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Mortgage Servicing Assets (Tables)
 12 Months Ended
Dec. 31, 2019
Servicing Asset [Abstract]  
Changes in Carrying Amount of Mortgage Servicing Assets
Changes in the carrying amount of commercial mortgage servicing assets are summarized as follows:
Year ended December 31,
in millions
2019
2018
Balance at beginning of period
$
502

$
412

Servicing retained from loan sales
108

117

Purchases
47

75

Amortization
(115
)
(102
)
Temporary impairments
(3
)
—

Balance at end of period
$
539

$
502

Fair value at end of period
$
665

$
757

 
 
 

Changes in the carrying amount of residential mortgage servicing assets are summarized as follows:
in millions
2019
2018
Balance at beginning of period
$
37

31

Servicing retained from loan sales
15

$
10

Purchases
—

—

Amortization
(6
)
(4
)
Balance at end of period
$
46

$
37

Fair value at end of period
$
50

$
52

 
 
 
Schedule of Range and Weighted-Average of Significant Unobservable Inputs The range and weighted-average of the significant unobservable inputs used to fair value our commercial mortgage servicing assets at December 31, 2019, and December 31, 2018, along with the valuation techniques, are shown in the following table:

dollars in millions
 
December 31, 2019
 
December 31, 2018
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
Discounted cash flow
Expected defaults
1.00 - 2.00% (1.13%)
 
1.00 - 2.00% (1.14%)
 
Residual cash flows discount rate
7.00 - 11.44% (9.32%)
 
7.00 - 15.00% (9.18%)
 
Escrow earn rate
1.44 - 2.32% (2.03%)
 
2.56 - 4.20% (3.35%)
 
Loan assumption rate
0.01 - 3.37% (1.37%)
 
0.00 - 3.22% (1.35%)
 
 
 
 
 
The range and weighted-average of the significant unobservable inputs used to fair value our residential mortgage servicing assets at December 31, 2019, along with the valuation techniques, are shown in the following table:
 
 
December 31, 2019
 
December 31, 2018
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
Discounted cash flow
Prepayment speed
10.38 - 61.51% (12.95%)
 
8.45 - 56.11% (9.08%)
 
Discount rate
7.50 - 8.50% (7.52%)
 
7.50 - 10.00% (7.54%)
 
Servicing cost
$62 - $4,375 ($68.73)
 
$62 - $5,125 ($68.25)