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
