RegCoeff_M(S, M, Ns, g, df, B, Nb, Nr)

% 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 y = RegCoeff_M(S, M, Ns, g, df, B, Nb, Nr)
% Calculates the regression coefficiients
v = g(:,end); % start for backward induction
f = zeros(Nb,Nr1);
% backward induction and regression from t_{Nr1} up to t_1
for i = Nr1:1:1
index = find(g(:,i+1) > 0); % all ITM paths
s = S(index,i+1); % values of S at given time points
m = M(index,i+1); % values of M at given time points
v = v * df(i+1); % option value at t_i
Acell = B(s,m); % evaluate basis function in cell array B
A = cell2mat(Acell{:,:}); % convert to matrix
f(:,i) = (A'*A)\(A'*v(index)); % determine coefficients
c = A*f(:,i); % continuation value
exercise = g(index,i+1) >= c; % early exercise
v(index(exercise)) = g(index(exercise),i+1);
end
y = f;
end

