%   Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter2exe6.m - supplementary program to                              %
% Ales Cerny (2009) Mathematical Techniques in Finance (2nd ed.)         % 
% Princeton University Press http://press.princeton.edu/titles/9079.html %
%************************************************************************%
    
% This code is provided 'as-is', without any express or implied warranty.  
% 
% Permission is granted to anyone to use this code for any purpose, 
% subject to the following restrictions:
% 
% 1. The origin of this code must not be misrepresented; you must not
%    claim that you wrote the original code.
% 2. Modified code versions must be plainly marked as such, and must not 
%    be misrepresented as being the original code.
% 3. This notice may not be removed from any source distribution.

% NOTICE TO STUDENTS: To avoid accusations of plagiarism, if you use this 
% code or its modifications in assessed work you should prepend it with a 
% note stating: 
%   "This is the original/modified version of the code chapter2exe6.m by 
%    Ales Cerny (2009), Mathematical Techniques in Finance (2nd ed.),  
%    Princeton University Press. The original version is available from 
%    http://www.martingales.info/mtfweb2".
% A similar acknowledgement should appear prominently inside your written 
% report.

format short g    
A=[ones(8,1) [0.8;0.9;0.95;1;1.05;1.1;1.2;1.3]];
b=[0;0;0;0;50;100;200;300];
p=[0.05;0.1;0.15;0.20;0.2;0.15;0.1;0.05];
Atil=A.*(sqrt(p)*[1 1]);
btil=b.*sqrt(p);
x=lscov(Atil,btil) %this is a numerically more stable way of writing x=inv(A'*A)*A'*b
eps=A*x-b %replication error
epstil=Atil*x-btil; %replication error multiplied by square root of corresponding probability
epstil'*epstil %expected squared replication error