Discussion :

[Srabax9]

Bonjour à tous,

Je fais actuellement mon mémoire de fin d'étude avec une personne ne et pour cela nous aurions besoin d'utiliser un code Matlab mais nous souhaiterions le code sous Excel VBA.
Ne connaissant pas Matlab et étant mauvais en VBA nous aurions grandement besoin de votre aide.

Le code est assez long mais je le poste ici et je le rajoute dans un fichier joint sous Word.

Merci d'avance à vous,

Sébastien et Francis

Code Matlab :

Code MATLAB :

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A.1 main.m
%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -14
% Edited : 2013 -12 -03
%
% Purpose : Main script for calculation of CVA under :
% 1. Internal Model Method (IMM)
% 2. Current Exposure Method ( CEM )
%
% Parameters : None
%
% Return : None
%
% dbstop if error
close all
clear all
clc
% Start time measurement
tic
%% Set Constants and read data files
fprintf ('\ nDefining Constants and reading data files... \n\n')
global year numYears horizon scenarioIndex irData swapFile cemFile
dateStr = '2013 -11 -05 ';
dateFormat = 'yyyy -mm -dd ';
dataPath = '.\ data \';
irData = strcat ( dataPath ,'euribor.xls ');
swapFile = strcat ( dataPath ,' swap_portfolio.xls ');
cemFile = strcat ( dataPath ,'data_cem.xls ');
[ rating , ratingMap ] = func_read_rating_data ();
numSwaps = numel ( rating.CounterpartyID );
numCounterparties = max( rating.CounterpartyID );
Settle = datenum ( dateStr , dateFormat );
RateSpec = func_create_rate_spec ( Settle , false );
swapData = func_read_swap_data ( RateSpec );
stdCVAimm = struct ( ...
    'Horizon ' ,[], ...
    'Weights ' ,[], ...
    'Maturities ' ,[], ...
    'EAD ' ,[], ...
    ' SinglehPrincipal ' ,[], ...
    ' SinglehMaturities ' ,[], ...
    'IndexhWeights ' ,[], ...
    ' IndexhPrincipal ' ,[], ...
    ' IndexhMaturites ' ,[]);
% set time horizon
year = 365;
numYears = 5;
horizon = 1;
scenarioIndex = 200;
% set counterparty data and hedges
w = zeros ( numCounterparties ,1);
for i=1: numCounterparties
    w(i) = ratingMap ( rating.Rating {i ,1});
end
stdCVAimm.Weights = w;
stdCVAimm.SinglehPrincipal = zeros ( numCounterparties ,1);
stdCVAimm.SinglehMaturities = zeros ( numCounterparties ,1);
% set data for index hedges ( here : no hedges are used )
numInd = 1;
stdCVAimm.Horizon = horizon ;
stdCVAimm.IndexhWeights = zeros (numInd ,1);
stdCVAimm.IndexhPrincipal = zeros (numInd ,1);
stdCVAimm.IndexhMaturities = zeros ( numInd ,1);
stdCVAcem = stdCVAimm ;
% display time passed
toc
%% Compute CVA under IMM
fprintf ('\ nComputing CVA under IMM... \n\n')
numScenarios = 500;
alpha = 1.4;
[EPEcp , EffMaturities ] = func_imm_epe ( numScenarios , Settle , false );
stdCVAimm.Maturities = EffMaturities ;
stdCVAimm.EAD = alpha * EPEcp ;
[ IMM_CVAcp , IMM_CVAport ] = func_compute_cva ( stdCVAimm );
% display time passed
toc
%% Compute CVA under CEM
fprintf ('\ nComputing CVA under CEM... \n\n')
stdCVAcem.Maturities = func_cem_eff_maturity ( swapData , Settle );
stdCVAcem.EAD = func_cem_ead ( stdCVAcem.Maturities );
[ CEM_CVAcp , CEM_CVAport ] = func_compute_cva ( stdCVAcem );
%% Display Results
fprintf ('CVA for each counterparty under IMM ( SEK ):\n')
disp ( IMM_CVAcp )
fprintf ('CVA for entire portfolio under IMM (SEK ):\ n')
disp ( IMM_CVAport )
fprintf ('Effective maturities for each counterperty under IMM ( years ):\ n')
disp ( stdCVAimm.Maturities )
fprintf ('CVA for each counterparty under CEM ( SEK ):\n')
disp ( CEM_CVAcp )
fprintf ('CVA for entire portfolio under CEM (SEK ):\ n')
disp ( CEM_CVAport )
fprintf ('Effective maturities for each counterperty under CEM ( years ):\ n')
disp ( stdCVAcem.Maturities )
% display time passed
toc
fprintf ('\ nSimulation Successful !\n')
end

A.2 func read rating data.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -21
% Edited : 2013 -12 -03
%
% Function : func_read_rating _data.m
%
% Purpose : reads the rating data and rating to weight mapping
% from 'swapFile '
%
% Parameters : None
%
% Return : rating - the rating of each counterparty on the form
% 'AAA ', 'AA ', e.t.c...
% ratingMap - the rating map ; mapping every possible rating
% to specific numeric weight
%
% Examples :
%
%
%
function [ rating , ratingMap ] = func_read_rating_data ( )
global swapFile
mapData = dataset ( ...
    'XLSFile ', swapFile , ...
    'Sheet ', 'RatingMap ');
ratingData = dataset ( ...
    'XLSFile ', swapFile , ...
    'Sheet ', 'Rating ');
ratingMap = containers.Map ( ...
mapData.Rating , ...
mapData.Weight );
rating = struct ( ...
    ' CounterpartyID ' ,[], ...
    'Rating ' ,[]);
rating.CounterpartyID = ratingData.CounterpartyID ;
rating.Rating = ratingData.Rating ;
end

A.3 func create rate spec.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -11 -04
% Edited : 2013 -12 -03
%
% Function : func_create_rate_spec.m
%
% Purpose : Creates structures containing information of an interest
% rate term structure.
%
% Parameters : Settle - settlement date of swaps
% display_on - boolean which determines if the historical
% euribor rates should be displayed in a plot
% or not
%
% Return : RateSpec - structure containing properties of an
% interest term structure
% RateCurveObj - interest rate curve represented with data
% Tenor - vector containing the number of months
% where swap rates are specified
%
function [ RateSpec , RateCurveObj , Tenor ] = func_create_rate_spec ( Settle , display_on )
global swapFile
zeroCurveData = dataset ( ...
    'XLSFile ',swapFile , ...
    'Sheet ','Swap Curve ');
Tenor = 12* zeroCurveData.Years + zeroCurveData.Months ;
ZeroRates = zeroCurveData.Rate ;
ZeroDates = datemnth ( Settle , Tenor );
Compounding = -1;
Basis = 0;
RateSpec = intenvset (...
    'StartDates ', Settle , ...
    'EndDates ', ZeroDates , ...
    'Rates ', ZeroRates , ...
    'Compounding ',Compounding , ...
    'Basis ',Basis );
% Create an IRCurve object. We will use this for computing instantaneous
% forward rates during the calculation of the Hull - White short rate path.
RateCurveObj = IRDataCurve ( ...
    'Zero ',Settle , ZeroDates , ZeroRates , ...
    'Compounding ', Compounding , ...
    'Basis ', Basis );
if display_on
    figure ;
    plot ( ZeroDates , ZeroRates , 'o-');
    xlabel ('Date ');
    datetick ('keeplimits ');
    ylabel ('Zero rate '); grid on;
    title ('Yield Curve at Settle Date ');
end
end

A.4 func read swap data.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -21
% Edited : 2013 -12 -03
%
% Function : func_read_swap_data.m
%
% Purpose : reads the swap data from the global variable 'swapFile '
% and uses the RateSpec to set the fixed rate so that the
% swap price is zero at time 0
%
% Parameters : RateSpec - structure containing properties of an
% interest term structure
%
% Return : swaps - structure containing all necessary data to
% price the swap instruments
%
function [ swaps ] = func_read_swap_data ( RateSpec )
global swapFile
% Read swaps from spreadsheet
swapData = dataset ( ...
    'XLSFile ',swapFile , ...
    'Sheet ','Swap Portfolio Short ');
swaps = struct ( ...
    'Counterparty ' ,[], ...
    'NettingID ' ,[], ...
    'Principal ' ,[], ...
    'Maturity ' ,[], ...
    'LegRate ' ,[], ...
    'LegType ' ,[], ...
    ' LatestFloatingRate ' ,[], ...
    ' FloatingResetDates ' ,[]);
swaps.Counterparty = swapData.CounterpartyID ;
swaps.NettingID = swapData.NettingID ;
swaps.Principal = swapData.Principal ;
swaps.Maturity = datenum ( swapData.Maturity , 'yyyy -mm -dd ');
swaps.LegType = [ swapData.LegType ~ swapData.LegType ];
swaps.LegRate = [ swapData.LegRateReceiving swapData.LegRatePaying ];
swaps.LatestFloatingRate = swapData.LatestFloatingRate ;
swaps.Period = swapData.Period ;
swaps.LegReset = ones ( size ( swaps.LegType ));
%% Set the fixed rate so that the swap price initially is zero
numCounterparties = max( swaps.Counterparty );
for i=1: numCounterparties
    LegRate = [ NaN swapData.LegRatePaying (i )];
    [~, swapData.LegRateReceiving (i)] = ...
    swapbyzero (...
        RateSpec , ...
        LegRate , ...
        RateSpec.StartDates , ...
        swaps.Maturity (i),...
        swaps.LegReset (i ,:) , ...
        RateSpec.Basis , ...
        swaps.Principal (i), ...
        swaps.LegType (i ,:));
end
swaps.LegRate = [ swapData.LegRateReceiving swapData.LegRatePaying ];
end

A.5 func imm epe.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Date : 2013 -11 -05
%
% Function : func_imm_epe.m
%
% Purpose : Computes the expected positive exposure (EPE ) and effective
% maturity under IMM.
%
% Parameters : numScenarios - the number of interest rate scenario
% simulations performed
% Settle - the settlement date of the contracts given
% in MATLAB date number format
% print_on - boolean value indicating if function should
% print status messages when running
%
% Return : EPEcp - effective positive exposure per
% counterparty
% EffMaturity - effective maturity of each netting set
%
function [ EPEcp , EffMaturity ] = func_imm_epe ( numScenarios , Settle , print_on )
global irData numYears scenarioIndex
%% Create RateSpec from the Interest Rate Curve
if print_on
    fprintf ('Creating Rate Curve Object... \n\n')
end
[ RateSpec , RateCurveObj , Tenor ] = func_create_rate_spec ( Settle , false );
% ZeroDates = RateSpec.EndDates ;
%% Read Swap Portfolio
if print_on
    fprintf ('Reading Swap Portfolio... \n\n')
end
swaps = func_read_swap_data ( RateSpec );
numSwaps = numel ( swaps.Counterparty );
numCounterparties = max( swaps.Counterparty );
%% Set Simulation Parameters
if print_on
    fprintf ('Setting Simulation Parameter... \n\n')
end
% Compute monthly simulation dates , then quarterly dates later.
simDates = datemnth ( Settle ,0:1:(12* numYears )) ';
    numDates = numel ( simDates );
    %% Compute Floating Reset Dates
    if print_on
    fprintf ('Computing Floating Rates... \n\n')
end
floatDates = cfdates ( Settle -360 , swaps.Maturity , swaps.Period );
swaps.FloatingResetDates = zeros ( numSwaps , numDates );
for i = numDates : -1:1
    thisDate = simDates (i);
    floatDates ( floatDates > thisDate ) = 0;
    swaps.FloatingResetDates (:,i) = max ( floatDates ,[] ,2);
end
%% Read Euribor data
if print_on
    fprintf ('Reading EURIBOR Data... \n\n')
end
[num ,~ ,~] = xlsread ( irData );
% date_string = txt (2: end ,1);
% date = datenum ( date_string ,'yyyy -mm -dd ');
euribor_3m = num (: ,3);
% plot (date , euribor_3m );
% datetick ('x '), xlabel ('Date '), ylabel (' Annual Yield (%)
%% Fit model to data
if print_on
    fprintf ('Fitting Interest Rate Model Parameters To Data... \n\n')
end
yields = euribor_3m ;
regressors = [ ones ( length ( yields ) - 1, 1) yields (1: end -1)];
[ coefficients , ~, residuals ] = regress ( diff ( yields ), regressors );
% The time increment is set depending on the simulation date frequency
dt = mean ( diff ( simDates ));
% Alpha = Speed : mean - reversion speed
Alpha = - coefficients (2)/ dt;
% Level : mean - reversion level
% Level = - coefficients (1)/ coefficients (2);
% Sigma : instantaneous volatility rate
Sigma = nanstd ( residuals )/ sqrt (dt );
%% Setup Hull - White Single Factor Model
if print_on
    fprintf ('Setting up Hull - White Single Factor Model... \n\n')
end
r0 = RateCurveObj.getZeroRates ( Settle +1, 'Compounding ' , -1);
%r0 = swaps.LatestFloatingRate (1);
t0 = Settle ;
% Construct SDE object
FwdRates = RateCurveObj.getForwardRates (...
    t0 +1: max ( swaps.Maturity ), ...
    'Compounding ', -1);
hullwhite1 = hwv (...
    Alpha , ...
    @(t,x) func_hw_level (t0 ,t, FwdRates ,Alpha , Sigma ), ...
    Sigma , ...
    'StartState ',r0 );
% Store all model calibration information
calibration.RateCurveObj = RateCurveObj ;
calibration.Tenor = Tenor ;
calibration.ShortRateModel = hullwhite1 ;
calibration.Alpha = Alpha ;
calibration.Sigma = Sigma ;
%% Simulate Scenarios
if print_on
    fprintf ('Simulating Interest Rate Scenarios... \n\n')
end
% Use reproducible random number generator ( vary the seed to produce
% different random scenarios ).
prevRNG = rng (0);
% Compute interest rate scenarios are their respective discount factors
[ scenarios , dfactors ] = ...
hgenerateScenario ( ...
calibration ,...
simDates , ...
numScenarios );
% Restore random number generator state
rng ( prevRNG );
%% Inspect a Scenario
if print_on
    fprintf ('Plotting Yield Curve Evolution for Single Scenarios... \n\n')
end
figure ;
surf (Tenor , simDates , scenarios (: ,: , scenarioIndex ))
axis tight
datetick ('y','mmm yy ');
xlabel ('Tenor ( Months )');
ylabel ('Observation Date ');
zlabel ('Rates ');
set (gca ,'View ' ,[ -49 32]);
title ( sprintf ('Scenario %d Yield Curve Evolution \n', scenarioIndex ));
%% Compute Mark to Market Swap Prices
if print_on
    fprintf ('Computing Mark to Market Swap Prices... \n\n')
end
% Compute all mark -to - market values for this scenario. We use an
% approximation function here to improve performance.
values = hcomputeMTMValues (swaps , simDates , scenarios , Tenor );
% The swap value at time t=0 is not simulated , but set to zero.
% The fixed rate set above assures that the price at t=0 equals zero.
values (1 ,: ,:) = 0;
%% Inspect Scenario Prices
if print_on
    fprintf ('Displaying Single Scenario Prices... \n\n')
end
figure ;
plot ( simDates , values (:,:, scenarioIndex ));
datetick ;
ylabel ('Mark -To - Market Price ');
title ( sprintf ('Swap prices along scenario %d', scenarioIndex ));
%% Visualize Simulated Portfolio Values
if print_on
    fprintf ('Displaying Portfolio Value in all Scenarios... \n\n')
end
% View portfolio value over time
figure ;
totalPortValues = squeeze ( sum( values , 2));
plot ( simDates , totalPortValues );
title ('Total MTM Portfolio Value for All Scenarios ');
datetick ('x','mmm yy ')
ylabel ('Portfolio Value (SEK)')
xlabel ('Simulation Dates ')
%% Compute Exposure by Counterparty
if print_on
    fprintf ('Computing Exposures for each Counterparty... \n\n')
end
instrument_exposures = zeros ( size ( values ));
unnettedIdx = swaps.NettingID == 0;
instrument_exposures (:, unnettedIdx ,:) = max ( values (:, unnettedIdx ,:) ,0);
% We compute exposures per netting agreement , but in this case each
% counterparty has only a single netting agreement.
for i = 1: numCounterparties
    nettedIdx = swaps.NettingID == i;
    numInst = sum ( nettedIdx );
    % Exposures for instruments under netting agreements
    nettingSetValues = values (:, nettedIdx ,:);
    nettedExposure = max ( sum ( nettingSetValues ,2) ,0);
    positiveIdx = repmat ( nettedExposure > 0 ,[1 numInst ]);
    % Individual instrument contributions to netting set exposure
    instrument_exposures (:, nettedIdx ,:) = nettingSetValues .* positiveIdx ;
end
% Sum the instrument exposures for each counterparty
exposures = zeros ( numDates , numCounterparties , numScenarios );
for i = 1: numCounterparties
    cpSwapIdx = swaps.Counterparty == i;
    exposures (:,i ,:) = sum ( instrument_exposures (:, cpSwapIdx ,:) ,2);
end
% View portfolio exposure over time
figure ;
totalPortExposure = squeeze ( sum ( exposures ,2));
plot ( simDates , totalPortExposure );
title ('Portfolio Exposure for All Scenarios ');
datetick ('x','mmm yy ')
ylabel ('Exposure ( SEK )')
xlabel ('Simulation Dates ')
%% Exposure Profiles
if print_on
    fprintf ('Computing All Exposure Types... \n\n')
end
% Expected Exposure
EEcp = mean ( exposures ,3);
% Expected Positive Exposure : Weighted average over time of EE
% Here computed using a " trapezoidal " approach
simTimeInterval = yearfrac (Settle , simDates , 1);
simTotalTime = simTimeInterval ( end )- simTimeInterval (1);
EPEcp = 0.5 *( EEcp (1: end -1 ,:)+ EEcp (2: end ,:)) ' ...
* diff ( simTimeInterval )/ simTotalTime ;
% EPEport = 0.5 *( EEport (1: end -1)+ EEport (2: end ))' ...
% * diff ( simTimeInterval )/ simTotalTime ;
%% Compute effective maturity under IMM
EffMaturity = func_imm_eff_maturity ( simDates , dfactors , EEcp );
end

A.6 func imm eff maturity.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -28
% Edited : 2013 -12 -03
%
% Function : func_imm_epe.m
%
% Purpose : Computes the effective maturity under IMM
%
% Parameters : simDates - vector of simulation dates on MATLAB serial
% date form
% dFactors - vector of discount factors corresponding to
% the simulation dates
% EE - vectors of expected exposures corresponding to
% the simulation dates
%
% Return : effMaturity - the effective maturity under IMM
%
% Examples :
%
%
%
function [ effMaturity ] = func_imm_eff_maturity ( simDates , dFactors , EE)
global year horizon
% Effective Expected Exposure : Max EE up to time simTimeInterval
EEE = zeros ( size (EE ));
for i = 1: size (EE ,2)
    % Compute cumulative maximum
    m = EE (1,i);
    for j = 1: numel ( simDates )
        if EE(j,i) > m
            m = EE(j,i);
        end
        EEE (j,i) = m;
    end
end
DF = mean ( dFactors , 2);
DF = DF (2: end ,:);
EE = EE (2: end ,:);
EEE = EEE (2: end ,:);
dt = diff ( simDates ) / 365;
limit = simDates (1) + year ;
hIndex = find ( simDates > limit , 1, 'first ');
Numerator = EE( hIndex :end ,:) '*( DF( hIndex :end ,:) .*dt( hIndex :end ,:));
Denominator = EEE (1: hIndex -1 ,:) '*( DF (1: hIndex -1 ,:).*dt (1: hIndex -1 ,:));
effMaturity = horizon * (1 + Numerator. / Denominator );
end

A.7 func cem ead.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -21
% Edited : 2013 -12 -03
%
% Function : func_cem_ead.m
%
% Purpose : Computes the expected positive exposure (EPE ) and effective
% maturity under IMM.
%
% Parameters : Maturities - a vector of the maturities of all swap
% instruments
%
% Return : EAD - the exposure at default for each netting
% set ( each counterparty )
%
function [ EAD ] = func_cem_ead ( Maturities )
global swapFile cemFile
% Read data from spreadsheets
swapData = dataset ( ...
    'XLSFile ', swapFile ,...
    'Sheet ', 'Swap Portfolio ');
cemData = dataset ( ...
    'XLSFile ', cemFile ,...
    'Sheet ', 'CCF ');
% init structs
swaps = struct ( ...
    ' CounterpartyID ' ,[], ...
    'Principal ' ,[], ...
    'Maturity ' ,[]);
CCF = struct (...
    'Maturity ' ,[], ...
    'IR ' ,[], ...
    'FX ' ,[], ...
    'Equities ' ,[], ...
    'Metals ' ,[], ...
    'Other ' ,[]);
% fill structs with data
swaps.CounterpartyID = swapData.CounterpartyID ;
swaps.Principal = swapData.Principal ;
swaps.Maturity = datenum ( swapData.Maturity , 'yyyy -mm -dd ');
CCF.Maturity = cemData.Maturity ;
CCF.IR = cemData.InterestRate ;
CCF.FX = cemData.ForeignExchange ;
CCF.Equities = cemData.Equities ;
CCF.Metals = cemData.Metals ;
CCF.Other = cemData.Other ;
numSwaps = numel ( swaps.CounterpartyID );
numCounterparties = max( swaps.CounterpartyID );
rho = 0.85; % Basel value
CE = 0; % current exposure
Collateral = 0; % collateral
EAD = zeros ( numCounterparties ,1);
for i=1: numCounterparties
    PFE = [];
    MtM = [];
    for j=1: numSwaps
        if swaps.CounterpartyID (j) == i
            %
            MtM = [ MtM ; 0]; % MtM equals 0 at time 0
            if Maturities (j) < 1
                index = 1;
            elseif Maturities (j) < 5
                index = 2;
            else
                index = 3;
            end
            % potential future exposure (add -on)
            PFE = [ PFE ; swaps.Principal (j)* CCF.IR ( index )/100];
        end
    end
    % calculate NGR depending on MtM
    if sum ( MtM. ^2) == 0
        NGR = 1;
    elseif sum (max(MtM , 0)) == 0
        NGR = 0;
    else
        NGR = max ( sum ( MtM ), 0) / sum ( max (MtM , 0));
    end
    % compute EAD
    Addon = (1- rho + rho * NGR ) * sum ( PFE );
    EAD (i) = CE + Addon - Collateral ;
end
end

A.8 func cem eff maturity.m

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%
% Author : Otto Sjoholm and Dan Franzen
% Created : 2013 -10 -21
% Edited : 2013 -12 -03
%
% Function : func_cem_eff_maturity.m
%
% Purpose : Computes the effective maturity under CEM for the given
% swap maturities and principals
%
% Parameters : swapData - structure containing the information
% to price all swaps in the portfolio
% Settle - the settlement date for the swaps
%
% Return : eff_maturity - the effective maturity for each netting set
% under CEM
%
function [ eff_maturity ] = func_cem_eff_maturity ( swapData , Settle )
global year
contracts = struct ( ...
' CounterpartyID ' ,[], ...
'Principal ' ,[], ...
'Maturity ' ,[]);
contracts.CounterpartyID = swapData.NettingID ;
contracts.Principal = swapData.Principal ;
contracts.Maturity = ( swapData.Maturity - Settle ) / year ;
numCounterparties = max( contracts.CounterpartyID );
numContracts = length ( contracts.CounterpartyID );
eff_maturity = zeros ( numCounterparties ,1);
for i=1: numCounterparties
    maturities = [];
    principals = [];
    for j=1: numContracts
        if contracts.CounterpartyID (j) == i
            maturities = [ maturities ; contracts.Maturity (j)];
            principals = [ principals ; contracts.Principal (j )];
        end
    end
    eff_maturity (i) = max (1, ( maturities'* principals ) / (sum( principals )));
end
end

A.9 func hw level.m

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%
% Author : MathWorks
% Created : -
% Edited : -
%
% Function : func_hw_level.m
%
% Purpose : a built in matlab function to compute the mean - reversion
% level of the Hull - White / Vasicek mean - reverting Gaussian
% diffusion model
%
% Parameters : t0 - start time
% dt - time step
% FdwRates - vector of forward rates
% Alpha - mean - reversion speed
% Sigma - instantaneous volatility rate
%
% Return : level - mean reversion level of hwv model
%
function level = func_hw_level (t0 ,dt , FwdRates ,Alpha , Sigma )
% Compute the level function for the single factor Hull - White short rate
% model.
% Theta function
t = max (t0 + round (dt * 365) , t0 +1);
theta = Ft(t) + Alpha * F(t) + ( Sigma ^2/(2* Alpha )) * (1 - exp ( -2* Alpha *dt ));
% HW1 level is theta / alpha
level = theta / Alpha / 100;
function r = F(t)
% Instantaneous forward rate
r = FwdRates (t+1- t0 );
end
function dr = Ft(t)
% Derivative of the instantaneous forward rate w/ respect to time
Rates = FwdRates (t-t0:t+2- t0 );
dr = ( Rates (3) - Rates (2)) / (1/365);
end
end