vega=bsVega(CallPutFlag, S,X,T,r,r_f, sigma)

function vega=bsVega(CallPutFlag, S,X,T,r,r_f, sigma) 
    %sigma=sigma+0.0000000001;
    %T=T+0.0000000001;
    d1=(log(S./X)+(r-r_f+(sigma.^2)./2).*T)./(sigma.*sqrt(T));
    nd1=(1./sqrt(2.*pi))*exp(-d1.^2/2);
    vega=S.*exp(-r_f.*T).*nd1.*sqrt(T);
end

% Vega (CallPutFlag, S, X, T, r, r_f, sigma) 
% 
% Returns Garman-Kohlhagen Vega for a European currency option

%   version: v1.0
%   author: Yazann Romahi [[e-mail]]