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Highlights from
American Monte Carlo

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American Monte Carlo



Algorithms for pricing American Style derivatives with Monte Carlo Simulation

RegCoeff(S, 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 978-0-470-74489-5
% Date: 02.05.2012
% Authors:  Joerg Kienitz
%           Daniel Wetterau
% Please send comments, suggestions, bugs, code etc. to
% (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 f = RegCoeff(S, g, df, B, Nb, Nr)
% calculates regression coefficients to be used with longstaff-schwartz

v = g(:,end);   % start for backward induction

f = zeros(Nb, Nr-1);

% backward induction and regression from t_{Nr-1} up to t_1
for i = Nr-1:-1:1
        index = find(g(:,i) > 0); % all ITM paths
        s = S(index,i+1);         % values of S at given time point 
        v = v * df(i+1);          % option value at t_i

        Acell = B(s);             % 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) >= c;    % early exercise
        v(index(exercise)) = g(index(exercise),i);


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