Intermediate variables value at the optimisation achievement

Question

Sid S 2011-7-16

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https://ww2.mathworks.cn/matlabcentral/answers/11740-intermediate-variables-value-at-the-optimisation-achievement

回答： Daniel Frisch 2020-10-7

Hello,

I'am trying unsuccessfuly since several weeks to get the value of intermediate variables at the achievement of fmincon optimisation. I want to have the value of "call" and "e", so please what may I add to the code ??? please I very need help !

My code :

function monOptimisation
%Contraintes
A = [ 1 1 1 1 ; -1 0 0 0 ; 0 -1 0 0 ; 0 0 0 0 ; 0 0 0 -1];
b = [1 ; 0 ; 0 ; 0 ; 0];
x0=[0;0;0;0;0];
load data
prix=data;
load data2 
strike_vec = data2;
load data3 
sp = data3;
sig0 = 0.0005;
r = 0; 
nbr_sim = 300;
options=optimset('algorithm','interior-point','display','iter'); 
par= fmincon (@(x)erreursfun(x,prix,strike_vec,sp,sig0,r,nbr_sim),x0,A,b,[],[],[],[],[],options)
function f = erreursfun (par,prix,strike_vec,sp,sig0,r,nbr_sim)
nbr_strike = 36; %size(strike_vec,1)
mat = 257; %size(prix,1)
epsil = randn (nbr_sim,mat);
% Calcul des calls via MC
som_var = zeros(nbr_sim,mat);
som_et = zeros(nbr_sim,mat);
sigma = zeros(nbr_sim,mat);
st = zeros(nbr_sim,mat);
payoff = zeros(nbr_sim,mat);
som_payoff= zeros(mat,nbr_strike);
call= zeros(mat,nbr_strike);
for i = 1: nbr_strike
      strike = strike_vec (i);
      for j =1 : nbr_sim
          sigma (j,1)=(par(1) + par(2) *( epsil(j,1)-par(3)^2)*sig0^2+par(4)*sig0^2)^0.5;
          for k = 2 : mat
              sigma (j,k)=(par(1) + par(2) * (epsil(j,k)-par(3)^2)*sigma(j,k-1)^2+par(4)*sigma(j,k- 1)^2)^0.5;
          end
          som_var(j,mat)= sigma (j,mat); %%%
          som_et(j,mat)=sigma (j,mat)^0.5*epsil(j,mat); %%%
          for k = mat -1 : 1:-1
              som_var(j,k)= som_var(j,k+1)+sigma (j,k+1); %%%
              som_et(j,k)=som_et(j,k+1)+sigma (j,k+1)^0.5*epsil(j,k+1); %%%
          end
          for k = 1 : mat
              st(j,k)= sp(k)*(exp(r*(mat-k))-(0.5*som_var(j,k))+som_et(j,k)*epsil(j,k));  
              payoff(j,k)= max(st(j,k)-strike,0);
              som_payoff(k,i)=som_payoff(k,i)+payoff(j,k); %%%
          end
      end
      for k = 1  : mat
          call(k,i)=exp(r*(mat-k))*((som_payoff(k,i)/nbr_sim));
      end
  end
% Calcul des erreurs
e=zeros(mat,nbr_strike);
ee=zeros(mat);
eee=0;
for i = 1 : mat
    for j = 1 : nbr_strike
          e(i,j)=(prix(i,j)- call(i,j))^2;
          ee(i)=ee(i)+e(i,j);
      end
      eee=eee+ee(i);
  end
f= eee;

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Answer 1

Andrew Newell 2011-7-17

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The newsgroup thread Intermediate results of Optimization has a nice solution to this problem.

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Andrew Newell 2011-7-17

You reply below that you don't have the resources to calculate the parameters. But if you can't calculate them, how can you expect to save them? Anyway, my impression is that you do calculate them during the optimization.

To implement growdata, just create the function - in its own file or below erreursfun - and call it from erreursfun.

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Answer 2

Sid S 2011-7-17

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Thanks for your answer, but I don't see how to use growdata where puting it, adding to this growdata takes additional CPU ressources, I need to estimate 4 parameters with 5000 simulations of 10000 observations and my CPU is not powerful.