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Mortgage Servicing Assets (Tables)
 12 Months Ended
Dec. 31, 2018
Servicing Asset [Abstract]  
Changes in Carrying Amount of Mortgage Servicing Assets Changes in the carrying amount of residential mortgage servicing assets are summarized as follows:
in millions
2018
2017
Balance at beginning of period
$
31

28

Servicing retained from loan sales
10

$
7

Purchases
—

—

Amortization
(4
)
(4
)
Balance at end of period
$
37

$
31

Fair value at end of period
$
52

$
37

 
 
 

Changes in the carrying amount of commercial mortgage servicing assets are summarized as follows:
Year ended December 31,
in millions
2018
2017
Balance at beginning of period
$
412

$
356

Servicing retained from loan sales
117

110

Purchases
75

36

Amortization
(102
)
(90
)
Balance at end of period
$
502

$
412

Fair value at end of period
$
757

$
537

 
 
 
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 residential mortgage servicing assets at December 31, 2018, along with the valuation techniques, are shown in the following table:
 
 
December 31, 2018
 
December 31, 2017
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
Discounted cash flow
Prepayment speed
8.45 - 56.11% (9.08%)
 
9.16 - 51.52% (10.46%)
 
Discount rate
7.50 - 10.00% (7.54%)
 
8.50 - 11.00% (8.54%)
 
Servicing cost
$62 - $5,125 ($68.25)
 
$76 - $4,385 ($83.11)

The range and weighted-average of the significant unobservable inputs used to fair value our commercial mortgage servicing assets at December 31, 2018, and December 31, 2017, along with the valuation techniques, are shown in the following table:

dollars in millions
 
December 31, 2018
 
December 31, 2017
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
Discounted cash flow
Expected defaults
1.00 - 2.00% (1.14%)
 
1.00 - 3.00% (1.20%)
 
Residual cash flows discount rate
7.00 - 15.00% (9.18%)
 
7.00 - 15.00% (9.10%)
 
Escrow earn rate
2.56 - 4.20% (3.35%)
 
.90 - 3.10% (2.50%)
 
Loan assumption rate
0.00 - 3.22% (1.35%)
 
0.00 - 3.00% (1.22%)