solve non linear equation

ok so I have a non linear function that I want to solve for 'x', one equation and one unknown variable 'x'.

I have a function Black_Imp_Vol.m of the variable 'x'.

function F = Black_Imp_Vol(x)
F = exp(-r*t)*(P*normcdf(((log(P/K)+t*x^2/2)/(x*sqrt(t))),0,1)-K*normcdf(((log(P/K)-t*x^2/2)/(x*sqrt(t))),0,1))-C ;

Now my code

clear;
r=0.01;
P=1.4334;
K=1.46;
C=0.0230;
t=0.26;
x0 = 0.3;         

    options=optimset('Display','iter');  

    [x,fval] = fsolve(@Black_Imp_Vol,x0,options)

will solve for 'x' using fsolve. Great!

However the above hard codes in the known variables r, P, K, C and t

I want to read the known variables r,P,K,C and t, from a .mat file where there are stored in a matrix 'q' a 150 by 5 matrix, each row hold one set of the known parameters and I want to call this fsolve row by row and compute 'x'.

So I coded this

clear;
load eurofx146_c_a_3.mat;
r=q(:,4);
P=q(:,2);
K=q(:,5);
C=q(:,1);
t=q(:,3);
n=size(q);
N=n(1);
s0 = 0.3;           

for i=1:N
  x(i) = fsolve(@Black_Imp_Vol,x0);
end

But I get an error

??? Undefined function or variable 'r'.

Error in ==> Black_Imp_Vol at 2
F = exp(-r*t)*(P*normcdf(((log(P/K)+t*x^2/2)/(x*sqrt(t))),0,1)-K*normcdf(((log(P/K)-t*x^2/2)/(x*sqrt(t))),0,1))-C ;
Error in ==> fsolve at 254
            fuser = feval(funfcn{3},x,varargin{:});

Error in ==> black2 at 15
  x(i) = fsolve(@Black_Imp_Vol,x0);

Caused by:
    Failure in initial user-supplied objective function evaluation. FSOLVE cannot continue.

anyone have an idea about how I can do this?

NOTE: this is NOT a simultaneous equation, is one equation, one unknown. just repeated for each data row.

Answer 1

[Bjorn Gustavsson]

I'd change the definition of your function Black_Imp_Vol to:

function F = Black_Imp_Vol(x,r,t,P,K,C)
F = exp(-r*t)*(P*normcdf(((log(P/K)+t*x^2/2)/(x*sqrt(t))),0,1)-K*normcdf(((log(P/K)-t*x^2/2)/(x*sqrt(t))),0,1))-C ;

...and then call fzero in a loop:

for i1=1:N
  x(i1) = fsolve(@(x) Black_Imp_Vol(x,r(i1),t(i1),P(i1),K(i1),C(i1)),x0);
end

HTH