7. Capitalized servicing assets

Changes in capitalized servicing assets were as follows:

	Residential Mortgage Loans									Commercial Mortgage Loans
For the Year Ended December 31,	2017			2016			2015			2017			2016			2015
	(In thousands)
Beginning balance	$	117,351		$	118,303		$	109,871		$	103,764		$	83,692		$	72,939
Originations		28,792			28,618			35,556			34,620			40,117			29,914
Purchases		699			638			243			—			—			—
Amortization		(31,864	)		(30,208	)		(27,367	)		(24,308	)		(20,045	)		(19,161	)
		114,978			117,351			118,303			114,076			103,764			83,692
Valuation allowance		—			—			—			—			—			—
Ending balance, net	$	114,978		$	117,351		$	118,303		$	114,076		$	103,764		$	83,692

	Other									Total
For the Year Ended December 31,	2017			2016			2015			2017			2016			2015
	(In thousands)
Beginning balance	$	—		$	729		$	4,107		$	221,115		$	202,724		$	186,917
Originations		—			—			—			63,412			68,735			65,470
Purchases		—			—			—			699			638			243
Amortization		—			(729	)		(3,378	)		(56,172	)		(50,982	)		(49,906	)
		—			—			729			229,054			221,115			202,724
Valuation allowance		—			—			—			—			—			—
Ending balance, net	$	—		$	—		$	729		$	229,054		$	221,115		$	202,724

Residential mortgage loans serviced for others were $22.6 billion at December 31, 2017, $22.8 billion at December 31, 2016 and $23.9 billion at December 31, 2015. Excluded from residential mortgage loans serviced for others were loans sub-serviced for others of $56.6 billion, $30.4 billion and $37.8 billion at December 31, 2017, 2016, and 2015, respectively. Commercial mortgage loans serviced for others were $13.6 billion at December 31, 2017, $11.8 billion at December 31, 2016 and $11.0 billion at December 31, 2015. Excluded from commercial mortgage loans serviced for others were loans sub-serviced for others of $2.6 billion at December 31, 2017.

The estimated fair value of capitalized residential mortgage loan servicing assets was approximately $234 million at December 31, 2017 and $235 million at December 31, 2016. The fair value of capitalized residential mortgage loan servicing assets was estimated using weighted-average discount rates of 12.2% at each of December 31, 2017 and 2016 and contemporaneous prepayment assumptions that vary by loan type. At December 31, 2017 and 2016, the discount rate represented a weighted-average option-adjusted spread (“OAS”) of 1,067 basis points (hundredths of one percent) and 1,095 basis points, respectively, over market implied forward London Interbank Offered Rates (“LIBOR”). The estimated fair value of capitalized residential mortgage loan servicing rights may vary significantly in subsequent periods due to changing interest rates and the effect thereof on prepayment speeds. The estimated fair value of capitalized commercial mortgage loan servicing assets was approximately $132 million and $119 million at December 31, 2017 and 2016, respectively. An 18% discount rate was used to estimate the fair value of capitalized commercial mortgage loan servicing rights at December 31, 2017 and 2016 with no prepayment assumptions because, in general, the servicing agreements allow the Company to share in customer loan prepayment fees and thereby recover the remaining carrying value of the capitalized servicing rights associated with such loan. The Company’s ability to realize the carrying value of capitalized commercial mortgage servicing rights is more dependent on the borrowers’ abilities to repay the underlying loans than on prepayments or changes in interest rates.

The key economic assumptions used to determine the fair value of significant portfolios of capitalized servicing rights at December 31, 2017 and the sensitivity of such value to changes in those assumptions are summarized in the table that follows. Those calculated sensitivities are hypothetical and actual changes in the fair value of capitalized servicing rights may differ significantly from the amounts presented herein. The effect of a variation in a particular assumption on the fair value of the servicing rights is calculated without changing any other assumption. In reality, changes in one factor may result in changes in another which may magnify or counteract the sensitivities. The changes in assumptions are presumed to be instantaneous.

	Residential			Commercial
Weighted-average prepayment speeds		12.16	%
Impact on fair value of 10% adverse change	$	(8,935,000	)
Impact on fair value of 20% adverse change		(17,159,000	)
Weighted-average OAS		10.67	%
Impact on fair value of 10% adverse change	$	(6,838,000	)
Impact on fair value of 20% adverse change		(13,267,000	)
Weighted-average discount rate					18.00	%
Impact on fair value of 10% adverse change				$	(5,885,000	)
Impact on fair value of 20% adverse change					(11,342,000	)