Fair Value

(a) Fair Value of Financial Instrument Assets

The fair value hierarchy prioritizes the inputs to valuation techniques used to measure fair value by maximizing the use of observable inputs and minimizing the use of unobservable inputs by requiring that the most observable inputs be used when available. Observable inputs are inputs that market participants would use in pricing an asset or liability based on market data obtained from sources independent of the Company. Unobservable inputs are inputs that reflect the Company’s assumptions about what market participants would use in pricing the asset or liability based on the best information available in the circumstances. The level in the hierarchy within which a given fair value measurement falls is determined based on the lowest level input that is significant to the measurement.

The Company determines the appropriate level in the hierarchy for each financial instrument that it measures at fair value. In determining fair value, the Company uses various valuation approaches, including market, income and cost approaches. The hierarchy is broken down into three levels based on the observability of inputs as follows:


•	Level 1 inputs—Unadjusted, quoted prices in active markets for identical assets or liabilities that the Company has the ability to access.

The Company’s financial instruments that it measures at fair value using Level 1 inputs generally include equities listed on a major exchange.


•	Level 2 inputs—Quoted prices in active markets for similar assets or liabilities, quoted prices for identical or similar assets or liabilities in inactive markets and significant directly or indirectly observable inputs, other than quoted prices, used in industry accepted models.

The Company’s financial instruments that it measures at fair value using Level 2 inputs generally include: U.S. government issued bonds; U.S. government sponsored enterprises bonds; certain U.S. state, territory and municipal entities bonds; non-U.S. sovereign government, supranational and government related bonds; investment grade and high yield corporate bonds; asset-backed securities; mortgage-backed securities; short-term investments; certain common and preferred equities; foreign exchange forward contracts; foreign currency option contracts; and interest rate swaps..


•	Level 3 inputs—Unobservable inputs.

The Company’s financial instruments that it measures at fair value using Level 3 inputs generally include: inactively traded fixed maturities including U.S. state, territory and municipal bonds; special purpose financing asset-backed bonds; unlisted or private equities; certain other mutual fund equities; privately placed corporate loans, notes and loans receivable and notes securitizations included in Other invested assets; and certain other derivatives, including weather derivatives, longevity insurance-linked securities and total return swaps included in Other invested assets.

At December 31, 2019 and 2018, the Company’s financial instruments measured at fair value were classified between Levels 1, 2 and 3 as follows (in thousands of U.S. dollars):



December 31, 2019	Quoted prices in active markets for identical assets (Level 1)		Significant other observable inputs (Level 2)			Significant unobservable inputs (Level 3)			Total
Fixed maturities
U.S. government and government sponsored enterprises	$	—	$	1,421,716		$	—		$	1,421,716
U.S. states, territories and municipalities	—		13,807			143,427			157,234
Non-U.S. sovereign government, supranational and government related	—		3,255,154			—			3,255,154
Corporate bonds	—		2,643,402			18,687			2,662,089
Asset-backed securities	—		—			18,228			18,228
Residential mortgage-backed securities	—		3,166,290			—			3,166,290
Other mortgage-backed securities	—		3			—			3
Fixed maturities	$	—	$	10,500,372		$	180,342		$	10,680,714
Short-term investments	$	—	$	1,003,421		$	—		$	1,003,421
Equities
Finance	$	31,315	$	2		$	126		$	31,443
Consumer cyclical	20,117		—			—			20,117
Insurance	5,284		273			9,403			14,960
Consumer noncyclical	13,126		—			—			13,126
Basic materials	5,295		—			—			5,295
Industrials	4,042		—			—			4,042
Technology	3,027		—			—			3,027
Real estate	—		—			2,385			2,385
Communications	922		—			—			922
Mutual funds	—		—			1,199,847			1,199,847
Equities	$	83,128	$	275		$	1,211,761		$	1,295,164
Other invested assets
Derivative assets
Foreign exchange forward contracts	$	—	$	4,363		$	—		$	4,363
Total return swaps	—		—			1,448			1,448
Insurance-linked securities	—		—			2,728			2,728
Foreign currency option contracts	—		266			—			266
Other
Corporate loans ⁽¹⁾	—		—			1,879,105			1,879,105
Notes and loans receivable and notes securitization	—		—			3,085			3,085
Private equities	—		—			533,744			533,744
Derivative liabilities
Foreign exchange forward contracts	—		(5,643		)	—			(5,643		)
Total return swaps	—		—			(2,962		)	(2,962		)
Interest rate swaps	—		(12,378		)	—			(12,378		)
Insurance-linked securities	—		—			(3,871		)	(3,871		)
Other invested assets	$	—	$	(13,392	)	$	2,413,277		$	2,399,885
Total	$	83,128	$	11,490,676		$	3,805,380		$	15,379,184

(1)

Corporate loans includes a portfolio of third-party, individually managed privately issued corporate loans that are managed under an externally managed mandate with a fair value of $1.4 billion and $0.4 billion at December 31, 2019 and 2018, respectively. The mandate primarily invests in U.S. floating rate, first lien, senior secured broadly syndicated loans with a focus on facility sizes greater than $300 million. Corporate loans also includes $0.5 billion of other privately issued corporate loans at December 31, 2019.



December 31, 2018	Quoted prices in active markets for identical assets (Level 1)		Significant other observable inputs (Level 2)			Significant unobservable inputs (Level 3)			Total
Fixed maturities
U.S. government and government sponsored enterprises	$	—	$	2,345,008		$	—		$	2,345,008
U.S. states, territories and municipalities	—		13,695			120,898			134,593
Non-U.S. sovereign government, supranational and government related	—		2,158,642			—			2,158,642
Corporate bonds	—		5,590,208			21,470			5,611,678
Asset-backed securities	—		41,087			17,596			58,683
Residential mortgage-backed securities	—		2,331,230			—			2,331,230
Other mortgage-backed securities	—		11			—			11
Fixed maturities	$	—	$	12,479,881		$	159,964		$	12,639,845
Short-term investments ⁽¹⁾	$	—	$	493,726		$	—		$	493,726
Equities
Finance	$	11,307	$	1		$	13,710		$	25,018
Technology	5,492		—			12,256			17,748
Consumer noncyclical	13,334		—			—			13,334
Consumer cyclical	6,435		—			—			6,435
Industrials	4,797		—			—			4,797
Insurance	1,771		1,189			—			2,960
Communications	1,451		—			—			1,451
Other	799		—			—			799
Mutual funds	—		—			621,759			621,759
Equities	$	45,386	$	1,190		$	647,725		$	694,301
Other invested assets
Derivative assets
Foreign exchange forward contracts	$	—	$	17,820		$	—		$	17,820
Insurance-linked securities	—		—			2,824			2,824
Total return swaps	—		—			1,697			1,697
Interest rate swaps	—		10			—			10
Other
Corporate loans	—		—			401,702			401,702
Notes and loans receivable and notes securitization	—		—			6,507			6,507
Private equities	—		—			372,710			372,710
Derivative liabilities
Foreign exchange forward contracts	—		(3,673		)	—			(3,673		)
Total return swaps	—		—			(3,232		)	(3,232		)
Interest rate swaps	—		(9,194		)	—			(9,194		)
Insurance-linked securities	—		—			(2,568		)	(2,568		)
Other invested assets	$	—	$	4,963		$	779,640		$	784,603
Total	$	45,386	$	12,979,760		$	1,587,329		$	14,612,475


(1)	Short-term investments includes $229 million of available-for-sale securities with readily determinable fair values. These securities were purchased in 2018 and are recorded at fair value, which approximated amortized cost given the short term to maturity of approximately three to four months, and matured during 2019.

At December 31, 2019 and 2018, the aggregate carrying amounts of items included in Other invested assets that the Company did not measure at fair value were $866 million and $704 million, respectively, which related to the Company’s investments that are accounted for using the equity method of accounting. Refer to Note 4(f) for further information on the Company's equity method investment in Almacantar Group S.A. (Almacantar).

At December 31, 2019 and 2018, the carrying value of accrued investment income approximated fair value due to its short-term nature.

During the year ended December 31, 2019, an equity security issued by a financial services company valued at $14 million was transferred from Level 3 to Level 1 due to the availability of quoted prices in active markets. During the year ended December 31, 2018, a corporate longevity bond valued at $25 million was transferred from Level 2 to Level 3 due to the lack of multiple independent pricing services. Transfers into Level 3 during 2018 also included four private equity securities valued at $31 million that were previously held at cost and were measured to fair value upon adoption of new accounting guidance. During the years ended December 31, 2019 and 2018, there were no transfers between Level 1 and Level 2.

Disclosures about the fair value of financial instruments that the Company does not measure at fair value exclude insurance contracts and certain other financial instruments. At December 31, 2019 and 2018, the fair values of financial instrument assets recorded in the Consolidated Balance Sheets not described above approximate their carrying values.

The reconciliations of the beginning and ending balances for financial instruments measured at fair value using Level 3 inputs for the years ended December 31, 2019 and 2018, were as follows (in thousands of U.S. dollars):



For the year ended December 31, 2019	Balance at beginning of year			Realized and unrealized investment gains (losses) included in net income			Purchases			Settlements and sales ⁽¹⁾			Net transfers (out of) into Level 3			Balance at end of year			Change in unrealized investment gains (losses) relating to assets held at end of year
Fixed maturities
U.S. states, territories and municipalities	$	120,898		$	12,959		$	10,455		$	(885	)	$	—		$	143,427		$	12,951
Asset-backed securities	17,596			1,274			—			(642		)	—			18,228			1,274
Corporate	21,470			157			—			(2,940		)	—			18,687			157
Fixed maturities	$	159,964		$	14,390		$	10,455		$	(4,467	)	$	—		$	180,342		$	14,382
Equities
Finance	$	13,710		$	100		$	—		$	—		$	(13,684	)	$	126		$	(3	)
Technology	12,256			(1,538		)	—			(10,718		)	—			—			—
Mutual funds	621,759			388,024			206,685			(16,621		)	—			1,199,847			385,317
Insurance	—			7,514			1,889			—			—			9,403			7,514
Real estate	—			—			2,385			—			—			2,385			—
Equities	$	647,725		$	394,100		$	210,959		$	(27,339	)	$	(13,684	)	$	1,211,761		$	392,828
Other invested assets
Derivatives, net	$	(1,279	)	$	115		$	(2,000	)	$	507		$	—		$	(2,657	)	$	(111	)
Corporate loans	401,702			9,237			1,828,802			(360,636		)	—			1,879,105			9,940
Notes and loan receivables and notes securitization	6,507			(717		)	—			(2,705		)	—			3,085			139
Private equities	372,710			49,759			132,256			(20,981		)	—			533,744			37,159
Other invested assets	$	779,640		$	58,394		$	1,959,058		$	(383,815	)	$	—		$	2,413,277		$	47,127
Total	$	1,587,329		$	466,884		$	2,180,472		$	(415,621	)	$	(13,684	)	$	3,805,380		$	454,337


(1)	Settlements and sales of Equities and Other invested assets included sales of $27 million and $289 million, respectively. Sales of Other invested assets of $289 million included sales of corporate loans of $270 million, notes and loan receivables and notes securitization of $2 million, and private equities of $17 million.



For the year ended December 31, 2018	Balance at beginning of year		Realized and unrealized investment (losses) gains included in net income			Purchases			Settlements and sales ⁽¹⁾			Net transfers into (out of) Level 3		Balance at end of year			Change in unrealized investment (losses) gains relating to assets held at end of year
Fixed maturities
U.S. states, territories and municipalities	$	128,806	$	(4,417	)	$	—		$	(3,491	)	$	—	$	120,898		$	(4,320	)
Asset-backed securities	20,738		(2,552		)	—			(590		)	—		17,596			(2,552		)
Corporate	—		(139		)	—			(3,745		)	25,354		21,470			(139		)
Fixed maturities	$	149,544	$	(7,108	)	$	—		$	(7,826	)	$	25,354	$	159,964		$	(7,011	)
Equities
Finance	$	21,926	$	5,065		$	—		$	(13,281	)	$	—	$	13,710		$	(3,544	)
Technology	10,961		1,295			—			—			—		12,256			1,295
Mutual funds	558,736		10,996			55,027			(3,000		)	—		621,759			10,996
Equities	$	591,623	$	17,356		$	55,027		$	(16,281	)	$	—	$	647,725		$	8,747
Other invested assets
Derivatives, net	$	11,221	$	5,038		$	(1,623	)	$	(15,915	)	$	—	$	(1,279	)	$	372
Corporate loans	205,331		(21,522		)	367,975			(150,082		)	—		401,702			(20,823		)
Notes and loan receivables and notes securitization	108,563		(4,054		)	—			(98,002		)	—		6,507			(3,884		)
Private equities	331,932		(12,422		)	55,114			(32,994		)	31,080		372,710			(15,048		)
Other invested assets	$	657,047	$	(32,960	)	$	421,466		$	(296,993	)	$	31,080	$	779,640		$	(39,383	)
Funds held–directly managed	$	2,067	$	238		$	268		$	(2,573	)	$	—	$	—		$	—
Total	$	1,400,281	$	(22,474	)	$	476,761		$	(323,673	)	$	56,434	$	1,587,329		$	(37,647	)


(1)	Settlements and sales of Equities, Other invested assets, and Funds held–directly managed included sales of $16 million, $248 million and $3 million, respectively. Sales of Other invested assets of $248 million included sales of derivatives of $16 million, corporate loans of $107 million, notes and loan receivables and notes securitization of $96 million, and private equities of $29 million.

The significant unobservable inputs used in the valuation of financial instruments measured at fair value using Level 3 inputs at December 31, 2019 and 2018 were as follows (fair value in thousands of U.S. dollars):



December 31, 2019	Fair value			Valuation techniques	Unobservable inputs	Range (Weighted average)
Fixed maturities
U.S. states, territories and municipalities	$	143,427		Discounted cash flow	Credit spreads	-0.1% – 9.6% (3.5%)
Asset backed securities	18,228			Discounted cash flow	Credit spreads	4.7% (4.7%)
Equities
Insurance	9,403			Weighted market comparables	Revenue multiple	2.6x (2.6x)
					Adjusted earnings multiple	7.7x (7.7x)
					Liquidity discount	30.0% (30.0%)
Other invested assets
Total return swaps, net	(1,514		)	Discounted cash flow	Credit spreads	2.3% – 24.0% (16.9%)
Insurance-linked securities – longevity swaps	2,728			Discounted cash flow	Credit spreads	1.9% (1.9%)
Insurance-linked securities – pandemic swaps	(1,871		)	Discounted cash flow	Credit spreads	56.2% (56.2%)
Notes and loans receivables	2,153			Discounted cash flow	Credit spreads	17.5% (17.5%)
					Gross revenue/fair value ratios	1.1 (1.1)
Note securitization	932			Discounted cash flow	Credit spreads	1.2% (1.2%)
Private equity – other	15,800			Discounted cash flow	Effective yield	3.0% (3.0%)
Private equity – funds	167,804			Lag reported market value	Net asset value, as reported	100.0% (100.0%)
				Lag reported market value	Market adjustments	1.9% – 15.0% (9.7%)



December 31, 2018	Fair value			Valuation techniques	Unobservable inputs	Range (Weighted average)
Fixed maturities
U.S. states, territories and municipalities	$	120,898		Discounted cash flow	Credit spreads	0.2% – 10.2% (4.3%)
Asset backed securities	17,596			Discounted cash flow	Credit spreads	6.7% (6.7%)
Equities
Finance⁽¹⁾	13,710			Lag reported market value	Transaction price	12.0 (12.0)
Technology	12,256			Reported market value	Tangible book value multiple	1.0 (1.0)
Other invested assets
Total return swaps, net	(1,535		)	Discounted cash flow	Credit spreads	2.5% – 23.0% (16.0%)
Insurance-linked securities – longevity swaps	2,824			Discounted cash flow	Credit spreads	2.6% (2.6%)
Insurance-linked securities – pandemic swaps	(1,301		)	Discounted cash flow	Credit spreads	27.3% (27.3%)
Insurance-linked securities – weather index swap	(1,267		)	Proprietary option model	Index value (temperature)	80.7 – 3,293.8 (175.3)
Notes and loans receivable	2,660			Discounted cash flow	Credit spreads	41.5% – 41.9% (41.5%)
Notes and loans receivable	2,688			Discounted cash flow	Credit spreads	17.5% (17.5%)
Notes and loans receivable				Discounted cash flow	Gross revenue/fair value ratios	1.1 (1.1)
Note securitization	1,159			Discounted cash flow	Credit spreads	0.8% (0.8%)
Private equity – direct	1,889			Weighted market comparables	Revenue multiple	1.1 (1.1)
					Adjusted earnings multiple	9.8 (9.8)
					Liquidity discount	30% (30%)
Private equity – funds	14,438			Reported market value	Net asset value, as reported	100.0% (100.0%)
				Reported market value	Market adjustments	-6.5% (-6.5%)
Private equity – other	19,997			Discounted cash flow	Effective yield	4.1% (4.1%)

(1) During 2018, the Company sold a portion of its investment and used the arm's length transaction price as an estimate of the fair value of the remaining holdings.

The tables above do not include financial instruments that are measured using unobservable inputs (Level 3) where the unobservable inputs were obtained from external sources and used without adjustment. These financial instruments include corporate bonds (included within Fixed maturities), certain common stock equities and mutual fund investments (included within Equities), certain private equity funds (private equities included within Other invested assets), privately placed corporate loans (included within Other invested assets) and certain derivatives (included within Other invested assets).

The Company has established a Valuation Committee which is responsible for determining the Company’s invested asset valuation procedures, reviewing significant changes in the fair value measurements of securities classified as Level 3 and ensuring that there is appropriate oversight, on at least an annual basis, of the fair value measurements of significant securities that are classified as Level 3. The Valuation Committee is comprised of members of the Company’s senior management team.

Changes in the fair value of the Company’s financial instruments subject to the fair value option during the years ended December 31, 2019, 2018 and 2017 were as follows (in thousands of U.S. dollars):



	2019		2018			2017
Fixed maturities and short-term investments	$	190,343	$	(150,926	)	$	124,033
Equities	403,011		2,791			60,460
Other invested assets	50,857		(12,987		)	28,144
Funds held–directly managed ⁽¹⁾	—		(6,484		)	(5,612		)
Total	$	644,211	$	(167,606	)	$	207,025

(1) The funds held–directly managed account was settled in 2018 upon commutation of the related Paris Re Reserve Agreement. See Note 7(a).

Substantially all of the above changes in fair value are included in Net realized and unrealized investment gains (losses) in the Consolidated Statements of Operations. The change in the fair value of Other invested assets subject to the fair value option does not include certain derivatives.

The following methods and assumptions were used by the Company in estimating the fair value of each class of financial instrument recorded in the Consolidated Balance Sheets. There have been no material changes in the Company’s valuation techniques during the periods presented.

Fixed maturities

•

U.S. government and government sponsored enterprises—consists primarily of bonds issued by the U.S. Treasury and corporate debt securities issued by government sponsored enterprises and federally owned or established corporations. These securities are generally priced by independent pricing services. The independent pricing services may use actual transaction prices for securities that have been actively traded. For securities that have not been actively traded, each pricing source has its own proprietary method to determine the fair value, which may incorporate option adjusted spreads (OAS), interest rate data and market news. The Company generally classifies these securities in Level 2.

•

U.S. states, territories and municipalities—consists primarily of bonds issued by U.S. states, territories and municipalities and the Federal Home Loan Mortgage Corporation. Certain of the bonds that are issued by municipal housing authorities and the Federal Home Loan Mortgage Corporation are not actively traded and are priced based on internal models using unobservable inputs (credit spreads). Accordingly, the Company classifies these securities in Level 3. A significant increase (decrease) in credit spreads in isolation could result in a significantly lower (higher) fair value measurement. The remaining securities are generally priced by independent pricing services using the techniques described for U.S. government and government sponsored enterprises above. The Company generally classifies these securities in Level 2.

•

Non-U.S. sovereign government, supranational and government related—consists primarily of bonds issued by non-U.S. national governments and their agencies, non-U.S. regional governments and supranational organizations. These securities are generally priced by independent pricing services using the techniques described for U.S. government and government sponsored enterprises above. The Company generally classifies these securities in Level 2.

•

Corporate—consists primarily of bonds issued by U.S. and foreign corporations covering a variety of industries and issuing countries. Corporate securities also include real estate investment trusts, catastrophe bonds, longevity and mortality bonds and government guaranteed corporate debt. These securities are generally priced by independent pricing services and brokers. The pricing provider incorporates information including credit spreads, interest rate data and market news into the valuation of each security. The Company generally classifies these securities in Level 2. When a corporate security is inactively traded or the valuation model uses unobservable inputs, the Company classifies the security in Level 3.

•

Asset-backed securities—primarily consists of bonds issued by U.S. and foreign corporations that are predominantly backed by student loans, automobile loans, credit card receivables, equipment leases, and special purpose financing. With the exception of special purpose financing securities, these asset-backed securities are generally priced by independent pricing services and brokers. The pricing provider applies dealer quotes and other available trade information, prepayment speeds, yield curves and credit spreads to the valuation. The Company generally classifies these securities in Level 2. Special purpose financing securities are generally inactively traded and are priced based on valuation models using unobservable inputs (credit spreads). The Company generally classifies these securities in Level 3. A significant increase (decrease) in credit spreads in isolation could result in a significantly lower (higher) fair value measurement.

•

Residential mortgage-backed securities—primarily consists of bonds issued by the Government National Mortgage Association, the Federal National Mortgage Association, the Federal Home Loan Mortgage Corporation, as well as private, non-agency issuers. These residential mortgage-backed securities are generally priced by independent pricing services and brokers. When current market trades are not available, the pricing provider or the Company will employ proprietary models with observable inputs including other trade information, prepayment speeds, yield curves and credit spreads. The Company generally classifies these securities in Level 2.


•	Other mortgage-backed securities—primarily consists of commercial mortgage-backed securities. These securities are generally priced by independent pricing services and brokers. The pricing provider applies dealer quotes and other available trade information, prepayment speeds, yield curves and credit spreads to the valuation. The Company generally classifies these securities in Level 2.

In general, the methods employed by the independent pricing services to determine the fair value of the securities that have not been actively traded primarily involve the use of “matrix pricing” in which the independent pricing source applies the credit spread for a comparable security that has traded recently to the current yield curve to determine a reasonable fair value. The Company generally uses one pricing source per security and uses a pricing service ranking to consistently select the most appropriate pricing service in instances where it receives multiple quotes on the same security. When fair values are unavailable from these independent pricing sources, quotes are obtained directly from broker-dealers who are active in the corresponding markets. Most of the Company’s fixed maturities are priced from the pricing services or dealer quotes. The Company will typically not make adjustments to prices received from pricing services or dealer quotes; however, in instances where the quoted external price for a security uses significant unobservable inputs, the Company will classify that security as Level 3. The methods used to develop and substantiate the unobservable inputs used are based on the Company’s valuation policy and are dependent upon the facts and circumstances surrounding the individual investments which are generally transaction specific. The Company’s inactively traded fixed maturities are classified as Level 3. For all fixed maturity investments, the bid price is used for estimating fair value.

To validate prices, the Company compares the fair value estimates to its knowledge of the current market and will investigate prices that it considers not to be representative of fair value. The Company also reviews an internally generated fixed maturity price validation report which converts prices received for fixed maturity investments from the independent pricing sources and from broker-dealers quotes and plots OAS and duration on a sector and rating basis. The OAS is calculated using established algorithms developed by an independent risk analytics platform vendor. The OAS on the fixed maturity price validation report are compared for securities in a similar sector and having a similar rating, and outliers are identified and investigated for price reasonableness. In addition, the Company completes quantitative analyses to compare the performance of each fixed maturity investment portfolio to the performance of an appropriate benchmark, with significant differences identified and investigated.

Short-term investments

Short-term investments are valued in a manner similar to the Company’s fixed maturity investments and are generally classified in Level 2. At December 31, 2018, short-term investments included investments in foreign currency denominated bonds issued by a foreign government with durations to maturity of three to four months, as discussed in footnote (1) to the fair value table above, which matured during 2019. See also Notes 2(g) and 2(n) for further details.

Equities

Equity securities include U.S. and foreign common and preferred stocks, real estate investment trusts and mutual funds. Publicly traded equities are generally classified in Level 1 as the Company uses prices received from independent pricing sources based on quoted prices in active markets. Equities classified as Level 2 are generally mutual funds invested in fixed income securities, where the net asset value of the fund is provided on a daily basis, and certain common and preferred equities. Equities classified as Level 3 are generally mutual funds invested in securities other than the common stock of publicly traded companies, where the net asset value is not provided on a daily basis, and inactively traded common stocks. The significant unobservable inputs used in the fair value measurement of inactively traded common stocks classified as Level 3 include market return information, weighted using management’s judgment, from comparable selected publicly traded companies in the same industry, in a similar region and of a similar size, including transactional prices, tangible book value multiples, revenue multiples and adjusted earnings multiples. Significant increases (decreases) in any of these inputs could result in a significantly higher (lower) fair value measurement. Significant unobservable inputs used in measuring the fair value measurement of inactively traded common stocks also include a liquidity discount. A significant increase (decrease) in the liquidity discount could result in a significantly lower (higher) fair value measurement.

To validate prices, the Company completes quantitative analyses to compare the performance of each equity investment portfolio to the performance of an appropriate benchmark, with significant differences identified and investigated.

Other invested assets

The Company’s foreign exchange forward contracts, foreign currency option contracts, interest rate swaps and TBAs are generally classified as Level 2 within the fair value hierarchy and are priced by independent pricing services.

Included in the Company’s Level 3 classification, in general, are certain derivatives, including weather derivative insurance-linked securities and total return swaps; privately placed corporate loans; notes and loans receivable and notes securitizations; and private equities. For Level 3 instruments, the Company will generally (i) receive a price based on a manager’s or trustee’s valuation for the asset; (ii) develop an internal discounted cash flow model to measure fair value; or (iii) use market return information, adjusted if necessary and weighted using management’s judgment, from comparable selected publicly traded equity funds in a similar region and of a similar size. Where the Company receives prices from the manager or trustee, these prices are based on the manager’s or trustee’s estimate of fair value for the assets and are generally audited on an annual basis. Where the Company develops its own discounted cash flow models, the inputs will be specific to the asset in question, based on appropriate historical information, adjusted as necessary, and using appropriate discount rates. The significant unobservable inputs used in the fair value measurement of Other invested assets classified as Level 3 include variation in regional temperatures, credit spreads, gross revenue to fair value ratios and other valuation ratios. Significant increases (decreases) in any of these inputs in isolation could result in a significantly lower (higher) fair value measurement. Significant unobservable inputs used in the fair value measurement of Other invested assets classified as Level 3 also include market return information, weighted using management’s judgment, from comparable selected publicly traded companies in the same industry, in a similar region and of a similar size, net income multiples and effective yields. Significant increases (decreases) in these inputs in isolation could result in a significantly higher (lower) fair value measurement. As part of the Company’s modeling to determine the fair value of an investment, the Company considers counterparty credit risk as an input to the model, however, the majority of the Company’s counterparties are investment grade rated institutions and the failure of any one counterparty would not have a significant impact on the Company’s consolidated financial statements.

To validate prices, the Company will compare them to benchmarks, where appropriate, or to the business results generally within that asset class and specifically to those particular assets.

(b) Fair Value of Financial Instrument Liabilities

At December 31, 2019 and 2018, the carrying values of financial instrument liabilities recorded in the Consolidated Balance Sheets approximate their fair values, with the exception of the long-term debt related to senior notes and capital efficient notes (CENts). The fair value of the debt related to senior notes as of December 31, 2019 and 2018 was calculated based on discounted cash flow models using observable market yields and contractual cash flows based on the aggregate principal amount outstanding. The fair value of the debt related to CENts as of December 31, 2019 and 2018 was calculated based on market data valuation models using observable inputs based on the aggregate principal amount outstanding of the intercompany debt.

See Note 9 for further details related to the Company's debt, including the carrying values and fair values.

At December 31, 2019 and 2018, the Company’s debt related to the senior notes and CENts was classified as Level 2 in the fair value hierarchy.

Disclosures about the fair value of financial instrument liabilities exclude insurance contracts.