mu = ret(10);
theta = vol(10);
pos = time.Year == 2019;
n = length(pos(pos == 1));
close_2019 = close(pos);simup = zeros(length(close_2019),5);
simup(1,:) = close_2019(1);for iter = 1:5day = 1;for i = 0:0.5/118:1day = day+1;eps = normrnd(0,1);simup(day,iter) = exp(log(simup((day-1),iter))+(mu - theta^2/2)*(0.5/118)...+ theta * eps * sqrt(0.5/118));end
end

function resultplot(close_2019,simup)m = length(close_2019);
plot(close_2019,'black');
hold on
plot(simup(1:m,:));

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