main.m

clc
clear all

% set test values...
E = 105;
r = 0.02;
S = 100;
sigma = 0.2;
tau = 0.25;

% % textbook values... for easy comparison.
% % European value should be 7.7531, American should be 8.0000
% E = 10;
% r = 0.1;
% S = 2;
% sigma = 0.4;
% tau = 0.25;

% print initial conditions to console...
formatString = ['Asset price = %.2f, Strike price = %.2f,' ...
        ' Interest rate = %.4f, Volatility = %.4f, Time to expiry = %.4f\n'];
fprintf(formatString, S, E, r, sigma, tau);

% start off by evaluating European options
fprintf('Evaluating pricing of European options...\n');

fprintf('  Calculating the closed-form solution and explicit Euler solutions...\n');
% evaluating "simple" numerical methods
bse = BSEqnEuropean(S, tau, E, r, sigma);
addpath('simple');
ee = ExplicitEuropean(S, tau, E, r, sigma);
fprintf('  Using builtin matrix inversion for solving linear systems...\n');
tic
ie = ImplicitEuropean(S, tau, E, r, sigma);
cne = CrankNicolsonEuropean(S, tau, E, r, sigma);
fprintf('    ');
toc

fprintf('  Using SOR for solving linear systems...\n');
% evaluating European options with successive over-relaxation...
addpath('sor');
sor_ee = NaN; % doesn't apply here. SOR only solves linear systems.
tic
sor_ie = sorImplicitEuropean(S, tau, E, r, sigma);
sor_cne = sorCrankNicolsonEuropean(S, tau, E, r, sigma);
fprintf('    ');
toc

% Generate table for European options
methodNamesEuropean = {'Black-Scholes'; 'Explicit'; 'Implicit'; 'Crank-Nicolson'};
simple = [bse; ee; ie; cne];
sor = [bse; sor_ee; sor_ie; sor_cne];
euroTable = table(simple, sor, 'RowNames', methodNamesEuropean)

% evaluate American options...
fprintf('Evaluating pricing of American options using PSOR...\n');
addpath('psor')
tic
psor_ie  = psorImplicitAmerican(S, tau, E, r, sigma);
psor_cne = psorCrankNicolsonAmerican(S, tau, E, r, sigma);
fprintf('    ');
toc

fprintf('Evaluating pricing of American options using penalty method...\n');
addpath('penalty')
tic
penalty_ie  = penaltyImplicitAmerican(S, tau, E, r, sigma);
penalty_cne = penaltyCrankNicolsonAmerican(S, tau, E, r, sigma);
fprintf('    ');
toc

% Generate table for American options
methodNamesAmerican = {'Implicit'; 'Crank-Nicolson'};
psor = [psor_ie; psor_cne];
penalty = [penalty_ie; penalty_cne];
amerTable = table(psor, penalty, 'RowNames', methodNamesAmerican)

% % Using Monte-Carlo Methods
% fprintf('Evaluating pricing of American options using Monte-Carlo method (1st try)...\n');
% addpath('montecarlo');
% tic
% montecarlo1 = montecarloAmerican(S, tau, E, r, sigma);
% toc
% fprintf('Evaluating pricing of American options using Monte-Carlo method (2nd try)...\n');
% tic
% montecarlo2 = montecarloAmerican(S, tau, E, r, sigma);
% toc
%
% % Generate table for Monte-Carlo methods
% methodNamesMonteCarlo = {'Try 1'; 'Try 2'};
% montecarlo = [montecarlo1; montecarlo2];
% mcTable = table(montecarlo, 'RowNames', methodNamesMonteCarlo)


% Using binomial trees for American and European options...
fprintf('Evalutaing option pricing using tree-based methods...\n');
addpath('tree');
fprintf('  Evaluating european options...');
tic
bitree_e = BiTreeEuropean(S, tau, E, r, sigma);
fprintf('    ');
toc

fprintf('  Evaluating american options...');
tic
bitree_a = BiTreeAmerican(S, tau, E, r, sigma);
fprintf('    ');
toc

% Generate table for tree-based methods
methodNamesTree = {'Binomial Tree (European)'; 'Binomial Tree (American)'};
tree = [bitree_e; bitree_a];
treeTable = table(tree, 'RowNames', methodNamesTree)