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%%%
%%% Option pricer for European option under Black-Scholes-Merton model using
%%% the quadrature of Fourier transform of option value
%%% 
%%% Copyright (C) 2008  Vladimir Surkov
%%%
%%%
%%% This program is free software: you can redistribute it and/or modify
%%% it under the terms of the GNU General Public License as published by
%%% the Free Software Foundation, either version 3 of the License, or
%%% (at your option) any later version.
%%%
%%% This program is distributed in the hope that it will be useful,
%%% but WITHOUT ANY WARRANTY; without even the implied warranty of
%%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%%% GNU General Public License for more details.
%%% 
%%% You should have received a copy of the GNU General Public License
%%% along with this program.  If not, see <http://www.gnu.org/licenses/>.
%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [values_call, values_put, time] = FourierProductQuadrature_European_BlackScholesMerton(S, K, T, sigma, r, q)


values_call = zeros(length(S), length(K));
values_put = zeros(length(S), length(K));

time = cputime;

for iter_s = 1:length(S)
    for iter_k = 1:length(K)
        
        %Set FT transforms of payoff and pdf
        payoff_ft = @(u)(exp(log(K(iter_k))*(1+i*u))./(i*u.*(1+i*u)));
        dist_ft = @(u)(exp(i*u*log(S(iter_s))+i*u*(r-q-sigma^2/2)*T-u.^2*sigma^2*T/2));

        integrand = @(u)(exp(-r*T)*real(payoff_ft(u+1.1i).*dist_ft(-(u+1.1i))));
        values_call(iter_s, iter_k) = quad(integrand, -8.0, 8.0)/(2*pi);
        integrand = @(u)(exp(-r*T)*real(payoff_ft(u-0.1i).*dist_ft(-(u-0.1i))));
        values_put(iter_s, iter_k) = quad(integrand, -8.0, 8.0)/(2*pi);
    end
end

time = cputime - time;