Creating a table from a variable inside a for loop - matlab

Question

I am writing a for loop to calculate the value of four different variables. The first variable is M. M increases from 10^2 to 10^5,
M = [10^2,10^3,10^4,10^5];
The other three variables needed for the table are shown in the code below.
confmc
confcv
confmcSize/confcvSize
I first create a for loop to iterate through the four different values of M. I then create the table outside of the for loop.
How could I adjust the implementation so that the table displays all four values of M?
randn('state',100)
%%%%%% Problem and method parameters %%%%%%%%%
S = 5; E = 6; sigma = 0.3; r = 0.05; T = 1;
Dt = 1e-2; N = T/Dt; M = [10^2,10^3,10^4,10^5];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
for k=1:numel(M)
%%%%%%%%% Geom Asian exact mean %%%%%%%%%%%%
sigsqT= sigma^2*T*(N+1)*(2*N+1)/(6*N*N);
muT = 0.5*sigsqT + (r - 0.5*sigma^2)*T*(N+1)/(2*N);
d1 = (log(S/E) + (muT + 0.5*sigsqT))/(sqrt(sigsqT));
d2 = d1 - sqrt(sigsqT);
N1 = 0.5*(1+erf(d1/sqrt(2)));
N2 = 0.5*(1+erf(d2/sqrt(2)));
geo = exp(-r*T)*( S*exp(muT)*N1 - E*N2 );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Spath = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*randn(M(k),N)),2);
% Standard Monte Carlo
arithave = mean(Spath,2);
Parith = exp(-r*T)*max(arithave-E,0); % payoffs
Pmean = mean(Parith);
Pstd = std(Parith);
confmc = [Pmean-1.96*Pstd/sqrt(M(k)), Pmean+1.96*Pstd/sqrt(M(k))];
confmcSize = [(Pmean+1.96*Pstd/sqrt(M(k)))-(Pmean-1.96*Pstd/sqrt(M(k)))];
% Control Variate
geoave = exp((1/N)*sum(log(Spath),2));
Pgeo = exp(-r*T)*max(geoave-E,0); % geo payoffs
Z = Parith + geo - Pgeo; % control variate version
Zmean = mean(Z);
Zstd = std(Z);
confcv = [Zmean-1.96*Zstd/sqrt(M(k)), Zmean+1.96*Zstd/sqrt(M(k))];
confcvSize = [(Zmean+1.96*Zstd/sqrt(M(k)))-(Zmean-1.96*Zstd/sqrt(M(k)))];
end
T = table(M,confmc,confcv,confmcSize/confcvSize)
The current code returns
T =
1×4 table
M confmc confcv Var4
_____ ____________________ ____________________ ______
1e+05 0.096756 0.1007 0.097306 0.097789 8.1622
How could I change my implementation so that all four values of M are computed?

Answer 1

I just modified few things.Take a look at the following code.
randn('state',100)
%%%%%% Problem and method parameters %%%%%%%%%
S = 5; E = 6; sigma = 0.3; r = 0.05; T = 1;
Dt = 1e-2; N = T/Dt; M = [10^2,10^3,10^4,10^5];
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
confmc = zeros(numel(M), 2);
confcv = zeros(numel(M), 2);
confmcSize = zeros(numel(M), 1);
confcvSize = zeros(numel(M), 1);
for k=1:numel(M)
%%%%%%%%% Geom Asian exact mean %%%%%%%%%%%%
sigsqT= sigma^2*T*(N+1)*(2*N+1)/(6*N*N);
muT = 0.5*sigsqT + (r - 0.5*sigma^2)*T*(N+1)/(2*N);
d1 = (log(S/E) + (muT + 0.5*sigsqT))/(sqrt(sigsqT));
d2 = d1 - sqrt(sigsqT);
N1 = 0.5*(1+erf(d1/sqrt(2)));
N2 = 0.5*(1+erf(d2/sqrt(2)));
geo = exp(-r*T)*( S*exp(muT)*N1 - E*N2 );
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Spath = S*cumprod(exp((r-0.5*sigma^2)*Dt+sigma*sqrt(Dt)*randn(M(k),N)),2);
% Standard Monte Carlo
arithave = mean(Spath,2);
Parith = exp(-r*T)*max(arithave-E,0); % payoffs
Pmean = mean(Parith);
Pstd = std(Parith);
confmc(k,:) = [Pmean-1.96*Pstd/sqrt(M(k)), Pmean+1.96*Pstd/sqrt(M(k))];
confmcSize(k,1) = [(Pmean+1.96*Pstd/sqrt(M(k)))-(Pmean-1.96*Pstd/sqrt(M(k)))];
% Control Variate
geoave = exp((1/N)*sum(log(Spath),2));
Pgeo = exp(-r*T)*max(geoave-E,0); % geo payoffs
Z = Parith + geo - Pgeo; % control variate version
Zmean = mean(Z);
Zstd = std(Z);
confcv(k,:) = [Zmean-1.96*Zstd/sqrt(M(k)), Zmean+1.96*Zstd/sqrt(M(k))];
confcvSize(k,1) = [(Zmean+1.96*Zstd/sqrt(M(k)))-(Zmean-1.96*Zstd/sqrt(M(k)))];
end
T = table(M',confmc,confcv,confmcSize./confcvSize)
In short, I just used a matrix instead of a vector or scalar as the members of the table. In your code, the variables (confmc, confcv, confmcSize, confcvSize) were getting overwritten.