(Matlab) Using multiple argument anonymous function & bisection method to find the roots of a function

1
votes

As indicated by the title, I am using these codes to solve the question indicated above, so basically, there are two arrays, mid_call and strike that are iterated using i, and for each mid_call(i) and k(i), there should be a corresponding root, sigma. However, whenever I try to run the program, i always get this error:

Error using @(sigma, k) s.*normcdf((log(s./(q_tau.k))+tausigma.^2/2)./(sqrt(tau).*sigma)) - q_tau.*k.*normcdf(((log(s./(q_tau.k))+tausigma.^2/2)./(sqrt(tau).*sigma))-sqrt(tau).*sigma)- mid_call(i) Not enough input arguments

I will be forever grateful for your help!

Start of the code:

mid_call = 47.4350,37.7800,28.4400,19.6800,11.8800,5.6150,1.7250,0.3150,0.0600

iv_list = []; 
tol = 1.e-8;
maxit = 50;

for i = 1:1:9
    tau = 5/12;
    q_tau = 1.0000;
    s = 197.07; 
    strike = 150:10:230;
    k = strike(i);
    syms sigma;
    d = @(sigma, k) (log(s./(q_tau.*k))+tau*sigma.^2/2)./(sqrt(tau).*sigma);
    f = @(sigma, k) s.*normcdf((log(s./(q_tau.*k))+tau*sigma.^2/2)./(sqrt(tau).*sigma)) -    q_tau.*k.*normcdf(((log(s./(q_tau.*k))+tau*sigma.^2/2)./(sqrt(tau).*sigma))-sqrt(tau).*sigma)- mid_call(i);

    %starting value
    sigma_lo = zeros(size(mid_call(i)));
    sigma_hi = 10*ones(size(mid_call(i)));
    f_lo = f(sigma_lo);
    f_hi = f(sigma_hi);

    % can we vectorize this?
    if sign(f_lo)==sign(f_hi), disp('*** Error: solution not bracketed'), end 

    %let's rollllll
    for it = 1:maxit      
        sigma_new = (sigma_lo + sigma_hi)/2;      % cut interval in half 
        f_new = f(sigma_new);
        diff_x = max(abs(sigma_lo - sigma_hi));
        diff_f = max(abs(f_new));
        [it sigma_new];

        if max(diff_x,diff_f) < tol, break, end

        if sign(f_new)==sign(f_lo)
            sigma_lo = sigma_new; 
            f_lo = f_new;
        else 
            sigma_hi = sigma_new;
            f_hi = f_new;
        end 
    end 
    iv_list(end+1) = sigma_new ;
end

I know this is quite a long question but any help would be extremely appreciated!

1
matlabfor-loopanonymous-functionbisection
Where is the call for d? I did not find it in your code. Also, f needs to be called with two arguments, f = @(sigma, k). However, you only call it with one: f_lo = f(sigma_lo);, ' f_hi = f(sigma_hi);', f_new = f(sigma_new);. In all three cases, k is missing. - Nemesis

1 Answers

0
votes

in your code, k is missing in the calls of f. Change your lines from

f_lo = f(sigma_lo);
f_hi = f(sigma_hi);

f_new = f(sigma_new);

to

f_lo = f(sigma_lo,k);
f_hi = f(sigma_hi,k);

f_new = f(sigma_new,k);

and the code does not throw any error.