%   Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter5sect3.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 chapter5sect3.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.
% This program implements binomial option pricing model

clear;                    % clear the workspace 
clc;                      % clear screen 

%************************%
%        market          %
%************************%
S0 = 5100;                                  % initial stock price  
strike = 5355;
Rsafe = 1.0033;				                % monthly safe return  
R = [1.053 0.965];                          % monthly stock return 

%************************%
%      Risk-neutral      %
%      probabilities     %
%************************%
QDistr=[Rsafe-R(2) R(1)-Rsafe]./(R(1)-R(2));

%************************%
%   grid indexation      %
%************************%
Tidx=4;                                     % number of trading dates            
dlnS=log(R(1))-log(R(2));                   % increment on log price grid        
highlnR=log(R(1));                          % the highest return over one period

% there are tt live cells at time tt, highest stock price at the top
% log price at cell  1 at time tt is ln(S0)+(tt-1)*highlnR   
% log price at cell ii at time tt is ln(S0)+(tt-1)*highlnR-(ii-1)*dlnS

C = zeros(Tidx,Tidx);                       % initialize the grid for call option price
stock = zeros(Tidx,Tidx);                   % initialize the grid for stock price 
delta = zeros(Tidx,Tidx);                   % initialize the grid for option delta

%************************%
%     option payoff      %
%************************%
S_T = log(S0)+(Tidx-1)*highlnR-(0:(Tidx-1))*dlnS;   % log of stock price at maturity 
S_T=exp(S_T');                                      % stock price at maturity          
C_T=max([(S_T-strike)';zeros(1,length(S_T))]);      % option payoff at maturity         
stock(:,Tidx)=S_T;                                  % stock price grid at maturity     
C(:,Tidx)= C_T';                                    % option price =option payoff at T 

%************************%
%       main loop        %
%************************%
for tt = Tidx-1 : -1 : 1
    for ii = 1 : 1 : tt
        stock(ii,tt)=S0*exp((tt-1)*highlnR-(ii-1)*dlnS);
        C(ii,tt)=(QDistr*C(ii:ii+1,tt+1))/Rsafe;    % risk-neutral pricing
        delta(ii,tt)=(C(ii,tt+1)-C(ii+1,tt+1))...
                     /(R(1)-R(2))/stock(ii,tt); 
    end
end

%*********************%
%       output        %
%*********************%


disp( '__________________________________________');
disp('                stock price                ');
disp(' ');
disp(num2str(stock,'%12.1f'));
disp( '__________________________________________');
disp(' ');
disp(' ');
disp( '__________________________________________');
disp('                option price               ');
disp(' ');
disp(num2str(C,'%12.2f'));
disp( '__________________________________________');
disp(' ');
disp(' ');
disp( '__________________________________________');
disp('               dynamic delta               ');
disp(' ');
disp(num2str(delta,'%12.3f'));
disp( '__________________________________________');
disp(' ');
disp(' ');
disp( '__________________________________________');
disp('                bank account               ');
disp(' ');
disp(num2str(C-delta.*stock,'%11.1f'));
disp( '__________________________________________');
disp(' ');
disp(' ');