www.gusucode.com > fininst 案例源码程序 matlab代码 > fininst/CreatePACandSequentialCMOExample.m

    %% Create PAC and Sequential CMO  
% This example shows how to use an underlying mortgage-backed security (MBS)
% pool for a 30-year fixed-rate mortgage of 6% to define a PAC bond, and
% then define a sequential CMO from the PAC bond. Analyze the CMO by comparing
% the CMO spread to a zero-rate curve for a 30-year Treasury bond and then
% calculate the weighted-average life (WAL) for the PAC bond.    

% Copyright 2015 The MathWorks, Inc.


%% Step 1. Define the underlying mortgage pool. 
principal = 100000000;
grossrate = 0.06;
coupon = 0.05;
originalTerm = 360;
termRemaining = 360;
speed = 100;
delay = 14;

Settle      = datenum('1-Jan-2011');
IssueDate   = datenum('1-Jan-2011');
Maturity    = addtodate(IssueDate, 360, 'month');  

%% Step 2. Calculate underlying pool cash flow. 
[CFlowAmounts, CFlowDates, ~, ~, ~, UnitPrincipal, UnitInterest, ...
UnitPrepayment] = mbscfamounts(Settle, Maturity, IssueDate, grossrate, ...
coupon, delay, speed, []);  

%% Step 3. Calculate prepayments. 
principalPayments = UnitPrincipal * principal;
netInterest = UnitInterest * principal;
prepayments = UnitPrepayment * principal;
dates = CFlowDates' + delay;  

%% Step 4. Generate a plot for underlying MBS payments. 
area([principalPayments'+prepayments', netInterest'])
title('Underlying MBS Payments');
legend('Principal Payments (incl. Prepayments)', 'Interest Payments')     

%% Step 5. Calculate the PAC schedule. 
pacSpeed = [80 300];
[balanceSchedule, pacInitBalance] = ...
cmosched(principal, grossrate, originalTerm, termRemaining, ...
pacSpeed, []);  

%% Step 6. Generate a plot for the PAC principal balance schedule. 
figure;
area([pacInitBalance'; balanceSchedule'])
title('PAC Principal Balance Schedule');
legend('Principal Balance Schedule');     

%% Step 7. Calculate PAC cash flow. 
pacTranchePrincipals = [pacInitBalance; principal-pacInitBalance];
pacTrancheCoupons = [0.05; 0.05];
[pacBalances, pacPrincipals, pacInterests] = ...
cmoschedcf(principalPayments+prepayments, ...
pacTranchePrincipals, pacTrancheCoupons, balanceSchedule);  

%% Step 8. Generate a plot for the PAC CMO tranches. 
% Generate a plot for the PAC CMO tranches: 
figure;
area([pacPrincipals' pacInterests']);
title('PAC CMO (PAC and Support Tranches)');
legend('PAC Principal Payments', 'Support Principal Payments', ...
'PAC Interest Payments', 'Support Interest Payments');     

%% Step 9. Create sequential CMO from the PAC bond. 
% CMO tranches, A, B, C, and D
seqTranchePrincipals = ...
[20000000; 20000000; 10000000; pacInitBalance-50000000];
seqTrancheCoupons = [0.05; 0.05; 0.05; 0.05];  

%% Step 10. Calculate cash flows for each tranche. 
[seqBalances, seqPrincipals, seqInterests] = ...
cmoseqcf(pacPrincipals(1, :), seqTranchePrincipals, ...
seqTrancheCoupons, false);  

%% Step 11. Generate a plot for the sequential PAC CMO. 
% Generate a plot for the sequential PAC CMO: 
figure
area([seqPrincipals' pacPrincipals(2, :)' pacInterests']);
title('Sequential PAC CMO (Sequential PAC and Support Tranches)');
legend('Sequential PAC Principals (A)', 'Sequential PAC Principals (B)', ...
'Sequential PAC Principals (C)', 'Sequential PAC Principals (D)', ...
'Support Principal Payments', 'PAC Interest Payments', ...
'Support Interest Payments');     

%% Step 12. Create the discount curve. 
CurveSettle = datenum('1-Jan-2011');
ZeroRates = [0.01 0.03 0.10 0.19 0.45 0.81 1.76 2.50 3.18 4.09 4.38]'/100;
CurveTimes = [1/12 3/12 6/12 1 2 3 5 7 10 20 30]';
CurveDates = daysadd(CurveSettle, 360 * CurveTimes, 1);
zeroCurve = intenvset('Rates', ZeroRates, 'StartDates', CurveSettle, ...
'EndDates', CurveDates);  

%% Step 13. Price the CMO cash flows. 
% The cash flow for the sequential PAC principal A tranche is calculated
% using the cash flow functions |cfbyzero|, |cfyield|, |cfprice|, and |cfspread|. 
cflows = seqPrincipals(1, :)+seqInterests(1, :);
cfdates = dates(2:end)';
price1 = cfbyzero(zeroCurve, cflows, cfdates, Settle, 4)
yield = cfyield(cflows, cfdates, price1, Settle, 'Basis', 4)
price2 = cfprice(cflows, cfdates, yield, Settle, 'Basis', 4)
spread = cfspread(zeroCurve, price2, cflows, cfdates, Settle, 'Basis', 4)
WAL = sum(cflows .* yearfrac(Settle, cfdates, 4)) / sum(cflows) 

%%
% The weighted average life (WAL) for the sequential PAC principal A tranche
% is 2.54 years.