Econometric, Option Valuation

Econometric, Option Valuation

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Institution

Date

Course

Mat lab code for Monte Carlo

%%%%%%%%%% Option parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

S = 55; % Value of the underlying

K = 50; % Strike (exercise price)

r = 0.05; % Risk free interest rate

sigma = 0.25; % Volatility

T = 3; % Time to expiry

%%%%%%%%%% Monte-Carlo Method Parameters %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

randn(’state’,0) % Repeatable trials on/off

M=1e7; % Number of Monte-Carlo trials

%%%%%%%%%% Use final values to compute

final_vals=S*exp((r-0.5*sigma^2)*T + sigma*sqrt(T)*randn(M,1));

option_values=max(K-final_vals,0); % Evaluate the Put option options

present_vals=exp(-r*T)*option_values; % Discount under r-n assumption

int=1.96*std(present_vals)/sqrt(M); % Compute confidence intervals

put_value=mean(present_vals); % Take the average

display(put_value)

display([put_value-int put_value+int])

Matlab code for data generating FTSE 100

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 %

% the FTSE100 , S&P500 , and NIKKEI225 i n d i c e s . %

% %

%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????%

% INPUTS: %

% % % This s c r i p t r e q u i r e s the Datastream Toolbox %

% %

% OUTPUTS: %

% % % 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 %

% 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 %

% 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 %

% s tandard de v i a t i on . % % %

%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????% % %

%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????% % Chr i s t o s De l i v o r i a s ???? OR MSc Student %

% The Uni v e r s i t y o f Edinburgh % % August 2012 %

%????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????%

% Clear e x i s t i n g data and f i g u r e s c l f ;

c l e a r a l l ;

c l o s e a l l ;

format sho r t ;

% Connect to Yahoo Finance and f e t c h data

Connect = yahoo ;

dataFTSE=f e t c h (Connect , ’^FTSE ’ , ’ Jan 1 1990 ’ , today , ’d ’ ) ;

dataN225=f e t c h (Connect , ’^N225 ’ , ’ Jan 1 1990 ’ , today , ’d ’ ) ;

dataGSPC=f e t c h (Connect , ’^GSPC’ , ’ Jan 1 1990 ’ , today , ’d ’ ) ;

c l o s e (Connect ) ;

% Ca l cul a t e d a i l y r e turns and GARCH SD f o r each index

dataFTSEret = [ 0 . 0 p r i c e 2 r e t (dataFTSE ( : , end ) ) ’ ] ;

retFTSE=f i n t s (dataFTSE ( : , 1 ) , dataFTSEret ’ , ’ retFTSE100 ’ , ’d ’ , . . .

’ retFTSE100 ’ ) ;

[ c o e f f 1 , e r r o r s 1 , LLF1 , innovat ions1 , sigmas1 ] = . . .

g a r c h f i t ( dataFTSEret ) ;

sigmaFTSE = f i n t s (dataFTSE ( : , 1 ) , sigmas1 ’ , ’ retFTSE100 ’ , . . .

’d ’ , ’ retFTSE100 ’ ) ;

dataN225ret = [ 0 . 0 p r i c e 2 r e t ( dataN225 ( : , end ) ) ’ ] ;

retN225=f i n t s ( dataN225 ( : , 1 ) , dataN225ret ’ , ’ retNIKKEI ’ , ’d ’ , . . .

’ retNIKKEI ’ ) ;

[ c o e f f 2 , e r r o r s 2 , LLF2 , innovat ions2 , sigmas2 ] = . . .

g a r c h f i t ( dataN225ret ) ;

sigmaN225 = f i n t s ( dataN225 ( : , 1 ) , sigmas2 ’ , ’ retNIKKEI ’ , . . .

v

’d ’ , ’ retNIKKEI ’ ) ;

dataGSPCret = [ 0 . 0 p r i c e 2 r e t (dataGSPC ( : , end ) ) ’ ] ;

retGSPC=f i n t s (dataGSPC( : , 1 ) , dataGSPCret ’ , ’ retSP500 ’ , ’d ’ , . . .

’ retSP500 ’ ) ;

[ c o e f f 3 , e r r o r s 3 , LLF3 , innovat ions3 , sigmas3 ] = . . .

g a r c h f i t ( dataGSPCret ) ;

sigmaGSPC = f i n t s (dataGSPC( : , 1 ) , sigmas3 ’ , ’ retSP500 ’ , . . .

’d ’ , ’ retSP500 ’ ) ;

% 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

tsFTSE=f i n t s (dataFTSE ( : , 1 ) ,dataFTSE ( : , end ) , . . .

’FTSE100 ’ , ’d ’ , ’FTSE100 ’ ) ;

tsN225=f i n t s ( dataN225 ( : , 1 ) , dataN225 ( : , end ) , . . .

’NiKKEI225 ’ , ’d ’ , ’NiKKEI225 ’ ) ;

tsGSPC=f i n t s (dataGSPC( : , 1 ) ,dataGSPC ( : , end ) , . . .

’ SP500 ’ , ’d ’ , ’ SP500 ’ ) ;

% Pl o t s the index p r i c e s

f i g u r e ( 1 ) ;

subplot 31 1;

pl o t ( tsFTSE) ;

x l a b e l ( ’Time ( date ) ’ ) ;

y l a b e l ( ’ Adjusted Close p r i c e ( $ ) ’ ) ;

subplot 31 2;

pl o t ( tsGSPC) ;

x l a b e l ( ’Time ( date ) ’ ) ;

y l a b e l ( ’ Adjusted Close p r i c e ( $ ) ’ ) ;

subplot 31 3;

pl o t ( tsN225 ) ;

x l a b e l ( ’Time ( date ) ’ ) ;

y l a b e l ( ’ Adjusted Close p r i c e ( $ ) ’ ) ;

yt = ge t ( gca , ’YTick ’ ) ;

s e t ( gca , ’YTickLabel ’ , s p r i n t f ( ’%.0 f | ’ , yt ) ) ;

% Plot the r e turns and GARCH

f i g u r e ( 2 ) ;

subplot 31 1; hold on ;

pl o t ( retFTSE) ; pl o t ( sigmaFTSE) ; hold o f f ;

subplot 31 2; hold on ;

pl o t ( retN225 ) ; pl o t ( sigmaN225 ) ; hold o f f ;

subplot 31 3; hold on ;

pl o t ( retGSPC) ; pl o t ( sigmaGSPC) ; hold o f f ;

Matlab code for FTSE 100

setdbprefs(‘DataReturnFormat’, ‘structure’)

connection = database(‘SDE_Data’, ”, ”);

cursor = exec(connection, ‘SELECT ALL Dates,Canada,France,Germany,Japan,UK,US,

Euribor3M FROM Simulation_Data ORDER BY Dates ASC’);

cursor = fetch(cursor);

close(cursor), close(connection)

SDE_Data = cursor.Data

SDE_Data =

Dates: [1359×1 double]

Canada: [1359×1 double]

France: [1359×1 double]

Germany: [1359×1 double]

Japan: [1359×1 double]

UK: [1359×1 double]

US: [1359×1 double]

Euribor3M: [1359×1 double]

fields = fieldnames(SDE_Data);

dates = SDE_Data.Dates;

countries = fields(2:end-1);

yields = SDE_Data.Euribor3M; % daily effective yields

yields = 360 * log(1 + yields); % continuous, annualized yields

for i = length(countries):-1:1

prices(:,i) = SDE_Data.(countries{i}); % daily closing prices

end

figure, plot(dates, ret2price(price2ret(prices))), datetick(‘x’)

xlabel(‘Date’), ylabel(‘Index Value’), title (‘Normalized Daily Index Closings’)

legend(countries, ‘Location’, ‘NorthWest’)

figure, plot(dates, 100 * yields)

datetick(‘x’), xlabel(‘Date’), ylabel(‘Annualized Yield (%)’)

title(‘Risk Free Rate (3-Month Euribor Continuously-Compounded)’)

Matlab code for estimating e-views

n = 200; k = 3; evec = randn(n,1);

xmat = [ones(n,1) randn(n,k)]; y = zeros(n,1); u = zeros(n,1);

beta = ones(k,1); beta(1,1) = 10.0; % constant term

for i=2:n; % generate a model with 1st order serial correlation

u(i,1) = 0.4*u(i-1,1) + evec(i,1);

y(i,1) = xmat(i,:)*beta + u(i,1);

end;

% truncate 1st 100 observations for startup

yt = y(101:n,1); xt = xmat(101:n,:);

n = n-100; % reset n to reflect truncation

Vnames = strvcat(‘y’,’cterm’,’x2′,’x3′);

result = ols(yt,xt); prt(result,Vnames); plt(result);