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Financial Instruments carried at Fair Value

12 Months Ended

Dec. 31, 2017

Financial Instruments carried at Fair Value [Abstract]

Disclosure of fair value of financial instruments [text block]

Financial Instruments carried at Fair Value

Valuation Methods and Control

The Group has an established valuation control framework which governs internal control standards, methodologies, and procedures over the valuation process.

Prices Quoted in Active Markets – The fair value of instruments that are quoted in active markets are determined using the quoted prices where they represent prices at which regularly and recently occurring transactions take place.

Valuation Techniques – The Group uses valuation techniques to establish the fair value of instruments where prices, quoted in active markets, are not available. Valuation techniques used for financial instruments include modelling techniques, the use of indicative quotes for proxy instruments, quotes from recent and less regular transactions and broker quotes.

For some financial instruments a rate or other parameter, rather than a price, is quoted. Where this is the case then the market rate or parameter is used as an input to a valuation model to determine fair value. For some instruments, modelling techniques follow industry standard models, for example, discounted cash flow analysis and standard option pricing models. These models are dependent upon estimated future cash flows, discount factors and volatility levels. For more complex or unique instruments, more sophisticated modelling techniques are required, and may rely upon assumptions or more complex parameters such as correlations, prepayment speeds, default rates and loss severity.

Frequently, valuation models require multiple parameter inputs. Where possible, parameter inputs are based on observable data or are derived from the prices of relevant instruments traded in active markets. Where observable data is not available for parameter inputs, then other market information is considered. For example, indicative broker quotes and consensus pricing information are used to support parameter inputs where they are available. Where no observable information is available to support parameter inputs then they are based on other relevant sources of information such as prices for similar transactions, historic data, economic fundamentals, and research information, with appropriate adjustment to reflect the terms of the actual instrument being valued and current market conditions.

Valuation Adjustments – Valuation adjustments are an integral part of the valuation process. In making appropriate valuation adjustments, the Group follows methodologies that consider factors such as bid-offer spreads, counterparty/own credit and funding risk. Bid-offer spread valuation adjustments are required to adjust mid market valuations to the appropriate bid or offer valuation. The bid or offer valuation is the best representation of the fair value for an instrument, and therefore its fair value. The carrying value of a long position is adjusted from mid to bid, and the carrying value of a short position is adjusted from mid to offer. Bid-offer valuation adjustments are determined from bid-offer prices observed in relevant trading activity and in quotes from other broker-dealers or other knowledgeable counterparties. Where the quoted price for the instrument is already a bid-offer price then no additional bid-offer valuation adjustment is necessary. Where the fair value of financial instruments is derived from a modelling technique, then the parameter inputs into that model are normally at a mid-market level. Such instruments are generally managed on a portfolio basis and, when specified criteria are met, valuation adjustments are taken to reflect the cost of closing out the net exposure the Bank has to individual market or counterparty risks. These adjustments are determined from bid-offer prices observed in relevant trading activity and quotes from other broker-dealers.

Where complex valuation models are used, or where less-liquid positions are being valued, then bid-offer levels for those positions may not be available directly from the market, and therefore for the close-out cost of these positions, models and parameters must be estimated. When these adjustments are designed, the Group closely examines the valuation risks associated with the model as well as the positions themselves, and the resulting adjustments are closely monitored on an ongoing basis.

Counterparty Credit Valuation Adjustments (CVAs) are required to cover expected credit losses to the extent that the valuation technique does not already include an expected credit loss factor relating to the non-performance risk of the counterparty. The CVA amount is applied to all relevant over-the-counter (OTC) derivatives, and is determined by assessing the potential credit exposure to a given counterparty and taking into account any collateral held, the effect of any relevant netting arrangements, expected loss given default and the probability of default, based on available market information, including Credit Default Swap (CDS) spreads. Where counterparty CDS spreads are not available, relevant proxies are used.

The fair value of the Group’s financial liabilities at fair value through profit or loss (i.e., OTC derivative liabilities and structured note liabilities designated at fair value through profit or loss) incorporates Debt Valuation Adjustments (DVA) to measure the change in the Group’s own credit risk of the financial liability. For derivative liabilities the Group considers its own creditworthiness by assessing all counterparties’ potential future exposure to the Group, taking into account any collateral posted by the Group, the effect of relevant netting arrangements, expected loss given default and the probability of default of the Group, based on the Group’s market CDS level. The change in the Group’s own credit risk for structured note liabilities is calculated by discounting the contractual cash flows of the instrument using the rate at which similar instruments would be issued at the measurement date as this reflects the value from the perspective of a market participant who holds the identical item as an asset.

When determining CVA and DVA, additional adjustments are made where appropriate to achieve fair value, due to the expected loss estimate of a particular arrangement, or where the credit risk being assessed differs in nature to that described by the available CDS instrument.

Funding Valuation Adjustments (FVA) are required to incorporate the market implied funding costs into the fair value of derivative positions. The FVA reflects a discounting spread applied to uncollateralized and partially collateralized derivatives and is determined by assessing the market-implied funding costs on both assets and liabilities.

Where there is uncertainty in the assumptions used within a modelling technique, an additional adjustment is taken to calibrate the model price to the expected market price of the financial instrument. Typically, such transactions have bid-offer levels which are less observable, and these adjustments aim to estimate the bid-offer by computing the liquidity-premium associated with the transaction. Where a financial instrument is of sufficient complexity that the cost of closing it out would be higher than the cost of closing out its component risks, then an additional adjustment is taken to reflect this.

Valuation Control – The Group has an independent specialized valuation control group within the Finance function which governs and develops the valuation control framework and manages the valuation control processes. The mandate of this specialist function includes the performance of the independent valuation control process for all businesses, the continued development of valuation control methodologies and techniques, as well as devising and governing the formal valuation control policy framework. Special attention of this independent valuation control group is directed to areas where management judgment forms part of the valuation process.

Results of the valuation control process are collected and analysed as part of a standard monthly reporting cycle. Variances of differences outside of preset and approved tolerance levels are escalated both within the Finance function and with Senior Business Management for review, resolution and, if required, adjustment.

For instruments where fair value is determined from valuation models, the assumptions and techniques used within the models are independently validated by an independent specialist model validation group that is part of the Group’s Risk Management function.

Quotes for transactions and parameter inputs are obtained from a number of third party sources including exchanges, pricing service providers, firm broker quotes and consensus pricing services. Price sources are examined and assessed to determine the quality of fair value information they represent, with greater emphasis given to those possessing greater valuation certainty and relevance. The results are compared against actual transactions in the market to ensure the model valuations are calibrated to market prices.

Price and parameter inputs to models, assumptions and valuation adjustments are verified against independent sources. Where they cannot be verified to independent sources due to lack of observable information, the estimate of fair value is subject to procedures to assess its reasonableness. Such procedures include performing revaluation using independently generated models (including where existing models are independently recalibrated), assessing the valuations against appropriate proxy instruments and other benchmarks, and performing extrapolation techniques. Assessment is made as to whether the valuation techniques produce fair value estimates that are reflective of market levels by calibrating the results of the valuation models against market transactions where possible.

Fair Value Hierarchy

The financial instruments carried at fair value have been categorized under the three levels of the IFRS fair value hierarchy as follows:

Level 1 – Instruments valued using quoted prices in active markets are instruments where the fair value can be determined directly from prices which are quoted in active, liquid markets and where the instrument observed in the market is representative of that being priced in the Group’s inventory.

These include: government bonds, exchange-traded derivatives and equity securities traded on active, liquid exchanges.

Level 2 – Instruments valued with valuation techniques using observable market data are instruments where the fair value can be determined by reference to similar instruments trading in active markets, or where a technique is used to derive the valuation but where all inputs to that technique are observable.

These include: many OTC derivatives; many investment-grade listed credit bonds; some CDS; many collateralized debt obligations (CDO); and many less-liquid equities.

Level 3 – Instruments valued using valuation techniques using market data which is not directly observable are instruments where the fair value cannot be determined directly by reference to market-observable information, and some other pricing technique must be employed. Instruments classified in this category have an element which is unobservable and which has a significant impact on the fair value.

These include: more-complex OTC derivatives; distressed debt; highly-structured bonds; illiquid asset-backed securities (ABS); illiquid CDO’s (cash and synthetic); monoline exposures; some private equity placements; many commercial real estate (CRE) loans; illiquid loans; and some municipal bonds.

Carrying value of the financial instruments held at fair value¹

	Dec 31, 2017			Dec 31, 2016
in € m.	Quoted prices in active market (Level 1)	Valuation technique observable parameters (Level 2)	Valuation technique unobservable parameters (Level 3)	Quoted prices in active market (Level 1)	Valuation technique observable parameters (Level 2)	Valuation technique unobservable parameters (Level 3)
Financial assets held at fair value:
Trading assets	106,075	69,543	9,043	89,943	70,415	10,686
Trading securities	105,792	62,770	4,634	89,694	62,220	5,012
Other trading assets	283	6,773	4,409	248	8,195	5,674
Positive market values from derivative financial instruments	12,280	341,413	7,340	8,802 ⁵	466,551 ⁵	9,798
Financial assets designated at fair value through profit or loss	6,547	83,242	1,488	10,118	75,867	1,601
Financial assets available for sale	29,579	15,713	4,104	35,626 ⁴	16,449 ⁴	4,153
Other financial assets at fair value	0	3,258 ²	47	28	3,618 ²	33
Total financial assets held at fair value	154,480	513,169	22,022	144,517	632,900	26,271

Financial liabilities held at fair value:
Trading liabilities	53,644	17,817	2	41,664	15,311	52
Trading securities	53,644	17,503	2	41,664	14,874	52
Other trading liabilities	0	314	0	0	437	0
Negative market values from derivative financial instruments	9,163	327,572	5,992	9,913 ⁶	445,089 ⁶	8,857
Financial liabilities designated at fair value through profit or loss	4	62,426	1,444	4	58,259	2,229
Investment contract liabilities	0	574	0	0	592	0
Other financial liabilities at fair value	0	1,294 ²	(298) ³	0	4,647 ²	(848) ³
Total financial liabilities held at fair value	62,810	409,683	7,139	51,581	523,898	10,290

¹Amounts in this table are generally presented on a gross basis, in line with the Group’s accounting policy regarding offsetting of financial instruments, as described in Note 1 “Significant Accounting Policies and Critical Accounting Estimates”.

²Predominantly relates to derivatives qualifying for hedge accounting.

³Relates to derivatives which are embedded in contracts where the host contract is held at amortized cost but for which the embedded derivative is separated. The separated embedded derivatives may have a positive or a negative fair value but have been presented in this table to be consistent with the classification of the host contract. The separated embedded derivatives are held at fair value on a recurring basis and have been split between the fair value hierarchy classifications.

⁴ Financial assets available for sale have been restated by € 6.9 billion in ‘Quoted prices in active market (Level 1)’ and negative € 6.9 billion in ‘Valuation technique observable parameters (Level 2)’.

⁵ Reassessment of trades have resulted a restatement in positive market values for derivatives financial instrument by € 5.0 billion in ‘Valuation technique observable parameters (Level 2)’ and negative € 5.0 billion in ‘Quoted prices in active market (Level 1)’.

⁶ Reassessment of trades have resulted a restatement in negative market values for derivatives financial instrument by € 3.7 billion in ‘Valuation technique observable parameters (Level 2)’ and negative € 3.7 billion in ‘Quoted prices in active market (Level 1)’

In 2017, there were transfers from Level 1 to Level 2 on financial assets available for sale (€ 1.0 billion of assets) due to changes in liquidity.

Valuation Techniques

The following is an explanation of the valuation techniques used in establishing the fair value of the different types of financial instruments that the Group trades.

Sovereign, Quasi-sovereign and Corporate Debt and Equity Securities – Where there are no recent transactions then fair value may be determined from the last market price adjusted for all changes in risks and information since that date. Where a close proxy instrument is quoted in an active market then fair value is determined by adjusting the proxy value for differences in the risk profile of the instruments. Where close proxies are not available then fair value is estimated using more complex modelling techniques. These techniques include discounted cash flow models using current market rates for credit, interest, liquidity and other risks. For equity securities modeling techniques may also include those based on earnings multiples.

Mortgage- and Other Asset-Backed Securities (MBS/ABS) include residential and commercial MBS and other ABS including CDOs. ABS have specific characteristics as they have different underlying assets and the issuing entities have different capital structures. The complexity increases further where the underlying assets are themselves ABS, as is the case with many of the CDO instruments.

Where no reliable external pricing is available, ABS are valued, where applicable, using either relative value analysis which is performed based on similar transactions observable in the market, or industry-standard valuation models making largest possible use of available observable inputs. The industry standard models calculate principal and interest payments for a given deal based on assumptions that can be independently price tested. The inputs include prepayment speeds, loss assumptions (timing and severity) and a discount rate (spread, yield or discount margin). These inputs/assumptions are derived from actual transactions, external market research and market indices where appropriate.

Loans – For certain loans fair value may be determined from the market price on a recently occurring transaction adjusted for all changes in risks and information since that transaction date. Where there are no recent market transactions then broker quotes, consensus pricing, proxy instruments or discounted cash flow models are used to determine fair value. Discounted cash flow models incorporate parameter inputs for credit risk, interest rate risk, foreign exchange risk, loss given default estimates and amounts utilized given default, as appropriate. Credit risk, loss given default and utilization given default parameters are determined using information from the loan or other credit markets, where available and appropriate.

Leveraged loans can have transaction-specific characteristics which can limit the relevance of market-observed transactions. Where similar transactions exist for which observable quotes are available from external pricing services then this information is used with appropriate adjustments to reflect the transaction differences. When no similar transactions exist, a discounted cash flow valuation technique is used with credit spreads derived from the appropriate leveraged loan index, incorporating the industry classification, subordination of the loan, and any other relevant information on the loan and loan counterparty.

Over-The-Counter Derivative Financial Instruments – Market standard transactions in liquid trading markets, such as interest rate swaps, foreign exchange forward and option contracts in G7 currencies, and equity swap and option contracts on listed securities or indices are valued using market standard models and quoted parameter inputs. Parameter inputs are obtained from pricing services, consensus pricing services and recently occurring transactions in active markets wherever possible.

More complex instruments are modeled using more sophisticated modeling techniques specific for the instrument and are calibrated to available market prices. Where the model output value does not calibrate to a relevant market reference then valuation adjustments are made to the model output value to adjust for any difference. In less active markets, data is obtained from less frequent market transactions, broker quotes and through extrapolation and interpolation techniques. Where observable prices or inputs are not available, management judgment is required to determine fair values by assessing other relevant sources of information such as historical data, fundamental analysis of the economics of the transaction and proxy information from similar transactions.

Financial Liabilities Designated at Fair Value through Profit or Loss under the Fair Value Option – The fair value of financial liabilities designated at fair value through profit or loss under the fair value option incorporates all market risk factors including a measure of the Group’s credit risk relevant for that financial liability. The financial liabilities include structured note issuances, structured deposits, and other structured securities issued by consolidated vehicles, which may not be quoted in an active market. The fair value of these financial liabilities is determined by discounting the contractual cash flows using the relevant credit-adjusted yield curve. The market risk parameters are valued consistently to similar instruments held as assets, for example, any derivatives embedded within the structured notes are valued using the same methodology discussed in the “Over-The-Counter Derivative Financial Instruments” section above.

Where the financial liabilities designated at fair value through profit or loss under the fair value option are collateralized, such as securities loaned and securities sold under repurchase agreements, the credit enhancement is factored into the fair valuation of the liability.

Investment Contract Liabilities – Assets which are linked to the investment contract liabilities are owned by the Group. The investment contract obliges the Group to use these assets to settle these liabilities. Therefore, the fair value of investment contract liabilities is determined by the fair value of the underlying assets (i.e., amount payable on surrender of the policies).

Analysis of Financial Instruments with Fair Value Derived from Valuation Techniques Containing Significant Unobservable Parameters (Level 3)

Some of the financial assets and financial liabilities in Level 3 of the fair value hierarchy have identical or similar offsetting exposures to the unobservable input. However, according to IFRS they are required to be presented gross.

Trading Securities – Certain illiquid emerging market corporate bonds and illiquid highly structured corporate bonds are included in this level of the hierarchy. In addition, some of the holdings of notes issued by securitization entities, commercial and residential MBS, collateralized debt obligation securities and other ABS are reported here. The decrease in the year is mainly due to a combination of sales, settlements and losses offset by purchases and transfers between Level 2 and Level 3 due to changes in the observability of input parameters used to value these instruments.

Positive and Negative Market Values from Derivative Instruments categorized in this level of the fair value hierarchy are valued based on one or more significant unobservable parameters. The unobservable parameters may include certain correlations, certain longer-term volatilities, certain prepayment rates, credit spreads and other transaction-specific parameters.

Level 3 derivatives includes certain options where the volatility is unobservable; certain basket options in which the correlations between the referenced underlying assets are unobservable; longer-term interest rate option derivatives; multi-currency foreign exchange derivatives; and certain credit default swaps for which the credit spread is not observable.

The decrease in assets was due to settlements and losses marginally offset by transfers between Level 2 and Level 3 due to changes in the observability of input parameters used to value these instruments. The decrease in liabilities was due to settlements, gains and transfers between Level 2 and Level 3.

Other Trading Instruments classified in Level 3 of the fair value hierarchy mainly consist of traded loans valued using valuation models based on one or more significant unobservable parameters. Level 3 loans comprise illiquid leveraged loans and illiquid residential and commercial mortgage loans. The balance decreased in the year due to sales, settlements and losses offset by purchases, issuances and transfers between Level 2 and Level 3 due to changes in the observability of input parameters used to value these instruments.

Financial Assets/Liabilities designated at Fair Value through Profit or Loss – Certain corporate loans and structured liabilities which were designated at fair value through profit or loss under the fair value option are categorized in this level of the fair value hierarchy. The corporate loans are valued using valuation techniques which incorporate observable credit spreads, recovery rates and unobservable utilization parameters. Revolving loan facilities are reported in the third level of the hierarchy because the utilization in the event of the default parameter is significant and unobservable.

In addition, certain hybrid debt issuances designated at fair value through profit or loss containing embedded derivatives are valued based on significant unobservable parameters. These unobservable parameters include single stock volatility correlations. Assets marginally decreased during the year due to sales, settlements, losses and transfers between Level 2 and Level 3 offset by purchases and issuances. Liabilities decreased in the year due to settlements, gains and transfers between Level 2 and Level 3 offset by issuances.

Financial Assets Available for Sale include non-performing loan portfolios where there is no trading intent and unlisted equity instruments where there is no close proxy and the market is very illiquid. The marginal decrease in assets in the year is due to sales and settlements offset by purchases, transfers between Level 2 and Level 3 and gains.

Reconciliation of financial instruments classified in Level 3

	Dec 31, 2017
in € m.	Balance, beginning of year	Changes in the group of consoli- dated com- panies	Total gains/ losses ¹	Purchases	Sales	Issu- ances ²	Settle- ments ³	Transfers into Level 3 ⁴	Transfers out of Level 3 ⁴	Balance, end of year
Financial assets held at fair value:
Trading securities	5,012	(1)	(153)	2,144	(1,660)	0	(818)	772	(662)	4,634
Positive market values from derivative financial instruments	9,798	(0)	(610)	0	0	0	(1,889)	2,298	(2,257)	7,340
Other trading assets	5,674	(7)	(283)	2,095	(2,328)	636	(1,803)	950	(524)	4,409
Financial assets designated at fair value through profit or loss	1,601	0	(78)	807	(118)	63	(710)	58	(134)	1,488
Financial assets available for sale	4,153	(40)	205 ⁵	722	(249)	0	(1,206)	539	(21)	4,104
Other financial assets at fair value	33	0	33	0	0	0	(26)	7	0	47
Total financial assets held at fair value	26,271	(47)	(886) ^6,7	5,768	(4,356)	699	(6,453)	4,624	(3,598)	22,022
Financial liabilities held at fair value:
Trading securities	52	0	(6)	0	0	0	(46)	1	0	2
Negative market values from derivative financial instruments	8,857	(5)	(64)	0	0	0	(1,827)	924	(1,892)	5,992
Other trading liabilities	0	0	(0)	0	0	0	0	0	0	0
Financial liabilities designated at fair value through profit or loss	2,229	(7)	(128)	0	0	146	(564)	154	(387)	1,444
Other financial liabilities at fair value	(848)	0	268	0	0	0	286	(18)	15	(298)
Total financial liabilities held at fair value	10,290	(12)	69 ^6,7	0	0	146	(2,151)	1,061	(2,265)	7,139

¹Total gains and losses predominantly relate to net gains (losses) on financial assets/liabilities at fair value through profit or loss reported in the consolidated statement of income. The balance also includes net gains (losses) on financial assets available for sale reported in the consolidated statement of income and unrealized net gains (losses) on financial assets available for sale and exchange rate changes reported in other comprehensive income, net of tax. Further, certain instruments are hedged with instruments in Level 1 or Level 2 but the table above does not include the gains and losses on these hedging instruments. Additionally, both observable and unobservable parameters may be used to determine the fair value of an instrument classified within Level 3 of the fair value hierarchy; the gains and losses presented below are attributable to movements in both the observable and unobservable parameters.

²Issuances relate to the cash amount received on the issuance of a liability and the cash amount paid on the primary issuance of a loan to a borrower.

³Settlements represent cash flows to settle the asset or liability. For debt and loan instruments this includes principal on maturity, principal amortizations and principal repayments. For derivatives all cash flows are presented in settlements.

⁴Transfers in and transfers out of Level 3 are related to changes in observability of input parameters. During the year they are recorded at their fair value at the beginning of year. For instruments transferred into Level 3 the table shows the gains and losses and cash flows on the instruments as if they had been transferred at the beginning of the year. Similarly for instruments transferred out of Level 3 the table does not show any gains or losses or cash flows on the instruments during the year since the table is presented as if they have been transferred out at the beginning of the year.

⁵Total gains and losses on available for sale include a gain of € 94 million recognized in other comprehensive income, net of tax, and a loss of € 8 million recognized in the income statement presented in net gains (losses) on financial assets available for sale.

⁶This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a loss of € 565 million and for total financial liabilities held at fair value this is a gain of € 123 million. The effect of exchange rate changes is reported in other comprehensive income, net of tax.

⁷For assets positive balances represent gains, negative balances represent losses. For liabilities positive balances represent losses, negative balances represent gains.

	Dec 31, 2016
in € m.	Balance, beginning of year	Changes in the group of consoli- dated com- panies	Total gains/ losses ¹	Purchases	Sales	Issu- ances ²	Settle- ments ³	Transfers into Level 3 ⁴	Transfers out of Level 3 ⁴	Balance, end of year
Financial assets held at fair value:
Trading securities	6,669	(0)	143	1,736	(3,605)	0	(990)	1,589	(528)	5,012
Positive market values from derivative financial instruments	9,445	(60)	(88)	0	0	0	(1,290)	4,158	(2,367)	9,798
Other trading assets	6,082	66	56	2,196	(3,606)	735	(1,527)	2,616	(944)	5,674
Financial assets designated at fair value through profit or loss	4,478	(509)	40	2	(273)	131	(1,073)	86	(1,282)	1,601
Financial assets available for sale	4,874	(1)	255 ⁵	920	(630)	0	(1,377)	187	(74)	4,153
Other financial assets at fair value⁶	0	0	0	0	0	0	0	33	0	33
Total financial assets held at fair value	31,549	(504)	405 ^6,7	4,853	(8,114)	866	(6,257)	8,669	(5,195)	26,271
Financial liabilities held at fair value:
Trading securities	18	0	0	0	0	0	34	0	(0)	52
Negative market values from derivative financial instruments	7,879	(317)	620	0	0	0	(508)	3,316	(2,134)	8,857
Other trading liabilities	0	0	0	0	0	0	0	0	0	0
Financial liabilities designated at fair value through profit or loss	3,053	0	(75)	0	0	587	(729)	245	(851)	2,229
Other financial liabilities at fair value	(1,146)	0	135	0	0	0	3	(26)	187	(848)
Total financial liabilities held at fair value	9,805	(317)	680 ^6,7	0	0	587	(1,200)	3,534	(2,799)	10,290

²Issuances relate to the cash amount received on the issuance of a liability and the cash amount paid on the primary issuance of a loan to a borrower.

⁵Total gains and losses on available for sale include a loss of € 94 million recognized in other comprehensive income, net of tax, and a gain of € 187 million recognized in the income statement presented in net gains (losses) on financial assets available for sale.

⁶This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a gain of € 4 million and for total financial liabilities held at fair value this is a gain of € 50 million. The effect of exchange rate changes is reported in other comprehensive income, net of tax.

⁷For assets positive balances represent gains, negative balances represent losses. For liabilities positive balances represent losses, negative balances represent gains.

Sensitivity Analysis of Unobservable Parameters

Where the value of financial instruments is dependent on unobservable parameter inputs, the precise level for these parameters at the balance sheet date might be drawn from a range of reasonably possible alternatives. In preparing the financial statements, appropriate levels for these unobservable input parameters are chosen so that they are consistent with prevailing market evidence and in line with the Group’s approach to valuation control detailed above. Were the Group to have marked the financial instruments concerned using parameter values drawn from the extremes of the ranges of reasonably possible alternatives then as of December 31, 2017 it could have increased fair value by as much as € 1.6 billion or decreased fair value by as much as € 1.0 billion. As of December 31, 2016 it could have increased fair value by as much as € 1.8 billion or decreased fair value by as much as € 1.0 billion.

The changes in sensitive amounts from December 31, 2016 to December 31, 2017 show a material reduction to the positive fair value movement, and a smaller reduction to the negative fair value movement from using reasonable possible alternatives.

These moves are primarily driven by the overall reduction in the Level 3 population in the same period (e.g. Group Level 3 assets down from € 26.3 billion at the end of 2016 to € 22.0 billion at the end of 2017), with this largely the result of de-risking / asset sales. The reduction in positive fair value movement moved in line with the reduction in the Level 3 population, whilst the reduction in negative fair value movement was proportionally smaller due to idiosyncratic factors across a number of trades.

Our sensitivity calculation of unobservable parameters for Level 3 aligns to the approach used to assess valuation uncertainty for Prudent Valuation purposes. Prudent Valuation is a capital requirement for assets held at fair value. It provides a mechanism for quantifying and capitalising valuation uncertainty in accordance with the European Commission Delegated Regulation (EU) 2016/101, which supplements Article 34 of Regulation (EU) No. 575/2013 (CRR), requiring institutions to apply as a deduction from CET 1 for the amount of any additional value adjustments on all assets measured at fair value calculated in accordance with Article 105(14). This utilises exit price analysis performed for the relevant assets and liabilities in the Prudent Valuation assessment. The downside sensitivity may be limited in some cases where the fair value is already demonstrably prudent.

This disclosure is intended to illustrate the potential impact of the relative uncertainty in the fair value of financial instruments for which valuation is dependent on unobservable input parameters. However, it is unlikely in practice that all unobservable parameters would be simultaneously at the extremes of their ranges of reasonably possible alternatives. Hence, the estimates disclosed above are likely to be greater than the true uncertainty in fair value at the balance sheet date. Furthermore, the disclosure is neither predictive nor indicative of future movements in fair value.

For many of the financial instruments considered here, in particular derivatives, unobservable input parameters represent only a subset of the parameters required to price the financial instrument, the remainder being observable. Hence for these instruments the overall impact of moving the unobservable input parameters to the extremes of their ranges might be relatively small compared with the total fair value of the financial instrument. For other instruments, fair value is determined based on the price of the entire instrument, for example, by adjusting the fair value of a reasonable proxy instrument. In addition, all financial instruments are already carried at fair values which are inclusive of valuation adjustments for the cost to close out that instrument and hence already factor in uncertainty as it reflects itself in market pricing. Any negative impact of uncertainty calculated within this disclosure, then, will be over and above that already included in the fair value contained in the financial statements.

Breakdown of the sensitivity analysis by type of instrument¹

	Dec 31, 2017		Dec 31, 2016
in € m.	Positive fair value movement from using reasonable possible alternatives	Negative fair value movement from using reasonable possible alternatives	Positive fair value movement from using reasonable possible alternatives	Negative fair value movement from using reasonable possible alternatives
Securities:
Debt securities	126	90	213	137
Commercial mortgage-backed securities	6	6	13	12
Mortgage and other asset-backed securities	26	28	46	40
Corporate, sovereign and other debt securities	94	56	154	85
Equity securities	95	67	116	68
Derivatives:
Credit	155	125	238	158
Equity	164	138	209	150
Interest related	340	173	429	187
Foreign Exchange	65	12	32	21
Other	106	73	143	92
Loans:
Loans	504	320	377	227
Other	0	0	0	0
Total	1,556	999	1,758	1,040

¹Where the exposure to an unobservable parameter is offset across different instruments then only the net impact is disclosed in the table.

Quantitative Information about the Sensitivity of Significant Unobservable Inputs

The behaviour of the unobservable parameters on Level 3 fair value measurement is not necessarily independent, and dynamic relationships often exist between the other unobservable parameters and the observable parameters. Such relationships, where material to the fair value of a given instrument, are explicitly captured via correlation parameters, or are otherwise controlled via pricing models or valuation techniques. Frequently, where a valuation technique utilizes more than one input, the choice of a certain input will bound the range of possible values for other inputs. In addition, broader market factors (such as interest rates, equity, credit or commodity indices or foreign exchange rates) can also have effects.

The range of values shown below represents the highest and lowest inputs used to value the significant exposures within Level 3. The diversity of financial instruments that make up the disclosure is significant and therefore the ranges of certain parameters can be large. For example, the range of credit spreads on mortgage backed securities represents performing, more liquid positions with lower spreads then the less liquid, non-performing positions which will have higher credit spreads. As Level 3 contains the less liquid fair value instruments, the wide ranges of parameters seen is to be expected, as there is a high degree of pricing differentiation within each exposure type to capture the relevant market dynamics. There follows a brief description of each of the principal parameter types, along with a commentary on significant interrelationships between them.

Credit Parameters are used to assess the creditworthiness of an exposure, by enabling the probability of default and resulting losses of a default to be represented. The credit spread is the primary reflection of creditworthiness, and represents the premium or yield return above the benchmark reference instrument (typically LIBOR, or relevant Treasury Instrument, depending upon the asset being assessed), that a bond holder would require to allow for the credit quality difference between that entity and the reference benchmark. Higher credit spreads will indicate lower credit quality, and lead to a lower value for a given bond or other loan-asset that is to be repaid to the holder or lender by the borrower. Recovery Rates represent an estimate of the amount a lender would receive in the case of a default of a loan, or a bond holder would receive in the case of default of the bond. Higher recovery rates will give a higher valuation for a given bond position, if other parameters are held constant. Constant Default Rate (CDR) and Constant Prepayment Rate (CPR) allow more complex loan and debt assets to be assessed, as these parameters estimate the ongoing defaults arising on scheduled repayments and coupons, or whether the borrower is making additional (usually voluntary) prepayments. These parameters are particularly relevant when forming a fair value opinion for mortgage or other types of lending, where repayments are delivered by the borrower through time, or where the borrower may pre-pay the loan (seen for example in some residential mortgages). Higher CDR will lead to lower valuation of a given loan or mortgage as the lender will ultimately receive less cash.

Interest rates, credit spreads, inflation rates, foreign exchange rates and equity prices are referenced in some option instruments, or other complex derivatives, where the payoff a holder of the derivative will receive is dependent upon the behaviour of these underlying references through time. Volatility parameters describe key attributes of option behaviour by enabling the variability of returns of the underlying instrument to be assessed. This volatility is a measure of probability, with higher volatilities denoting higher probabilities of a particular outcome occurring. The underlying references (interest rates, credit spreads etc.) have an effect on the valuation of options, by describing the size of the return that can be expected from the option. Therefore the value of a given option is dependent upon the value of the underlying instrument, and the volatility of that instrument, representing the size of the payoff, and the probability of that payoff occurring. Where volatilities are high, the option holder will see a higher option value as there is greater probability of positive returns. A higher option value will also occur where the payoff described by the option is significant.

Correlations are used to describe influential relationships between underlying references where a derivative or other instrument has more than one underlying reference. Behind some of these relationships, for example commodity correlation and interest rate-foreign exchange correlations, typically lie macroeconomic factors such as the impact of global demand on groups of commodities, or the pricing parity effect of interest rates on foreign exchange rates. More specific relationships can exist between credit references or equity stocks in the case of credit derivatives and equity basket derivatives, for example. Credit correlations are used to estimate the relationship between the credit performance of a range of credit names, and stock correlations are used to estimate the relationship between the returns of a range of equities. A derivative with a correlation exposure will be either long- or short-correlation. A high correlation suggests a strong relationship between the underlying references is in force, and this will lead to an increase in value of a long-correlation derivative. Negative correlations suggest that the relationship between underlying references is opposing, i.e., an increase in price of one underlying reference will lead to a reduction in the price of the other.

An EBITDA (‘earnings before interest, tax, depreciation and amortization’) multiple approach can be used in the valuation of less liquid securities. Under this approach the enterprise value (‘EV’) of an entity can be estimated via identifying the ratio of the EV to EBITDA of a comparable observable entity and applying this ratio to the EBITDA of the entity for which a valuation is being estimated. Under this approach a liquidity adjustment is often applied due to the difference in liquidity between the generally listed comparable used and the company under valuation. A higher EV/EBITDA multiple will result in a higher fair value.

Financial instruments classified in Level 3 and quantitative information about unobservable inputs

	Dec 31, 2017
	Fair value
in € m. (unless stated otherwise)	Assets	Liabilities	Valuation technique(s)¹	Significant unobservable input(s) (Level 3)	Range
Financial instruments held at fair value – held for trading, designated at fair value and available-for-sale:
Mortgage and other asset backed securities held for trading:
Commercial mortgage-backed securities	79	0	Price based	Price	0 %	102 %
			Discounted cash flow	Credit spread (bps)	136	2,217
Mortgage- and other asset-backed securities	714	0	Price based	Price	0 %	102 %
			Discounted cash flow	Credit spread (bps)	12	2,000
				Recovery rate	0 %	90 %
				Constant default rate	0 %	25 %
				Constant prepayment rate	0 %	29 %
Total mortgage- and other asset-backed securities	793	0
Debt securities and other debt obligations	3,870	1,307	Price based	Price	0 %	176 %
Held for trading	3,559	2	Discounted cash flow	Credit spread (bps)	34	500
Corporate, sovereign and other debt securities	3,559
Available-for-sale	267
Designated at fair value	44	1,305
Equity securities	913	0	Market approach	Price per net asset value	60 %	100 %
Held for trading	282	0		Enterprise value/EBITDA (multiple)	1	14
Available-for-sale	480		Discounted cash flow	Weighted average cost capital	8 %	20 %
Designated at fair value	151
Loans	7,397	0	Price based	Price	0 %	161 %
Held for trading	4,376	0	Discounted cash flow	Credit spread (bps)	190	1,578
Designated at fair value	338			Constant default rate	–	–
Available-for-sale	2,684			Recovery rate	40 %	40 %
Loan commitments	0	8	Discounted cash flow	Credit spread (bps)	5	261
				Recovery rate	37 %	75 %
			Loan pricing model	Utilization	0 %	100 %
Other financial instruments	1,710 ²	131 ³	Discounted cash flow	IRR	1 %	24 %
				Repo rate (bps)	224	254
Total non-derivative financial instruments held at fair value	14,683	1,446

¹Valuation technique(s) and subsequently the significant unobservable input(s) relate to the respective total position.

²Other financial assets include € 34 million of other trading assets, € 956 million of other financial assets designated at fair value and € 674 million other financial assets available for sale.

³ Other financial liabilities include € 131 million of securities sold under repurchase agreements designated at fair value.

	Dec 31, 2017
	Fair value
in € m. (unless stated otherwise)	Assets	Liabilities	Valuation technique(s)	Significant unobservable input(s) (Level 3)	Range
Financial instruments held at fair value:
Market values from derivative financial instruments:
Interest rate derivatives	4,466	2,250	Discounted cash flow	Swap rate (bps)	(72)	1,036
				Inflation swap rate	(3) %	11 %
				Constant default rate	0 %	16 %
				Constant prepayment rate	2 %	38 %
			Option pricing model	Inflation volatility	0 %	5 %
				Interest rate volatility	0 %	103 %
				IR - IR correlation	(25) %	100 %
				Hybrid correlation	(85) %	90 %
Credit derivatives	630	909	Discounted cash flow	Credit spread (bps)	0	17,957
				Recovery rate	0 %	94 %
			Correlation pricing model	Credit correlation	37 %	90 %
Equity derivatives	728	1,347	Option pricing model	Stock volatility	6 %	90 %
				Index volatility	7 %	53 %
				Index - index correlation	–	–
				Stock - stock correlation	2 %	93 %
				Stock Forwards	0 %	7 %
				Index Forwards	0 %	95 %
FX derivatives	1,113	1,058	Option pricing model	Volatility	(6) %	31 %
Other derivatives	402	129 ¹	Discounted cash flow	Credit spread (bps)	–	–
			Option pricing model	Index volatility	0 %	79 %
				Commodity correlation	10 %	75 %
Total market values from derivative financial instruments	7,340	5,693

¹Includes derivatives which are embedded in contracts where the host contract is held at amortized cost but for which the embedded derivative is separated.

	Dec 31, 2016
	Fair value
in € m. (unless stated otherwise)	Assets	Liabilities	Valuation technique(s)¹	Significant unobservable input(s) (Level 3)	Range
Financial instruments held at fair value – held for trading, designated at fair value and available-for-sale:
Mortgage and other asset backed securities held for trading:
Commercial mortgage-backed securities	294	0	Price based	Price	0 %	103 %
			Discounted cash flow	Credit spread (bps)	119	2,000
Mortgage- and other asset-backed securities	1,071	0	Price based	Price	0 %	110 %
			Discounted cash flow	Credit spread (bps)	105	2,000
				Recovery rate	0 %	100 %
				Constant default rate	0 %	18 %
				Constant prepayment rate	0 %	29 %
Total mortgage- and other asset-backed securities	1,365	0
Debt securities and other debt obligations	3,626	1,757	Price based	Price	0 %	169 %
Held for trading	3,373	52	Discounted cash flow	Credit spread (bps)	26	882
Corporate, sovereign and other debt securities	3,373
Available-for-sale	253
Designated at fair value	0	1,705
Equity securities	937	0	Market approach	Price per net asset value	60 %	100 %
Held for trading	274	0		Enterprise value/EBITDA (multiple)	1	12
Available-for-sale	633		Discounted cash flow	Weighted average cost capital	8 %	22 %
Designated at fair value	30
Loans	7,571	0	Price based	Price	0 %	180 %
Held for trading	4,105	0	Discounted cash flow	Credit spread (bps)	180	4,612
Designated at fair value	980			Constant default rate	0 %	24 %
Available-for-sale	2,486			Recovery rate	25 %	80 %
Loan commitments	0	40	Discounted cash flow	Credit spread (bps)	0	481
				Recovery rate	30 %	99 %
			Loan pricing model	Utilization	0 %	100 %
Other financial instruments	2,974 ²	485 ³	Discounted cash flow	IRR	3 %	24 %
				Repo rate (bps)	178	214
Total non-derivative financial instruments held at fair value	16,474	2,282

¹Valuation technique(s) and subsequently the significant unobservable input(s) relate to the respective total position.

²Other financial assets include € 1.6 billion of other trading assets, € 592 million of other financial assets designated at fair value and € 780 million other financial assets available for sale.

³Other financial liabilities include € 444 million of securities sold under repurchase agreements designated at fair value and € 41 million of other financial liabilities designated at fair value.

	Dec 31, 2016
	Fair value
in € m. (unless stated otherwise)	Assets	Liabilities	Valuation technique(s)	Significant unobservable input(s) (Level 3)	Range
Financial instruments held at fair value:
Market values from derivative financial instruments:
Interest rate derivatives	5,587	3,446	Discounted cash flow	Swap rate (bps)	(0)	2,309
				Inflation swap rate	(1) %	16 %
				Constant default rate	0 %	15 %
				Constant prepayment rate	0 %	19 %
			Option pricing model	Inflation volatility	0 %	5 %
				Interest rate volatility	0 %	123 %
				IR - IR correlation	(12) %	99 %
				Hybrid correlation	(50) %	93 %
Credit derivatives	829	1,126	Discounted cash flow	Credit spread (bps)	0	8,427
				Recovery rate	0 %	100 %
			Correlation pricing model	Credit correlation	13 %	85 %
Equity derivatives	1,142	2,098	Option pricing model	Stock volatility	10 %	67 %
				Index volatility	10 %	44 %
				Index - index correlation	73 %	88 %
				Stock - stock correlation	8 %	88 %
				Stock Forwards	0 %	8 %
				Index Forwards	0 %	20 %
FX derivatives	1,654	1,780	Option pricing model	Volatility	(8) %	39 %
Other derivatives	586	(441) ¹	Discounted cash flow	Credit spread (bps)	0	0
			Option pricing model	Index volatility	5 %	110 %
				Commodity correlation	(21) %	85 %
Total market values from derivative financial instruments	9,798	8,008

¹Includes derivatives which are embedded in contracts where the host contract is held at amortized cost but for which the embedded derivative is separated.

Unrealized Gains or Losses on Level 3 Instruments held or in Issue at the Reporting Date

The unrealized gains or losses on Level 3 Instruments are not due solely to unobservable parameters. Many of the parameter inputs to the valuation of instruments in this level of the hierarchy are observable and the gain or loss is partly due to movements in these observable parameters over the period. Many of the positions in this level of the hierarchy are economically hedged by instruments which are categorized in other levels of the fair value hierarchy. The offsetting gains and losses that have been recorded on all such hedges are not included in the table below, which only shows the gains and losses related to the Level 3 classified instruments themselves held at the reporting date in accordance with IFRS 13.The unrealized gains and losses on Level 3 instruments are included in both net interest income and net gains on financial assets/liabilities at fair value through profit or loss in the consolidated income statement.

in € m.	Dec 31, 2017	Dec 31, 2016
Financial assets held at fair value:
Trading securities	(15)	28
Positive market values from derivative financial instruments	171	1,597
Other trading assets	55	(80)
Financial assets designated at fair value through profit or loss	2	(1)
Financial assets available for sale	123	90
Other financial assets at fair value	33	(6)
Total financial assets held at fair value	368	1,628
Financial liabilities held at fair value:
Trading securities	3	(2)
Negative market values from derivative financial instruments	(740)	(1,001)
Other trading liabilities	0	(0)
Financial liabilities designated at fair value through profit or loss	4	59
Other financial liabilities at fair value	(249)	(139)
Total financial liabilities held at fair value	(981)	(1,082)
Total	(613)	547

Recognition of Trade Date Profit

If there are significant unobservable inputs used in a valuation technique, the financial instrument is recognized at the transaction price and any trade date profit is deferred. The table below presents the year-to-year movement of the trade date profits deferred due to significant unobservable parameters for financial instruments classified at fair value through profit or loss. The balance is predominantly related to derivative instruments.

in € m.	2017	2016
Balance, beginning of year	916	955
New trades during the period	277	454
Amortization	(282)	(297)
Matured trades	(140)	(158)
Subsequent move to observability	(71)	(39)
Exchange rate changes	(11)	0
Balance, end of year	690	916