Thread Subject:

Problem using fmincon

Hi,
We are two students currently working on our masters thesis from Sweden.
As a part of our project we need to use minimize five variables regarding risk neutral probability density functions extracted from option prices.

Never having used MATLAB before we have encountered some difficulties and would greatly appreciate any help!

We are copying the code below!
x(1) x(2) x(3) x(4) and x(5) are the parameters to be minimized.
chat phat kc kp dtmc dtmp and F are variables we have imported into 1 column matrices from excel. c and p also needs to be calculated in MATLAB.

When using the optimtool we get an error saying that the length of the upper bound > the length of x and the optimization terminates.

The goal is to get the five values for x.

Here goes the code:

function [x0] = myfun1(x0)

    function f = myfun1(x0,c,chat,p,phat,F)
        f = ((sum(c-chat,0,14589)^2)+((sum(p-phat)^2))+((x0(5).*(exp(x0(1)+.5.*(x0(3).^2)))+(1-x0(5)).*(exp(x0(2)+.5.*x0(4).^2))-F)^2));
        
        function c = tcall (r, dtmc, q1, q2, q3, q4, kc)
            c=exp(-r.*dtmc).*(x0(5)).*(exp(x0(1)+.5.*(x0(3).^2).*(q1)-kc.*(q2)))+(1-x0(5)).*(exp(x0(2)+.5.*(x0(4).^2).*(q3)-kc.*(q4)));
            myfun1=@tcall;
            
        function p = tput (r, dtmp, q1, q2, q3, q4, kp)
            p=exp(-r.*dtmp).*(x0(5).*(exp(x0(1)+.5.*(x0(3).^2).*((-1)*q1)-kp.*((-1).*q2))))+(1-x0(5)).*(exp(x0(2)+.5.*(x0(4).^2).*((-1).*q3)-kp.*((-1).*q4)));
            myfun1=@tput;
            
            function q1 = qett (d1)
                q1=cdf('normal',d1,0,1);
                tput=@qett;
                tcall=@qett;
                
            function q2 = qtva (d2)
                q2=cdf('normal',d2,0,1);
                tput=@qtva;
                tcall=@qtva;
                
            function q3 = qtre (d3)
                q3=cdf('normal',d3,0,1);
                tput=@qtre;
                tcall=@qtre;
                
            function q4 = qfyra (d4)
                q4=cdf('normal',d4,0,1);
                tput=@qfyra;
                tcall=@qfyra;
               
                
                function d2 = dtva (d1, x0)
                    d2=d1-x0(3);
                    qett=@dtva;
                
         
                function d4 = dfyra (d3, x0)
                    d4=d3-x0(4);
                    qfyra=@dfyra;
                
                    
                    function d1 = dett (k, x0)
                        d1=(-log(k)+x0(1)+x0(3).^2)./x0(3);
                        dtva=@dett;
                    
                
                    function d3 = dtre (k, x0)
                        d3=(-log(k)+x0(2)+x0(4).^2)./x0(4);
                        dfyra=@dtre;
                    end
                    end
                end
                end
            end
            end
            end
            end
        end
        end
    end
end

Any help is much appreciated!

Thanks in advance!

"Per Wehl" wrote in message <jn5o8j$2q7$1@newscl01ah.mathworks.com>...
> Hi,
> We are two students currently working on our masters thesis from Sweden.
> As a part of our project we need to use minimize five variables regarding risk neutral probability density functions extracted from option prices.
>
> Never having used MATLAB before we have encountered some difficulties and would greatly appreciate any help!
>
> We are copying the code below!
> x(1) x(2) x(3) x(4) and x(5) are the parameters to be minimized.
> chat phat kc kp dtmc dtmp and F are variables we have imported into 1 column matrices from excel. c and p also needs to be calculated in MATLAB.
>
> When using the optimtool we get an error saying that the length of the upper bound > the length of x and the optimization terminates.
>
> The goal is to get the five values for x.
>
> Here goes the code:
>
> function [x0] = myfun1(x0)
>
> function f = myfun1(x0,c,chat,p,phat,F)
> f = ((sum(c-chat,0,14589)^2)+((sum(p-phat)^2))+((x0(5).*(exp(x0(1)+.5.*(x0(3).^2)))+(1-x0(5)).*(exp(x0(2)+.5.*x0(4).^2))-F)^2));
>
> function c = tcall (r, dtmc, q1, q2, q3, q4, kc)
> c=exp(-r.*dtmc).*(x0(5)).*(exp(x0(1)+.5.*(x0(3).^2).*(q1)-kc.*(q2)))+(1-x0(5)).*(exp(x0(2)+.5.*(x0(4).^2).*(q3)-kc.*(q4)));
> myfun1=@tcall;
>
> function p = tput (r, dtmp, q1, q2, q3, q4, kp)
> p=exp(-r.*dtmp).*(x0(5).*(exp(x0(1)+.5.*(x0(3).^2).*((-1)*q1)-kp.*((-1).*q2))))+(1-x0(5)).*(exp(x0(2)+.5.*(x0(4).^2).*((-1).*q3)-kp.*((-1).*q4)));
> myfun1=@tput;
>
> function q1 = qett (d1)
> q1=cdf('normal',d1,0,1);
> tput=@qett;
> tcall=@qett;
>
> function q2 = qtva (d2)
> q2=cdf('normal',d2,0,1);
> tput=@qtva;
> tcall=@qtva;
>
> function q3 = qtre (d3)
> q3=cdf('normal',d3,0,1);
> tput=@qtre;
> tcall=@qtre;
>
> function q4 = qfyra (d4)
> q4=cdf('normal',d4,0,1);
> tput=@qfyra;
> tcall=@qfyra;
>
>
> function d2 = dtva (d1, x0)
> d2=d1-x0(3);
> qett=@dtva;
>
>
> function d4 = dfyra (d3, x0)
> d4=d3-x0(4);
> qfyra=@dfyra;
>
>
> function d1 = dett (k, x0)
> d1=(-log(k)+x0(1)+x0(3).^2)./x0(3);
> dtva=@dett;
>
>
> function d3 = dtre (k, x0)
> d3=(-log(k)+x0(2)+x0(4).^2)./x0(4);
> dfyra=@dtre;
> end
> end
> end
> end
> end
> end
> end
> end
> end
> end
> end
> end
>
> Any help is much appreciated!
>


> Thanks in advance!

Hi,

as it is reported from matlab the lower bound array is smaller than x. On optitool gui-> go on files-> generate code and report here the code.

bye

Pietro

"pietro " <bracardi82@email.it> wrote in message
> Hi,
>
> as it is reported from matlab the lower bound array is smaller than x. On optitool gui-> go on files-> generate code and report here the code.
>
> bye
>
> Pietro

Hi! Thanks for your input!

Heres what we get when following these steps.


function [x,fval,exitflag,output,lambda,grad,hessian] = untitled(x0,lb,ub)
%% This is an auto generated MATLAB file from Optimization Tool.

%% Start with the default options
options = optimset;
%% Modify options setting
options = optimset(options,'Display', 'off');
options = optimset(options,'Algorithm', 'interior-point');
[x,fval,exitflag,output,lambda,grad,hessian] = ...
fmincon(@myfun1,x0,[],[],[],[],lb,ub,[],options);

Hope this helps!


/Per

"Per Wehl" <pew@gmail.com> wrote in message
news:jn5o8j$2q7$1@newscl01ah.mathworks.com...
> Hi,
> We are two students currently working on our masters thesis from Sweden.
> As a part of our project we need to use minimize five variables regarding
> risk neutral probability density functions extracted from option prices.
>
> Never having used MATLAB before we have encountered some difficulties and
> would greatly appreciate any help!
>
> We are copying the code below!
> x(1) x(2) x(3) x(4) and x(5) are the parameters to be minimized.

Okay, so all of the following inputs to FMINCON should be consistent with a
five-parameter problem:

* your objective function should accept a vector with 5 elements and return
a scalar
* your initial guess should be a vector with 5 elements
* A and Aeq should have 5 columns (or be empty, if you don't have that kind
of linear constraint.)
* lb and ub should be vectors with 5 elements (or empty, if you don't
need/want to specify bounds.)
* nonlcon should accept a vector with five elements and return two outputs
* any of the options you set in your options structure should be consistent
with a 5-element parameter vector

> chat phat kc kp dtmc dtmp and F are variables we have imported into 1
> column matrices from excel. c and p also needs to be calculated in MATLAB.
>
> When using the optimtool we get an error saying that the length of the
> upper bound > the length of x and the optimization terminates.

So your ub input is a vector with more than 5 elements.

> The goal is to get the five values for x.
>
> Here goes the code:
>
> function [x0] = myfun1(x0)
>
> function f = myfun1(x0,c,chat,p,phat,F)

I'm not sure what exactly you're doing here; that first function declaration
line shouldn't be there.

*snip*

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

Thanks for the reply and your advice!

We’ve now updated the code according to your descriptions, however we now get another error: “Error using runmyfun1 (line 3) Not enough input arguments.”

At line 3 it’s the following code; [x,fval] = fmincon(@myfun1,x0,A,b,[],[],lb,ub,options);

x0 is = [3,0.1, 3,0.25,0.5]

What could this error depend on?

Thanks in advance for your help!

Below follows the whole code as it is in our runmyfun1.m file:


function [x,fval] = runmyfun1(x0)
[x,fval] = fmincon(@myfun1,x0,A,b,[],[],lb,ub,options);

function f = myfun1(x,cdev,F,pdev)
     f = ((cdev)+(pdev))+((x(5).*(exp(x(1)+.5.*(x(3).^2)))+(1-x(5)).*(exp(x(2)+.5.*x(4).^2))-F)^2);
     for m=1;length(chat);
         cdev=(c(m)-chat(m)).^2;
         sum(cdev);
     for n=0,length(phat);
         pdev=(p(n)-phat(n)).^2;
         sum(pdev);
     end
     end
   
     function c = tcall (r, dtmc, q1, q2, q3, q4, kc)
         c=exp(-r.*dtmc).*(x(5)).*(exp(x(1)+.5.*(x(3).^2).*(q1)-kc.*(q2)))+(1-x(5)).*(exp(x(2)+.5.*(x(4).^2).*(q3)-kc.*(q4)));
         myfun1=@tcall;
  
       
     function p = tput (r, dtmp, q1, q2, q3, q4, kp)
         p=exp(-r.*dtmp).*(x(5).*(exp(x(1)+.5.*(x(3).^2).*((-1)*q1)-kp.*((-1).*q2))))+(1-x(5)).*(exp(x(2)+.5.*(x(4).^2).*((-1).*q3)-kp.*((-1).*q4)));
         myfun1=@tput;
       
         function q1 = qett (d1)
             q1=cdf('normal',d1,0,1);
             tput=@qett;
             tcall=@qett;
           
         function q2 = qtva (d2)
             q2=cdf('normal',d2,0,1);
             tput=@qtva;
             tcall=@qtva;
           
         function q3 = qtre (d3)
             q3=cdf('normal',d3,0,1);
             tput=@qtre;
             tcall=@qtre;
           
         function q4 = qfyra (d4)
             q4=cdf('normal',d4,0,1);
             tput=@qfyra;
             tcall=@qfyra;
          
           
             function d2 = dtva (d1, x)
                 d2=d1-x(3);
                 qett=@dtva;
           
    
             function d4 = dfyra (d3, x)
                 d4=d3-x(4);
                 qfyra=@dfyra;
           
               
                 function d1 = dett (k, x)
                     d1=(-log(k)+x(1)+x(3).^2)./x(3);
                     dtva=@dett;
               
           
                 function d3 = dtre (k, x)
                     d3=(-log(k)+x(2)+x(4).^2)./x(4);
                     dfyra=@dtre;
                 end
                 end
             end
             end
         end
         end
         end
         end
     end
     end
end
end

"Per Wehl" <pew@gmail.com> wrote in message
news:jn71kj$5e5$1@newscl01ah.mathworks.com...
> Thanks for the reply and your advice!
>
> Weve now updated the code according to your descriptions, however we now
> get another error: Error using runmyfun1 (line 3) Not enough input
> arguments.
>
> At line 3 its the following code; [x,fval] =
> fmincon(@myfun1,x0,A,b,[],[],lb,ub,options);
>
> x0 is = [3,0.1, 3,0.25,0.5]
>
> What could this error depend on?
>
> Thanks in advance for your help!
>
> Below follows the whole code as it is in our runmyfun1.m file:
>
>
> function [x,fval] = runmyfun1(x0)
> [x,fval] = fmincon(@myfun1,x0,A,b,[],[],lb,ub,options);

You haven't defined any of A, b, lb, ub, or options in the scope of the
runmyfun1 function. You will need to either create them inside runmyfun1 or
pass them into runmyfun1 as input arguments.

> function f = myfun1(x,cdev,F,pdev)

This is only ever being called with one input by FMINCON. I can see that you
tried to define the extra input variables here so that they exist in the
scope of this function and so all your nested functions can write to them;
that could make this program very difficult to debug. Since I'm getting the
sense that you're fairly new to MATLAB, I'd hold off on the nested functions
for now and use plain old subfunctions instead.

*snip*

--
Steve Lord
slord@mathworks.com
To contact Technical Support use the Contact Us link on
http://www.mathworks.com

Hi!

Thanks for your help! Indeed as you thought we are first time MATLAB users.
We've had some progress with our code and it now process the minimum x values for x1-x5 as intended using fmincon.

Another issue has however risen. To calculate c and p from "function c" and "function p" we need values from the cdf command in MATLAB, and these values depend on the variables d1-d4. d1-d4 are however different for function c and function p. Hence we would need two sets of the code calculating the process going from d1-d4 to q1-q4. One where we use kc as input, and one with kp.

When we try to add these functions MATLAB says we exceed the maximum limit of nested functions. Is there a smart way around this, how do you suggest we go about this issue?

Thanks in advance and best regards

/Per Wehl

Full code below:

        function c = tcall (r, dtmc, q1, q2, q3, q4, kc)
            c=(exp(-r.*dtmc).*((x(5).*(exp(x(1)+(.5.*x(3).^2))).*(q1)-(kc.*(q2)))+((1-x(5)).*(exp(x(2)+(0.5.*x(4).^2))).*(q3)-(kc.*(q4)))));
            cdev=@tcall;
          
            %pdev=((p-phat).^2);
            whos c
            whos chat
            cdev=((c-chat).^2);

% function p = tput (r, dtmp, q1, q2, q3, q4, kp)
% p=(exp(-r.*dtmp).*((x(5).*(-exp(x(1)+(.5.*x(3).^2))).*(1-q1)+(kp.*(1-q2)))+((1-x(5)).*(-exp(x(2)+(0.5.*x(4).^2))).*(1-q3)+(kp.*(1-q4)))));
% pdev=@tput;
            
             function q1 = qett (d1)
                 q1=cdf('normal',d1,0,1);
                % tput=@qett;
                 tcall=@qett;
                 
             function q2 = qtva (d2)
                 q2=cdf('normal',d2,0,1);
               % tput=@qtva;
                 tcall=@qtva;
                
             function q3 = qtre (d3)
                 q3=cdf('normal',d3,0,1);
                % tput=@qtre;
                 tcall=@qtre;
                
             function q4 = qfyra (d4)
                 q4=cdf('normal',d4,0,1);
                 %tput=@qfyra;
                 tcall=@qfyra;
               
                
                 function d2 = dtva (d1, x)
                     d2=d1-x(3);
                     qett=@dtva;
                 
         
                 function d4 = dfyra (d3, x)
                     d4=d3-x(4);
                     qfyra=@dfyra;
                
              
                     function d1 = dett (kc, x)
                         d1=(-log(kc)+x(1)+(x(3).^2))./x(3);
                         dtva=@dett;
                
                     function d3 = dtre (kc, x)
                         d3=(-log(kc)+x(2)+(x(4).^2))./x(4);
                         dfyra=@dtre;