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%%%
%%% Option pricer for European option under Black-Scholes-Merton model using
%%% the FFT method of Carr, Madan 1999
%%% 
%%% 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/>.
%%%
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function [values_call, values_put, time] = CarrMadanFFT_European_BlackScholesMerton(S, K, T, sigma, r, q)


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

time = cputime;

N = 4096;
nu = 0.25;
alpha = 1.5;
lambda = 2*pi/(nu*N);
b = N*lambda/2;
m =1:N;
k = -b+lambda*(m-1);

%Set constants
const = @(m)(exp(-alpha*k(m))/pi);
kron = @(n)(n==0);
v = nu*(m-1);

for iter_s = 1:length(S)
    %Set Fourier transform of pdf and payoff
    pdf_ft = @(u)(exp(i*u*log(S(iter_s))+ i*u*(r-q-sigma^2/2)*T-u.^2*sigma^2*T/2));
    payoff_call_ft = @(u)(exp(-r*T).*pdf_ft(u-(alpha+1)*i)./(alpha^2+alpha-u.^2+i*(2*alpha+1)*u));

    integrand_call = @(j)(exp(i*b*v(j)).*payoff_call_ft(v(j))*(nu/3).*(3+(-1).^(j)-kron(j-1)));

    %Matlab uses -i in fft, thus use forward transform, not backward
    values = real(const(m).*fft(integrand_call(1:N)));
    values_call(iter_s,:) = interp1(exp(k), values, K);
    values_put(iter_s,:) = values_call(iter_s,:) - S(iter_s)*exp(-q*T) + K*exp(-r*T);
end

time = cputime - time;
time = time*2;  % because we use put-call parity for put options