Error in fzero usage

Hi, I am I created a function that I need to find the zero of a function using the function fzero but when I try to use it it gives me error saying that I used too many arguments in input.

Could someone tell me where I am going wrong and how to fix it. I leave below a code sketch

clear variables; close all; clc

S0 = 100;
K = 80;
r = 0.05;
T = 1.0;
mkt_price = 101.32;
q = 0.0;

resu = impliedVola(S0,K,r,T,mkt_price,q)


function resu = impliedVola(S0,K,r,T,mkt_price,q)
    options = optimset('fzero');
    options = optimset(options,'TolX',1e-9,'Display','off');
    
    [x,~,exitflag] = fzero(@difference, 0.5, options, ...
                           S0, K, r, T, mkt_price, q);
    

    if(exitflag ~= 1)
        disp('Did not find value')
        resu = 0;
    else
        resu = x;
    end

end

function resu = difference(sigma,S,K,r,T,mkt_price,q)
    bs_price = blackScholes(sigma,S,K,r,T,r,q);
    resu = mkt_price - bs_price;
end

function resu = blackScholes(sigma,S,K,r,T,q)
    d1 = (log(S./K) + (r - q + 0.5*sigma^2).*T) ./ (sigma.*sqrt(T));
    d2 = d1 - sigma*sqrt(T);
    resu = S*exp(-r*T)*normal(d1,0,1) - K*exp(-r*T)*normal(d2,0,1);
end

function resu = normal(x,mu,sigma)
    z = (x - mu) ./ sigma;
    resu = 0.5 * erfc(-z ./ sqrt(2));
end

Answer 1

[Torsten]

bs_price = blackScholes(sigma,S,K,r,T,r,q);
function resu = blackScholes(sigma,S,K,r,T,q)

Do you see the different number of input arguments in the function call and the function definition ?

And if you plot your function, you will see that it has no zeros:

S0 = 100;
K = 80;
r = 0.05;
T = 1.0;
mkt_price = 101.32;
q = 0.0;
sigma = 0.01:0.01:10;
resu = arrayfun(@(sigma)difference(sigma,S0,K,r,T,mkt_price,q),sigma);
plot(sigma,resu)

function resu = impliedVola(S0,K,r,T,mkt_price,q)
    options = optimset('fzero');
    options = optimset(options,'TolX',1e-9,'Display','off');
    
    [x,~,exitflag] = fzero(@difference, 0.5, options, ...
                           S0, K, r, T, mkt_price, q);
    

    if(exitflag ~= 1)
        disp('Did not find value')
        resu = 0;
    else
        resu = x;
    end

end

function resu = difference(sigma,S,K,r,T,mkt_price,q)
    bs_price = blackScholes(sigma,S,K,r,T,q);
    resu = mkt_price - bs_price;
end

function resu = blackScholes(sigma,S,K,r,T,q)
    d1 = (log(S./K) + (r - q + 0.5*sigma^2).*T) ./ (sigma.*sqrt(T));
    d2 = d1 - sigma*sqrt(T);
    resu = S*exp(-r*T)*normal(d1,0,1) - K*exp(-r*T)*normal(d2,0,1);
end

function resu = normal(x,mu,sigma)
    z = (x - mu) ./ sigma;
    resu = 0.5 * erfc(-z ./ sqrt(2));
end

[Simone Perotti]

Oh my god what a shame, I apologize terribly for the stupid question I didn't even realize it. Thank you very much in the meanwhile

[Torsten]

If I had to apologize for all my stupid programming errors, there would be quite a long list -:)