% Copyright (c) 2001-2009 by Ales Cerny

%************************************************************************%
% chapter3sect9.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 chapter3sect9.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.

% One year horizon, NIKKEI 225 real returns 

clear;
clc;
format short;

%*******************%
%    parameters     %
%*******************%
Risky1 = -0.35 : 0.05 : 0.90;   % row vector of rates of return from -35% to 90% in 5% increments%
XDistr = [0.011                 % relative frequency of annual real returns on NIKKEI 225, monthly data 1960-2000
          0.023
          0.021
          0.041
          0.034
          0.061
          0.112
          0.095
          0.097
          0.081 
          0.091
          0.068
          0.074
          0.049
          0.047
          0.028
          0.015
          0.008
          0.013
          0.021
          0.000
          0.000 
          0.004
          0.000
          0.002
          0.004 ]'; 

strike   = 1.1;
SafeRate = 0.02;
vol      = sqrt((log(1+Risky1).^2)*XDistr'-(log(1+Risky1)*XDistr')^2);
Risky2   = max([zeros(1,length(Risky1));((1+Risky1)-strike)]);
BSprice2 = BScall(1,strike,SafeRate,1,vol); 
price2   =[-0.1; 0.1; 0.5; 0.75; 0.9; 1]*BSprice2;

IPPrecisionTolerance = 10^-6;

%****************************%
% main body of the programme %
%****************************%
SR        = zeros(length(price2),1);
beta      = zeros(length(price2),1);
SRm       = zeros(length(price2),1);
betam     = zeros(length(price2),1);
suboptSRm = zeros(length(price2),1);
for ii = 1 : 1 : length(price2);
    X  = (Risky2/price2(ii)-1-SafeRate);
    EX = X*XDistr';
    OmegaX = (X.*XDistr)*X';          % OmegaX = E[XX']
    [IPm,betam(ii)]=TrQUmax(X, XDistr, IPPrecisionTolerance);
    SRm(ii)=sqrt((1-IPm)^-2-1); 
    beta(ii)=inv(OmegaX)*EX;
    SR(ii)=sqrt(1/(1-EX'*beta(ii))-1);
    suboptSRm(ii)=SRmvalue(X, XDistr, beta(ii));
end;

disp(' ______________________________________________________________________________________________________________________ ');
disp(' ');
disp(' ');
disp(sprintf(' option price                    %6.4f      %6.4f      %6.4f      %6.4f      %6.4f      %6.4f',price2'));
disp(' ');
disp(sprintf(' standard beta                   %6.4f      %6.4f      %6.4f      %6.4f      %6.4f      %6.4f',beta'));
disp(' ');
disp(sprintf(' arbitrage-adj beta              %6.4f      %6.4f      %6.4f      %6.4f      %6.4f      %6.4f',betam'));
disp(' ');
disp(sprintf(' standard SR                      %6.3f      %6.3f      %6.3f      %6.3f      %6.3f      %6.3f',SR'));
disp(' ');
disp(sprintf(' arb-adj SR of std beta           %6.3f      %6.3f      %6.3f      %6.3f      %6.3f      %6.3f',suboptSRm'));
disp(' ');
disp(sprintf(' arbitrage-adj SR                 %6.3f      %6.3f      %6.3f      %6.3f      %6.3f      %6.3f',SRm'));
disp(' ');
disp(' _______________________________________________________________________________________________________________________ ');
disp(' ');
disp(' ');