FFTCOS_B_2(n, Nex, L, c, cp, type, S0, t, r, q, ...

% This is material illustrating the methods from the book
% Financial Modelling  Theory, Implementation and Practice with Matlab
% source
% Wiley Finance Series
% ISBN 9780470744895
%
% Date: 02.05.2012
%
% Authors: Joerg Kienitz
% Daniel Wetterau
%
% Please send comments, suggestions, bugs, code etc. to
% kienitzwetterau_FinModelling@gmx.de
%
% (C) Joerg Kienitz, Daniel Wetterau
%
% Since this piece of code is distributed via the mathworks fileexchange
% it is covered by the BSD license
%
% This code is being provided solely for information and general
% illustrative purposes. The authors will not be responsible for the
% consequences of reliance upon using the code or for numbers produced
% from using the code.
function price = FFTCOS_B_2(n, Nex, L, c, cp, type, S0, t, r, q, ...
strike, varargin)
dt = t / Nex; % time interval
Ngrid = 2 ^ n; % Grid points
Nstrike = size(strike,1); % number of strikes
x = double(log(S0 ./ strike)); % center
a = double(c(1) + x  L * sqrt(c(2) + sqrt(c(3)))); % lower trunc
b = double(c(1) + x + L * sqrt(c(2) + sqrt(c(3)))); % upper trunc
Grid_i = repmat((0:Ngrid1)',1,Nstrike); % Grid index
% Set up function handles
if cp == 1
vk = @(x) calcv_2(Grid_i, x, b, a, b, cp, strike);
cv = @(x,y) cvalue_2(a, x, a, b, Ngrid, y, type, dt, r, q, varargin{:});
else
vk = @(x) calcv_2(Grid_i, a, x, a, b, cp, strike);
cv = @(x,y) cvalue_2(x, b, a, b, Ngrid, y, type, dt, r, q, varargin{:});
end
initialGuess = 0; % guess for x^*(t_Nex1)
V = vk(0); % coeff V in t_Nex1
xstark = zeros(Nstrike,Nex1);
for m = Nex1:1:1 % backward induction
% could be fzero but Newton with some number of iteration is fine!
xstark(:,m) = xstar_2(initialGuess,cp, a, b, 50, Grid_i, type, ...
V, dt, r, q, strike, varargin{:}); % early exercise point
C = cv(xstark(:,m),V); % Cont value at t_m
V = vk(xstark(:,m)) + C; % Coeff V in t_m
initialGuess = xstark(:,m);
end
cfval = exp(feval(@CF, type,pi*Grid_i*diag(1./(ba)), dt,r,q,varargin{:}));
pF = cfval .* exp( 1i * pi * Grid_i * diag((x  a) ./ (b  a)) );
pF(1,:) = 0.5*pF(1,:);
price = exp(r * dt) * sum(real(pF) .* V) ; % Option value at t_0
end

