Code covered by the BSD License  

Highlights from
Modern Pricing Method using Transforms

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Modern Pricing Method using Transforms

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25 Jul 2012 (Updated )

COS, CONV, Lewis Option Pricing Methods including Bermudan and American Options.

cvalue_2(x1, x2, a, b, N, V, ...
% This is material illustrating the methods from the book
% Financial Modelling  - Theory, Implementation and Practice with Matlab
% source
% Wiley Finance Series
% ISBN 978-0-470-74489-5
%
% 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 file-exchange
% 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 result = cvalue_2(x1, x2, a, b, N, V, ...
    model, t, r, q, varargin)


Nstrike = length(x1);

exp2 = exp( 1i .* repmat((1:N)',1,Nstrike) * diag((x2 - a) ./ (b - a)) .* pi );    % init
exp1 = exp( 1i .* repmat((1:N)',1,Nstrike) * diag((x1 - a) ./ (b - a)) .* pi );    % init

m = zeros(3*N-1, Nstrike);                                        % init base

m(N,:) = 1i * pi * (x2 - x1) ./ (b - a);
m(N+1:2*N,:) = 1 ./ repmat((1:N)',1,Nstrike) .* ( exp2 - exp1 );
m(1:N-1,:) = - conj(flipud(m(N+1:2*N-1, :)));
m(2*N+1:3*N-1,:) = ( exp2(1:N-1,:) * diag(exp2(N, :)) - exp1(1:N-1,:) ...
    * diag(exp1(N,:)) ) ./ ( repmat((N+1:2*N-1)',1,Nstrike) );

Grid_j = (0:N-1)';                                          % fix grid

% compute u values
u = exp(feval(@CF, model,pi*repmat(Grid_j,1,Nstrike)*diag(1./(b-a)), t,r,q,varargin{:})) .* V;
u(1,:) = 0.5*u(1,:);

m_s = [m(N:-1:1, :); zeros(1,Nstrike); m(2*N-1:-1:N+1, :)];
u_s = [u; zeros(N, Nstrike)];
m_c = m(3*N-1:-1:N, :);

shortCut = 1;

% apply fft five times
if shortCut == 1
    zeta = -ones(2*N, Nstrike);
    zeta(2 .* (1:N)' - 1,:) = 1;

    fft_u_s = fft(u_s);
    xi_s = ifft((fft(m_s)) .* fft_u_s);
    xi_c = ifft((fft(m_c)) .* (zeta .* fft_u_s));

    result = exp(-r * t) / pi .* imag( xi_s(1:N,:) + flipud(xi_c(1:N,:)) );
else   
    M_c = zeros(N, N);
    M_s = zeros(N, N);
    
    result = zeros(N,Nstrike);
    
    for k = 1:Nstrike
        for n = 0:N-1
            M_c(:, n+1) = m(N+n:2*N-1+n,k);
            M_s(:, n+1) = m(N+n:-1:1+n,k);
        end

        result(:,k) = exp(-r*t) / pi .* imag((M_c + M_s) * u(:,k));
    end

end

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