lsqnonlinear

[mouna]

I have make an optimization program using the lsqnonlin function but I have some problem with it.

function F = myfun(lamda)
 
%--------------------------------------------------------------------------
 
% @description:    Attempt to estimate the parameter of the market price
 
 
 
%model of yields. We do this by using curve fitting to the observed data.
 
%
 
%    Xdata:      - vector of times to maturity .
 
%    ydata      - vector of observed yields-to-maturity that correspond to
 
%                the matching value by the yields-to-maturity correspinf to
 
%              the vasicek model wich has the following form:
 
% R(T) = R(alpha) +(r0 - (beta - R(alpha)) *
 
% (1- exp (- beta*T))/ (beta *T) +
 
%  ((sigma^2)*(1- exp (- beta*T))^2)/(4*(beta^3)*T).
 
%
 
%
 
%where R(alpha)= (beta - ((lamda * sigma)/ alpha)- ((sigma^2)/ (2*(alpha^2)))
 
% and T is time to maturity.
 
%
 
%                xdata    = [0.5 1 2 3 5 7 10];
 
%                ydata    =[0.079 0.0782 0.0791 0.0793 0.0791 0.0802 0.0798];
 
%--------------------------------------------------------------------------               
 
 
 
 
 
xdata = [0.5 1 2 3 5 7 10];
 
ydata = [0.079 0.0782 0.0791 0.0793 0.0791 0.0802 0.0798];
 
 
 
alpha = 0.035364;
 
beta = 0.0713;
 
sigma = 0.0110;
 
r = 0.012;
 
 
 
 
 
Ralpha =@(lamda) (beta -(lamda*sigma)/alpha)-(sigma.^2)/(2*(alpha.^2));
 
 
 
F =@(lamda,xdata,alpha,beta,sigma,r) Ralpha(lamda) +...
 
((1-exp(-beta*xdata))./(beta*xdata))*(r - Ralpha(lamda))+...
 
((sigma.^2)./(4*(beta.^3)*xdata).*((1-exp(-xdata)).^2));
 
 
 
 
 
   
 
lamda0 = - 0.03; %  initialisation of the parameter lamda%
 
options = optimset('TolFun',1e-15);
 
 
 
[lamda,resnorm] = lsqnonlin(@myfun,lamda0,[],[],options);

When I run it I get the following error message. That I haven’t understand the sense of it.

??? Error using ==> blsprice at 98

Volatilities cannot be negative.



Error in ==> myfun at 2

z = blsprice(36.12,35,0.07,7/52,x) - 2.15;

Error in ==> lsqnonlin at 203

initVals.F = feval(funfcn{3},xCurrent,varargin{:});



Error in ==> fit2 at 44

[lamda,resnorm] = lsqnonlin(@myfun,lamda0);



Caused by:

Failure in initial user-supplied objective function evaluation. LSQNONLIN cannot continue.


Please can you help me.