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Highlights from
American Option Prices and the Optimal Exercise Boundary

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from American Option Prices and the Optimal Exercise Boundary by Bram van den Broek
This demo computes American option prices and the corresponding optimal exercise boundary

FreeBoundary(S,t,V,K,type) 
function Sf = FreeBoundary(S,t,V,K,type)

Sf = zeros(1,length(t));
eps_star = K*1e-5;

switch type
    case 'put'
        for j = 1:length(t)
            Sf(j) = S(find(abs(V(:,j)-K+S)< eps_star, 1, 'last'));
        end
    case 'call'
        for j = 1:length(t)
            Sf(j) = S(find(abs(V(:,j)+K-S)< eps_star, 1, 'first'));
        end
end

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