How to price Balloon Mortgage

%load_ext autoreload
%autoreload 2

from absbox import API

#localAPI = API("http://localhost:8081",lang='english',check=False)
localAPI = API("https://absbox.org/api/dev",lang='english',check=False)

Connecting engine server -> https://absbox.org/api/dev

/home/docs/checkouts/readthedocs.org/user_builds/absbox-doc/envs/stable/lib/python3.11/site-packages/urllib3/connectionpool.py:1097: InsecureRequestWarning: Unverified HTTPS request is being made to host 'absbox.org'. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#tls-warnings
  warnings.warn(

✅Connected, local lib:0.52.3, server:0.52.3

mortgage = ["Mortgage"
            ,{"originBalance": 12000.0
              ,"originRate": ["fix",0.045]
              ,"originTerm": 60
              ,"freq": "Monthly"
              ,"type": ("Balloon",120)
              ,"originDate": "2021-02-01"}
            ,{"currentBalance": 12000.0
              ,"currentRate": 0.075
              ,"remainTerm": 12
              ,"status": "Current"}]

Typical Cashflow Profile for Balloon Mortgage

We model the balloon mortgage via change type to ("Balloon, xxx)

Then the mortgage will amortized as if it has a term xxx and have a final principal repayment at last period

p = localAPI.runAsset("2021-02-01"
                      ,[mortgage]
                      ,poolAssump=("Pool"
                                    ,("Mortgage",None ,None, None, None)
                                     ,None
                                     ,None)
                      ,read=True)
p[0]

/home/docs/checkouts/readthedocs.org/user_builds/absbox-doc/envs/stable/lib/python3.11/site-packages/urllib3/connectionpool.py:1097: InsecureRequestWarning: Unverified HTTPS request is being made to host 'absbox.org'. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#tls-warnings
  warnings.warn(
Balance Principal Interest Prepayment Default Recovery Loss WAC BorrowerNum PrepayPenalty CumPrincipal CumPrepay CumDelinq CumDefault CumRecovery CumLoss
Date
2025-02-01 12000.00 0.00 0.00 0 0 0 0 0.075 None None 0.00 0 0 0 0 0
2025-03-01 11867.52 132.48 75.00 0 0 0 0 0.075 None None 132.48 0 0 0 0 0
2025-04-01 11734.21 133.31 74.17 0 0 0 0 0.075 None None 265.79 0 0 0 0 0
2025-05-01 11600.06 134.15 73.33 0 0 0 0 0.075 None None 399.94 0 0 0 0 0
2025-06-01 11465.08 134.98 72.50 0 0 0 0 0.075 None None 534.92 0 0 0 0 0
2025-07-01 11329.25 135.83 71.65 0 0 0 0 0.075 None None 670.75 0 0 0 0 0
2025-08-01 11192.57 136.68 70.80 0 0 0 0 0.075 None None 807.43 0 0 0 0 0
2025-09-01 11055.04 137.53 69.95 0 0 0 0 0.075 None None 944.96 0 0 0 0 0
2025-10-01 10916.65 138.39 69.09 0 0 0 0 0.075 None None 1083.35 0 0 0 0 0
2025-11-01 10777.39 139.26 68.22 0 0 0 0 0.075 None None 1222.61 0 0 0 0 0
2025-12-01 10637.26 140.13 67.35 0 0 0 0 0.075 None None 1362.74 0 0 0 0 0
2026-01-01 10496.26 141.00 66.48 0 0 0 0 0.075 None None 1503.74 0 0 0 0 0
2026-02-01 0.00 10496.26 65.60 0 0 0 0 0.075 None None 12000.00 0 0 0 0 0

When “CDR” is failing

CDR is a constant annualized default rates which apply default amounts on each payment period.

The CDR works if the monthly payment are evenly distributed, because the payment obligation remains same during the life time of a mortgage.

The issue is, for Balloon Mortgage , does the last payment which has a larger portion share same default rate with previous payments ?

Imagine a borrower has obligation of paying:

  • 10 dollars per month and 10000 dollars at last payment

The lender shall expect a larger risk at the last payment from the borrower, in other term, a larger default risk. In such case, the CDR way may doesn’t present a pefect fit.

p = localAPI.runAsset("2021-02-01"
                      ,[mortgage]
                      ,poolAssump=("Pool"
                                    ,("Mortgage",{"CDR":0.05} ,None, None, None)
                                     ,None
                                     ,None)
                      ,read=True)
p[0]

/home/docs/checkouts/readthedocs.org/user_builds/absbox-doc/envs/stable/lib/python3.11/site-packages/urllib3/connectionpool.py:1097: InsecureRequestWarning: Unverified HTTPS request is being made to host 'absbox.org'. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#tls-warnings
  warnings.warn(
Balance Principal Interest Prepayment Default Recovery Loss WAC BorrowerNum PrepayPenalty CumPrincipal CumPrepay CumDelinq CumDefault CumRecovery CumLoss
Date
2025-02-01 12000.00 0.00 0.00 0 0.00 0 0.00 0.075 None None 0.00 0 0 0.00 0 0.00
2025-03-01 11820.92 131.96 74.70 0 47.12 0 47.12 0.075 None None 131.96 0 0 47.12 0 47.12
2025-04-01 11637.33 132.21 73.55 0 51.38 0 51.38 0.075 None None 264.17 0 0 98.50 0 98.50
2025-05-01 11455.90 132.48 72.42 0 48.95 0 48.95 0.075 None None 396.65 0 0 147.45 0 147.45
2025-06-01 11273.38 132.73 71.28 0 49.79 0 49.79 0.075 None None 529.38 0 0 197.24 0 197.24
2025-07-01 11092.97 132.99 70.16 0 47.42 0 47.42 0.075 None None 662.37 0 0 244.66 0 244.66
2025-08-01 10911.50 133.25 69.02 0 48.22 0 48.22 0.075 None None 795.62 0 0 292.88 0 292.88
2025-09-01 10730.58 133.49 67.90 0 47.43 0 47.43 0.075 None None 929.11 0 0 340.31 0 340.31
2025-10-01 10551.68 133.76 66.78 0 45.14 0 45.14 0.075 None None 1062.87 0 0 385.45 0 385.45
2025-11-01 10371.81 134.01 65.66 0 45.86 0 45.86 0.075 None None 1196.88 0 0 431.31 0 431.31
2025-12-01 10193.90 134.28 64.55 0 43.63 0 43.63 0.075 None None 1331.16 0 0 474.94 0 474.94
2026-01-01 10015.06 134.53 63.43 0 44.31 0 44.31 0.075 None None 1465.69 0 0 519.25 0 519.25
2026-02-01 0.00 9971.53 62.32 0 43.53 0 43.53 0.075 None None 11437.22 0 0 562.78 0 562.78

Solution from Absbox/Hastructure

A new assumption with 2 default rates is introduced by (Hastructure: 0.28.18,/Absbox: 0.28.14),

{"DefaultAtEndByRate":(A,B)}

  • A : a CDR will be applied for payment periods except last period

    • default rate = days between ( current period , last period), then annualized with CDR

  • B : a CDR will be applied for last payment period

    • default rate = days between ( current period , BEGIN period), then annualized with CDR

Now we can expect a larger portion of default in last period which factoring the life time span. ( The longer life of mortgage, the larger default rate)

mortgagePoolAssump = ("Pool"
                        ,("Mortgage",{"DefaultAtEndByRate":(0.05,0.05)} ,None, None, None)
                         ,None
                         ,None)

p = localAPI.runAsset("2021-02-01"
                      ,[mortgage]
                      ,poolAssump=mortgagePoolAssump
                      ,read=True)
p[0]

/home/docs/checkouts/readthedocs.org/user_builds/absbox-doc/envs/stable/lib/python3.11/site-packages/urllib3/connectionpool.py:1097: InsecureRequestWarning: Unverified HTTPS request is being made to host 'absbox.org'. Adding certificate verification is strongly advised. See: https://urllib3.readthedocs.io/en/latest/advanced-usage.html#tls-warnings
  warnings.warn(
Balance Principal Interest Prepayment Default Recovery Loss WAC BorrowerNum PrepayPenalty CumPrincipal CumPrepay CumDelinq CumDefault CumRecovery CumLoss
Date
2025-02-01 12000.00 0.00 0.00 0 0.00 0 0.00 0.075 None None 0.00 0 0 0.00 0 0.00
2025-03-01 11820.92 131.96 74.70 0 47.12 0 47.12 0.075 None None 131.96 0 0 47.12 0 47.12
2025-04-01 11637.33 132.21 73.55 0 51.38 0 51.38 0.075 None None 264.17 0 0 98.50 0 98.50
2025-05-01 11455.90 132.48 72.42 0 48.95 0 48.95 0.075 None None 396.65 0 0 147.45 0 147.45
2025-06-01 11273.38 132.73 71.28 0 49.79 0 49.79 0.075 None None 529.38 0 0 197.24 0 197.24
2025-07-01 11092.97 132.99 70.16 0 47.42 0 47.42 0.075 None None 662.37 0 0 244.66 0 244.66
2025-08-01 10911.50 133.25 69.02 0 48.22 0 48.22 0.075 None None 795.62 0 0 292.88 0 292.88
2025-09-01 10730.58 133.49 67.90 0 47.43 0 47.43 0.075 None None 929.11 0 0 340.31 0 340.31
2025-10-01 10551.68 133.76 66.78 0 45.14 0 45.14 0.075 None None 1062.87 0 0 385.45 0 385.45
2025-11-01 10371.81 134.01 65.66 0 45.86 0 45.86 0.075 None None 1196.88 0 0 431.31 0 431.31
2025-12-01 10193.90 134.28 64.55 0 43.63 0 43.63 0.075 None None 1331.16 0 0 474.94 0 474.94
2026-01-01 10015.06 134.53 63.43 0 44.31 0 44.31 0.075 None None 1465.69 0 0 519.25 0 519.25
2026-02-01 0.00 9514.31 59.46 0 500.75 0 500.75 0.075 None None 10980.00 0 0 1020.00 0 1020.00