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Mortgage Servicing Assets (Tables)
 12 Months Ended
Dec. 31, 2017
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
2017
2016
Balance at beginning of period
$
356

$
322

Servicing retained from loan sales
110

80

Purchases
36

41

Amortization
(90
)
(87
)
Balance at end of period
$
412

$
356

Fair value at end of period
$
537

$
459

 
 
 
Changes in the carrying amount of residential mortgage servicing assets are summarized as follows:
in millions
2017
2016
Balance at beginning of period
$
28

—

Servicing retained from loan sales
7

$
2

Purchases
—

28

Amortization
(4
)
(2
)
Balance at end of period
$
31

$
28

Fair value at end of period
$
37

$
33

 
 
 
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, 2017, along with the valuation techniques, are shown in the following table:
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
December 31, 2017
Residential mortgage servicing assets
Discounted cash flow
Prepayment speed
9.16 - 51.52% (10.46%)
 
 
Discount rate
8.50 - 11.00% (8.54%)
 
 
Servicing cost
$76 - $4,385 ($83.11)
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
December 31, 2016
Residential mortgage servicing assets
Discounted cash flow
Prepayment speed
7.79 - 18.61% (9.42%)
 
 
Discount rate
8.50 - 11.00% (8.55%)
 
 
Servicing cost
$76 - $3,335 ($83.04)
The range and weighted-average of the significant unobservable inputs used to fair value our commercial mortgage servicing assets at December 31, 2017, and December 31, 2016, along with the valuation techniques, are shown in the following table:

 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
December 31, 2017
Commercial mortgage servicing assets
Discounted cash flow
Expected defaults
1.00 - 3.00% (1.20%)
 
 
Residual cash flows discount rate
7.00 - 15.00% (9.10%)
 
 
Escrow earn rate
0.90 - 3.10% (2.50%)
 
 
Servicing cost
$150 - $38,500 ($1,468)
 
 
Loan assumption rate
0.00 - 3.00% (1.22%)
 
 
Percentage late
0.00 - 1.30% (.25%)
 
Valuation Technique
Significant
Unobservable Input
Range
(Weighted-Average)
December 31, 2016
Commercial mortgage servicing assets
Discounted cash flow
Expected defaults
1.00 - 3.00% (1.40%)
 
 
Residual cash flows discount rate
7.00 - 12.00% (8.00%)
 
 
Escrow earn rate
1.10 - 3.00% (2.40%)
 
 
Servicing cost
$150 - $2,700 ($1,124)
 
 
Loan assumption rate
0.00 - 3.00% (1.13%)
 
 
Percentage late
0.00 - 2.00% (.34%)