Econometric, Option Valuation<\/p>\n
Name<\/p>\n
Institution<\/p>\n
Date<\/p>\n
Course<\/p>\n
Mat lab code for Monte Carlo<\/p>\n
%%%%%%%%%% Option parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n
S = 55; % Value of the underlying<\/p>\n
K = 50; % Strike (exercise price)<\/p>\n
r = 0.05; % Risk free interest rate<\/p>\n
sigma = 0.25; % Volatility<\/p>\n
T = 3; % Time to expiry<\/p>\n
%%%%%%%%%% Monte-Carlo Method Parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% <\/p>\n
randn(\u2019state\u2019,0) % Repeatable trials on\/off<\/p>\n
M=1e7; % Number of Monte-Carlo trials<\/p>\n
%%%%%%%%%% Use final values to compute <\/p>\n
final_vals=S*exp((r-0.5*sigma^2)*T + sigma*sqrt(T)*randn(M,1));<\/p>\n
option_values=max(K-final_vals,0); % Evaluate the Put option options<\/p>\n
present_vals=exp(-r*T)*option_values; % Discount under r-n assumption<\/p>\n
int=1.96*std(present_vals)\/sqrt(M); % Compute confidence intervals<\/p>\n
put_value=mean(present_vals); % Take the average<\/p>\n
display(put_value)<\/p>\n
display([put_value-int put_value+int])<\/p>\n
Matlab code for data generating FTSE 100<\/p>\n
A s c r i p t to produce the p l o t s f o r the p r i c e s and GARCH( 1 , 1 ) o f %<\/p>\n
% the FTSE100 , S&P500 , and NIKKEI225 i n d i c e s . %<\/p>\n
% %<\/p>\n
%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????%<\/p>\n
% INPUTS: %<\/p>\n
% % % This s c r i p t r e q u i r e s the Datastream Toolbox %<\/p>\n
% %<\/p>\n
% OUTPUTS: %<\/p>\n
% % % Figure 1 ???? The thr e e i n d i c e s d a i l y adjus t ed c l o s i n g %<\/p>\n
% pr i c e s f r om 1990 to today ( July 2012) % % Figure 2 ???? The d a i l y c ont inous l y compounded r e turns %<\/p>\n
% o f a l l i n d i c e s from 1990 to today ( July 2012) ,% % ove r layed by the GARCH( 1 , 1 ) c o n d i t i o n a l %<\/p>\n
% s tandard de v i a t i on . % % %<\/p>\n
%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????% % %<\/p>\n
%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????% % Chr i s t o s De l i v o r i a s ???? OR MSc Student %<\/p>\n
% The Uni v e r s i t y o f Edinburgh % % August 2012 %<\/p>\n
%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????%<\/p>\n
% Clear e x i s t i n g data and f i g u r e s c l f ;<\/p>\n
c l e a r a l l ;<\/p>\n
c l o s e a l l ;<\/p>\n
format sho r t ;<\/p>\n
% Connect to Yahoo Finance and f e t c h data<\/p>\n
Connect = yahoo ;<\/p>\n
dataFTSE=f e t c h (Connect , \u2019^FTSE \u2019 , \u2019 Jan 1 1990 \u2019 , today , \u2019d \u2019 ) ;<\/p>\n
dataN225=f e t c h (Connect , \u2019^N225 \u2019 , \u2019 Jan 1 1990 \u2019 , today , \u2019d \u2019 ) ;<\/p>\n
dataGSPC=f e t c h (Connect , \u2019^GSPC\u2019 , \u2019 Jan 1 1990 \u2019 , today , \u2019d \u2019 ) ;<\/p>\n
c l o s e (Connect ) ;<\/p>\n
% Ca l cul a t e d a i l y r e turns and GARCH SD f o r each index<\/p>\n
dataFTSEret = [ 0 . 0 p r i c e 2 r e t (dataFTSE ( : , end ) ) \u2019 ] ;<\/p>\n
retFTSE=f i n t s (dataFTSE ( : , 1 ) , dataFTSEret \u2019 , \u2019 retFTSE100 \u2019 , \u2019d \u2019 , . . .<\/p>\n
\u2019 retFTSE100 \u2019 ) ;<\/p>\n
[ c o e f f 1 , e r r o r s 1 , LLF1 , innovat ions1 , sigmas1 ] = . . .<\/p>\n
g a r c h f i t ( dataFTSEret ) ;<\/p>\n
sigmaFTSE = f i n t s (dataFTSE ( : , 1 ) , sigmas1 \u2019 , \u2019 retFTSE100 \u2019 , . . .<\/p>\n
\u2019d \u2019 , \u2019 retFTSE100 \u2019 ) ;<\/p>\n
dataN225ret = [ 0 . 0 p r i c e 2 r e t ( dataN225 ( : , end ) ) \u2019 ] ;<\/p>\n
retN225=f i n t s ( dataN225 ( : , 1 ) , dataN225ret \u2019 , \u2019 retNIKKEI \u2019 , \u2019d \u2019 , . . .<\/p>\n
\u2019 retNIKKEI \u2019 ) ;<\/p>\n
[ c o e f f 2 , e r r o r s 2 , LLF2 , innovat ions2 , sigmas2 ] = . . .<\/p>\n
g a r c h f i t ( dataN225ret ) ;<\/p>\n
sigmaN225 = f i n t s ( dataN225 ( : , 1 ) , sigmas2 \u2019 , \u2019 retNIKKEI \u2019 , . . .<\/p>\n
v<\/p>\n
\u2019d \u2019 , \u2019 retNIKKEI \u2019 ) ;<\/p>\n
dataGSPCret = [ 0 . 0 p r i c e 2 r e t (dataGSPC ( : , end ) ) \u2019 ] ;<\/p>\n
retGSPC=f i n t s (dataGSPC( : , 1 ) , dataGSPCret \u2019 , \u2019 retSP500 \u2019 , \u2019d \u2019 , . . .<\/p>\n
\u2019 retSP500 \u2019 ) ;<\/p>\n
[ c o e f f 3 , e r r o r s 3 , LLF3 , innovat ions3 , sigmas3 ] = . . .<\/p>\n
g a r c h f i t ( dataGSPCret ) ;<\/p>\n
sigmaGSPC = f i n t s (dataGSPC( : , 1 ) , sigmas3 \u2019 , \u2019 retSP500 \u2019 , . . .<\/p>\n
\u2019d \u2019 , \u2019 retSP500 \u2019 ) ;<\/p>\n
% Create a f i n a n c i a l ins t rument f o r each index with d a i l y p r i c e s<\/p>\n
tsFTSE=f i n t s (dataFTSE ( : , 1 ) ,dataFTSE ( : , end ) , . . .<\/p>\n
\u2019FTSE100 \u2019 , \u2019d \u2019 , \u2019FTSE100 \u2019 ) ;<\/p>\n
tsN225=f i n t s ( dataN225 ( : , 1 ) , dataN225 ( : , end ) , . . .<\/p>\n
\u2019NiKKEI225 \u2019 , \u2019d \u2019 , \u2019NiKKEI225 \u2019 ) ;<\/p>\n
tsGSPC=f i n t s (dataGSPC( : , 1 ) ,dataGSPC ( : , end ) , . . .<\/p>\n
\u2019 SP500 \u2019 , \u2019d \u2019 , \u2019 SP500 \u2019 ) ;<\/p>\n
% Pl o t s the index p r i c e s<\/p>\n
f i g u r e ( 1 ) ;<\/p>\n
subplot 31 1;<\/p>\n
pl o t ( tsFTSE) ;<\/p>\n
x l a b e l ( \u2019Time ( date ) \u2019 ) ;<\/p>\n
y l a b e l ( \u2019 Adjusted Close p r i c e ( $ ) \u2019 ) ;<\/p>\n
subplot 31 2;<\/p>\n
pl o t ( tsGSPC) ;<\/p>\n
x l a b e l ( \u2019Time ( date ) \u2019 ) ;<\/p>\n
y l a b e l ( \u2019 Adjusted Close p r i c e ( $ ) \u2019 ) ;<\/p>\n
subplot 31 3;<\/p>\n
pl o t ( tsN225 ) ;<\/p>\n
x l a b e l ( \u2019Time ( date ) \u2019 ) ;<\/p>\n
y l a b e l ( \u2019 Adjusted Close p r i c e ( $ ) \u2019 ) ;<\/p>\n
yt = ge t ( gca , \u2019YTick \u2019 ) ;<\/p>\n
s e t ( gca , \u2019YTickLabel \u2019 , s p r i n t f ( \u2019%.0 f | \u2019 , yt ) ) ;<\/p>\n
% Plot the r e turns and GARCH<\/p>\n
f i g u r e ( 2 ) ;<\/p>\n
subplot 31 1; hold on ;<\/p>\n
pl o t ( retFTSE) ; pl o t ( sigmaFTSE) ; hold o f f ;<\/p>\n
subplot 31 2; hold on ;<\/p>\n
pl o t ( retN225 ) ; pl o t ( sigmaN225 ) ; hold o f f ;<\/p>\n
subplot 31 3; hold on ;<\/p>\n
pl o t ( retGSPC) ; pl o t ( sigmaGSPC) ; hold o f f ;<\/p>\n
Matlab code for FTSE 100<\/p>\n
setdbprefs(‘DataReturnFormat’, ‘structure’)<\/p>\n
connection = database(‘SDE_Data’, ”, ”);<\/p>\n
cursor = exec(connection, ‘SELECT ALL Dates,Canada,France,Germany,Japan,UK,US,<\/p>\n
Euribor3M FROM Simulation_Data ORDER BY Dates ASC’);<\/p>\n
cursor = fetch(cursor);<\/p>\n
close(cursor), close(connection)<\/p>\n
SDE_Data = cursor.Data<\/p>\n
SDE_Data =<\/p>\n
Dates: [1359×1 double]<\/p>\n
Canada: [1359×1 double]<\/p>\n
France: [1359×1 double]<\/p>\n
Germany: [1359×1 double]<\/p>\n
Japan: [1359×1 double]<\/p>\n
UK: [1359×1 double]<\/p>\n
US: [1359×1 double]<\/p>\n
Euribor3M: [1359×1 double]<\/p>\n
fields = fieldnames(SDE_Data);<\/p>\n
dates = SDE_Data.Dates;<\/p>\n
countries = fields(2:end-1);<\/p>\n
yields = SDE_Data.Euribor3M; % daily effective yields<\/p>\n
yields = 360 * log(1 + yields); % continuous, annualized yields<\/p>\n
for i = length(countries):-1:1<\/p>\n
prices(:,i) = SDE_Data.(countries{i}); % daily closing prices<\/p>\n
end<\/p>\n
figure, plot(dates, ret2price(price2ret(prices))), datetick(‘x’)<\/p>\n
xlabel(‘Date’), ylabel(‘Index Value’), title (‘Normalized Daily Index Closings’)<\/p>\n
legend(countries, ‘Location’, ‘NorthWest’)<\/p>\n
figure, plot(dates, 100 * yields)<\/p>\n
datetick(‘x’), xlabel(‘Date’), ylabel(‘Annualized Yield (%)’)<\/p>\n
title(‘Risk Free Rate (3-Month Euribor Continuously-Compounded)’)<\/p>\n
Matlab code for estimating e-views<\/p>\n
n = 200; k = 3; evec = randn(n,1);<\/p>\n
xmat = [ones(n,1) randn(n,k)]; y = zeros(n,1); u = zeros(n,1);<\/p>\n
beta = ones(k,1); beta(1,1) = 10.0; % constant term<\/p>\n
for i=2:n; % generate a model with 1st order serial correlation<\/p>\n
u(i,1) = 0.4*u(i-1,1) + evec(i,1);<\/p>\n
y(i,1) = xmat(i,:)*beta + u(i,1);<\/p>\n
end;<\/p>\n
% truncate 1st 100 observations for startup<\/p>\n
yt = y(101:n,1); xt = xmat(101:n,:);<\/p>\n
n = n-100; % reset n to reflect truncation<\/p>\n
Vnames = strvcat(‘y’,’cterm’,’x2′,’x3′);<\/p>\n
result = ols(yt,xt); prt(result,Vnames); plt(result);<\/p>\n","protected":false},"excerpt":{"rendered":"
Econometric, Option Valuation Name Institution Date Course Mat lab code for Monte Carlo %%%%%%%%%% Option parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% S = 55;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-37873","post","type-post","status-publish","format-standard","hentry"],"yoast_head":"\n