% Copyright (c) 2006-2009 by Ales Cerny

%************************************************************************%
% chapter12fig5.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:
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% 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 chapter12fig5.m by 
%    Ales Cerny (2009), Mathematical Techniques in Finance (2nd ed.),  
%    Princeton University Press. The original version is available from 
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clear;
format long g;
K=97; S=100; sig=0.2; T=1; r=0; dt=0.05; h=0.1;
z = BSCall(S,K,r,T,sig);
n=1:10;
for j=n;   
y(j)=BSCallEFD2(S,K,r,T,sig,h/j,dt/(j^2));
end
plot(n,y,'o-k',n,z*ones(1,length(n)),'--k')
xlabel('1/\alpha');
ylabel('price');
title('Convergence of option prices, K = 100, node at strike');