%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%
%%% Option pricer for European option under Black-Scholes-Merton model using
%%% the Fourier Space Time-stepping method
%%% 
%%% 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] = FST_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 = 8192;

% Real space
x_min = -7.5; x_max = 7.5;
dx=(x_max-x_min)/(N-1);
x=x_min:dx:x_max;
s = 0.5*(S(1)+S(end))*exp(x);

% Fourier space
w_max=pi/dx;
dw=2*w_max/N;
w=[0:dw:w_max, -w_max+dw:dw:-dw];

% FST method
char_exp_factor = exp((i*(r-0.5*sigma^2-q).*w-0.5*(sigma*w).^2-r)*T);

fftw('planner', 'measure');

for iter_k = 1:length(K)
    %FST algorithm
    payoff = max(s-K(iter_k),0);
    values = real(ifft(fft(payoff).*char_exp_factor));
    values_call(:,iter_k) = interp1(s,values,S,'cubic');

    payoff = max(K(iter_k)-s,0);
    values = real(ifft(fft(payoff).*char_exp_factor));
    values_put(:,iter_k) = interp1(s,values,S,'cubic');
end

time = cputime - time;