maximise a function and find paramete

Hi everybody,

i want to find lambda (single value) that determines the maturity at which the function achieves its max

((1-exp(-lambda*gmaturities))./(lambda*gmaturities)-exp(-lambda*gmaturities))

my code is

F=@(lambda)[((1-exp(-lambda*gmaturities))./(lambda*gmaturities)-exp(-lambda*gmaturities))];

lambda0=0.0609;

lambda=fsolve(F,lambda0)

and i got lambda = 1.005283084116551e+03,i know this is not correct

could you please help me?

gmaturities=[6;12;24;36;48;60;72;84;96;108;120;180;240]

Answer 1

[Walter Roberson]

gmaturities = [6;12;24;36;48;60;72;84;96;108;120;180;240]

F = @(lambda) -(((1-exp(-lambda*gmaturities))./(lambda*gmaturities)-exp(-lambda*gmaturities)));
lambda0 = 0.0609;
lambda = gamultiobj(F, lambda0)

The result will be a vector of values, because you are trying to maximize 13 equations at the same time -- each of the values of gmaturies effectively defines another equation, so you are asking to maximize the equations simultaneously.

I suspect you want something more like

gmaturities = [6;12;24;36;48;60;72;84;96;108;120;180;240];

lambda0 = 0.0609;

lambda = arrayfun(@(GM) fminsearch(@(lambda) -(((1-exp(-lambda*GM))./(lambda*GM)-exp(-lambda*GM))), lambda0), gmaturities);

[masoumeh solgi]

thank you for your reply.

lamda should be a single value that determines the maturity at which the function achieves its max

[Walter Roberson]

Your function has 13 values because your maturities is a vector. No one lambda can maximize it all simultaneously.

The code I posted second optimizes for each individual maturity value.

[masoumeh solgi]

Thank you