There are two type of Pricing Model: Stochastic for Growth, Factor for Mean Reversion. In both case mu for $ return or % return or factors can be observed and used in Simulation
% google get_hist_stock_data.m
[hist_date, hist_high, hist_low, hist_open, hist_close, hist_vol] =get_hist_stock_data('AAPL','2010');
R_dollar=hist_close(2:end)-hist_close(1:end-1);
R_pct=R_dollar./hist_close(1:end-1);
% $ return Random Walk
dT=1; %daily
mu=mean(R_dollar);
sigma=std(R_dollar);
St=zeros(100,1);
St(1)=560;
for i=1:1:100
St(i+1)=St(i)+mu+sigma*sqrt(dT)*normrnd(0,1);
end
f1=figure(1);
set(f1,'name','$ return Random Walk');
plot(0:100,St);
% % return Ramdom Walk
dT=1; %daily
mu=mean(R_pct);
sigma=std(R_pct);
St=zeros(100,1);
St(1)=560;
for i=1:1:100
St(i+1)=St(i)*exp((mu-sigma^2/2)*dT+sigma*sqrt(dT)*normrnd(0,1));
end
f2=figure(2);
set(f2,'name','% return Random Walk');
plot(0:100,St);
% % return Mean Reversion Factor Model
dT=1; %daily
mu=mean(R_dollar);
sigma=std(R_dollar);
St=zeros(100,1);
St(1)=560;
p=polyfit(hist_close(2:end),R_pct,1)
% google get_hist_stock_data.m
[hist_date, hist_high, hist_low, hist_open, hist_close, hist_vol] =get_hist_stock_data('USO','2010');
R_dollar=hist_close(2:end)-hist_close(1:end-1);
R_pct=R_dollar./hist_close(1:end-1);
days=100
% $ return Mean Reversion Factor Model
dT=1; %daily
mu=mean(hist_close);
sigma=std(hist_close);
St=zeros(days,1);
St(1)=hist_close(end);
b=regress(R_dollar,hist_close(2:end));
b
k=-b;
for i=1:1:days
St(i+1)=St(i)+k*(mu-St(i))+sigma*normrnd(0,1);
end
f1=figure(1);
set(f1,'name','$ return Mean Reversion Factor Model');
plot(0:days,St);
% % return Mean Reversion Factor Model---see MR Factor Model
