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.