v3.25.4
Financial Instruments Carried at Fair Value
 12 Months Ended
Dec. 31, 2025
Financial Instruments carried at Fair Value [Abstract]  
Financial Instruments Carried at Fair Value 13 — 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.
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 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 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 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 issued
note liabilities designated at fair value through profit or loss) incorporates valuation adjustments to measure the change
in the Group’s own credit risk (i.e., debt valuation adjustments for derivatives and own credit adjustment for issued note
liabilities). Issued note liabilities are discounted utilizing the spread at which similar instruments would be traded as at
the measurement date as this reflects the value from the perspective of a market participant who holds the identical
item as an asset. The change in this own credit component is reported under other comprehensive income.
For derivative liabilities the Group considers its own creditworthiness by assessing all counterparties expected future
exposure to the Group, taking into account any collateral posted by the Group, the effect of relevant netting
arrangements, the market price of the Group’s issued note liabilities, the market implied funding costs and the seniority
of derivative claims under resolution (statutory subordination).
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 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.
The Group uses the assumptions that market participants would use when pricing the asset or liability. Where relevant,
these assumptions may include assumptions about climate change. The Group has not made material adjustment to fair
value for climate change beyond that already priced into market inputs.
Valuation control – The Group has an independent specialized valuation control group within the Risk 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 analyzed 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.
Valuation techniques
The Group has an established valuation control framework which governs internal control standards, methodologies,
valuation techniques and procedures over the valuation process and fair value measurement.
The following explanations provide an overview 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 collateralized debt obligations (CDO). 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 CDS 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 (i.e., own credit adjustment (OCA) for
structured notes). Under IFRS 9, the own credit component of change in the fair value is reported under other
comprehensive income. Financial liabilities included in this classification are structured note issuances, structured
deposits, and other structured securities issued by consolidated vehicles. The fair value of these financial liabilities is
determined by discounting the contractual cash flows using the relevant credit-adjusted yield curve (i.e., utilizing the
spread at which similar instruments would be traded as at the measurement date as this reflects the value from the
perspective of a market participant who holds the identical item as an asset).
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
and obliges the Group to use these assets to settle the linked 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).
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.
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 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 significant inputs to that technique are observable.
These include: many OTC derivatives, many investment-grade listed credit bonds, some CDS.
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 input to that technique
which is unobservable and can have 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), some private equity placements, many CRE loans, illiquid loans, and some
municipal bonds.
Financial instruments held at fair value
Dec 31, 2025
Dec 31, 2024
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
64,552
78,554
10,705
52,387
78,237
9,148
Trading securities
62,958
63,987
3,635
52,387
69,507
2,964
Other trading assets
1,593
14,567
7,070
—
8,730
6,184
Positive market values from derivative
financial instruments
1,273
233,373
7,008
940
282,927
7,933
Non-trading financial assets mandatory
at fair value through profit or loss
1,570
117,244
5,681
1,346
107,173
5,805
Financial assets designated at fair value
through profit or loss
—
—
—
—
—
—
Financial assets at fair value through
other comprehensive income
25,262
16,034
2,348
21,901
16,806
3,383
Other financial assets at fair value
1,594
(821)1
22
1,460
(1,135)1
12
Total financial assets held at fair value
94,250
444,384
25,764
78,034
484,008
26,281
Financial liabilities held at fair value:
Trading liabilities
33,727
9,127
25
30,765
12,614
119
Trading securities
33,727
7,391
23
30,765
11,073
26
Other trading liabilities
—
1,735
2
—
1,542
93
Negative market values from derivative
financial instruments
2,770
217,119
5,938
2,238
265,464
8,707
Financial liabilities designated at fair
value through profit or loss
154
109,354
5,547
—
87,479
4,569
Investment contract liabilities
—
469
—
—
454
—
Other financial liabilities at fair value
375
(193)1
362
539
3,1011
(13)2
Total financial liabilities held at fair value
37,025
335,875
11,547
33,543
369,113
13,382
1Predominantly relates to derivatives qualifying for hedge accounting
2Relates to derivatives which are embedded in contracts where the host contract is held at amortized cost but for which the embedded derivative is bifurcated and
reported separately. The separated embedded derivatives may have a positive or a negative fair value and classification presented in this table is consistent with the
classification of the host contract
During the year 2025, there were transfers in trading securities and non-trading financial assets from Level 1 to Level 2
amounting to € 2.4 billion of assets and € 0.8 billion of liabilities; along with transfers from Level 2 to Level 1 of
€ 8.4 billion in assets and € 1.5 billion in liabilities. The assessment of Level 1 versus Level 2 is based on liquidity testing
procedures.
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 increase
in the period is driven by purchases and gains partially offset by sales, settlements and net 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 include 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 during the period are driven by net transfers between Level 2 and Level 3 due to changes in the
observability of input parameters used to value these instruments and settlements, partially offset by gains. The
decrease in liabilities during the period are driven by net transfers between Level 2 and Level 3 due to changes in the
observability of input parameters used to value these instruments and losses, partially offset by settlements.
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. The increase in the period is driven by
issuances, purchases and net transfers between Level 2 and Level 3 due to changes in the observability of input
parameters used to value these instruments partially offset by sales, settlements and losses.
Non-trading financial assets mandatory at fair value through profit or loss classified in Level 3 of fair value hierarchy
include any non-trading financial asset that does not fall into the Hold to Collect nor Hold to Collect and Sell business
models. This includes predominately reverse repurchase agreements which are managed on a fair value basis.
Additionally, any financial asset that falls into the Hold to Collect or Hold to Collect and Sell business models for which
the contractual cash flow characteristics are not SPPI. The decrease in the period is driven by net transfers between
Level 2 and Level 3 due to changes in the observability of input parameters used to value these instruments, settlements,
sales and losses partially offset by purchases and issuances.
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 were 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. There are no assets designated at fair value during the period. The increase in liabilities during the period is
driven by issuances partially offset by net transfers between Level 2 and Level 3 due to changes in the observability of
input parameters used to value these instruments, settlements and losses.
Financial assets at fair value through other comprehensive income include non-performing loan portfolios where there is
no trading intent, and the market is very illiquid. The decrease in the period is driven by settlements, sales, losses and net
transfers between Level 2 and Level 3 due to changes in the observability of input parameters used to value these
instruments partially offset by purchases and issuances.
Reconciliation of financial instruments classified in Level 3
Reconciliation of financial instruments classified in Level 3
Dec 31, 2025
in € m.
Balance,
beginning
of year
Changes in the
group of
consolidated
companies
Total gains/
losses1
Purchases
Sales
Issuances2
Settlements3
Transfers into
Level 34
Transfers out of
Level 34
Balance,
end of
year
Financial assets held at fair value:
Trading securities
2,964
—
39
2,986
(1,837)
4
(402)
508
(626)
3,635
Positive market values from derivative financial instruments
7,933
—
949
—
—
—
(351)
1,535
(3,058)
7,008
Other trading assets
6,184
—
(362)
1,231
(2,144)
3,301
(1,380)
447
(208)
7,070
Non-trading financial assets mandatory at fair value through profit or loss
5,805
(3)
(135)
1,849
(190)
782
(1,117)
71
(1,380)
5,681
Financial assets designated at fair value through profit or loss
—
—
—
—
—
—
—
—
—
—
Financial assets at fair value through other comprehensive income
3,383
—
(229)5
700
(431)
482
(1,552)
407
(412)
2,348
Other financial assets at fair value
12
—
(6)
—
—
—
—
20
(4)
22
Total financial assets held at fair value
26,281
(3)
2556,7
6,766
(4,602)
4,569
(4,802)
2,988
(5,688)
25,764
Financial liabilities held at fair value:
Trading securities
26
—
1
—
—
—
(4)
—
—
23
Negative market values from derivative financial instruments
8,707
—
(1,122)
—
—
—
217
1,182
(3,047)
5,938
Other trading liabilities
93
—
1
—
—
—
(92)
—
—
2
Financial liabilities designated at fair value through profit or loss
4,569
—
(134)
—
—
3,255
(690)
508
(1,960)
5,547
Other financial liabilities at fair value
(13)
—
118
—
—
—
(1)
13
(81)
36
Total financial liabilities held at fair value
13,382
—
(1,136)6,7
—
—
3,255
(569)
1,704
(5,088)
11,547
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 total also includes net gains (losses) on financial assets at fair value through other comprehensive income 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
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 periodic and lump sum principal payments. 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 financial assets at fair value through other comprehensive income include a gain of € 14 million recognized in other comprehensive income, net of tax and a gain of € 1 million recognized in the income statement presented in net gains (loss)
6This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a loss of € 802 million and for total financial liabilities held at fair value this is a gain of € 206 million
7For assets positive balances represent gains, negative balances represent losses. For liabilities positive balances represent losses, negative balances represent gains
Dec 31, 2024
in € m.
Balance,
beginning
of year
Changes in the
group of
consolidated
companies
Total gains/
losses1
Purchases
Sales
Issuances2
Settlements3
Transfers into
Level 34
Transfers
out of
Level 34
Balance,
end of
year
Financial assets held at fair value:
Trading securities
2,995
—
230
1,985
(1,558)
—
(482)
371
(577)
2,964
Positive market values from derivative financial instruments
8,198
—
454
—
—
—
(583)
2,257
(2,394)
7,933
Other trading assets
6,226
—
77
814
(1,378)
2,513
(2,016)
706
(756)
6,184
Non-trading financial assets mandatory at fair value through profit or loss
5,226
(1)
88
1,736
(80)
736
(1,098)
365
(1,170)
5,805
Financial assets designated at fair value through profit or loss
—
—
—
—
—
—
—
—
—
—
Financial assets at fair value through other comprehensive income
2,949
—
1265
776
(378)
978
(1,322)
716
(462)
3,383
Other financial assets at fair value
5
—
3
—
—
—
—
5
(1)
12
Total financial assets held at fair value
25,599
(1)
9776,7
5,311
(3,393)
4,227
(5,501)
4,421
(5,359)
26,281
Financial liabilities held at fair value:
Trading securities
26
—
—
—
—
—
—
—
—
26
Negative market values from derivative financial instruments
7,666
—
1,186
—
—
—
(175)
2,156
(2,126)
8,707
Other trading liabilities
—
—
—
—
—
—
93
—
—
93
Financial liabilities designated at fair value through profit or loss
3,248
—
129
—
—
2,958
(474)
377
(1,669)
4,569
Other financial liabilities at fair value
(85)
—
102
—
—
—
18
1
(49)
(13)
Total financial liabilities held at fair value
10,856
—
1,4176,7
—
—
2,958
(537)
2,533
(3,844)
13,382
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 total also includes net gains (losses) on financial assets at fair value through other comprehensive income 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
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 periodic and lump sum principal payments. 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 period 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 period since the table is presented as if they have been transferred out at the beginning of the year
5Total gains and losses on financial assets at fair value through other comprehensive income include a gain of € 29 million recognized in other comprehensive income, net of tax
6This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a gain of € 362 million and for total financial liabilities held at fair value this is a loss of € 19 million
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.
If the Group marked Level 3 financial instruments using parameter values drawn from the extremes of the ranges of
reasonably possible alternatives, as of December 31, 2025 it could have increased fair value by as much as € 2.1 billion or
decreased fair value by as much as € 1.3 billion. As of December 31, 2024 it could have increased fair value by as much as
€ 2.1 billion or decreased fair value by as much as € 1.3 billion.
The changes in sensitive amounts from December 31, 2024 to December 31, 2025 were an increase in positive fair value
movement of € 42 million, and a reduction in negative fair value movement of € 48 million.
The change in positive fair value movements from December 31, 2024 to December 31, 2025 represents a 2% increase
and the change in negative fair value movements represents a 4% reduction. The Group’s sensitivity calculation of
unobservable parameters for Level 3 continues to align 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
capitalizing valuation uncertainty in accordance with the European Commission Delegated Regulation (EU) 2016/101,
which supplements Article 34 of Regulation (EU) No. 2019/876 (CRR), requiring institutions to apply the requirements of
Article 105 (14) to all assets measured at fair value and to deduct any additional value adjustments from CET1 capital.
This utilizes an exit price analysis performed for the relevant assets and liabilities in the prudent valuation assessment.
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, 2025
Dec 31, 2024
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
237
219
308
276
Commercial mortgage-backed securities
13
13
17
17
Mortgage and other asset-backed securities
10
9
11
11
Corporate, sovereign and other debt securities
214
197
280
248
Equity securities
102
74
78
77
Derivatives:
Credit
261
127
207
105
Equity
74
36
36
33
Interest related
660
339
798
337
Foreign Exchange
64
46
56
24
Other
222
61
110
105
Loans
475
394
458
387
Other
—
—
—
—
Total
2,094
1,294
2,052
1,343
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 behavior 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 than 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. The table below provides 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 risk free rate, 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 bank 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 and constant prepayment rate 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 constant default rate 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
behavior of these underlying references through time. Volatility parameters describe key attributes of option behavior 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 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, 2025
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 -Non-Derivative financial
instruments held at fair value:
Mortgage and other asset backed
securities held for trading:
Commercial mortgage-backed
securities
42
—
Price based
Price
0%
101%
Discounted cash flow
Credit spread (bps)
194
1,019
Mortgage- and other asset-
backed
securities
91
—
Price based
Price
0%
105%
Discounted cash flow
Credit spread (bps)
98
1,166
Recovery rate
7%
85%
Constant default rate
0%
4%
Constant prepayment rate
1%
37%
Total mortgage- and other asset-
backed
securities
133
—
Debt securities and other debt
obligations
5,320
5,503
Price based
Price
0%
300%
Held for trading
3,447
19
Discounted cash flow
Credit spread (bps)
5
696
Corporate, sovereign and
other debt securities
3,447
Non-trading financial assets
mandatory at fair value through
profit or loss
1,474
Designated at fair value
through profit or loss
0
5,484
Financial assets at fair value
through other comprehensive
income
399
Equity securities
816
4
Market approach
Price per net asset value
0%
100%
Held for trading
55
4
Enterprise value/EBITDA
(multiple)
1
14
Enterprise value/Revenue
(multiple)
4
14
Non-trading financial assets
mandatory at fair value through
profit or loss
761
Discounted cash flow
Weighted average cost
capital
9%
20%
Designated at fair value
through profit or loss
0
Price based
Price
0%
2500%
Loans
11,293
2
Price based
Price
0%
300%
Held for trading
6,913
2
Discounted cash flow
Credit spread (bps)
94
3,106
Non-trading financial assets
mandatory at fair value through
profit or loss
2,490
Designated at fair value
through profit or loss
0
Recovery rate
40%
75%
Financial assets at fair value
through other comprehensive
income
1,890
Loan commitments
2
Discounted cash flow
Credit spread (bps)
153
978
Recovery rate
70%
84%
Loan pricing model
Utilization
0%
100%
Other financial instruments
1,1722
613
Discounted cash flow
IRR
7%
13%
Repo rate (bps)
8
285
Total non-derivative financial
instruments held at fair value
18,734
5,572
1 Valuation technique(s) and subsequently the significant unobservable input(s) relate to the respective total position
2Other financial assets include € 157 million of other trading assets, € 1 billion of other non-trading financial assets mandatory at fair value, and € 59 million other financial
assets at fair value through other comprehensive income
3Other financial liabilities include € 61 million of securities sold under repurchase agreements designated at fair value
Dec 31, 2025
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
3,798
2,950
Discounted cash flow
Swap rate (bps)
(720)
3,818
Inflation swap rate
0%
8%
Constant default rate
1%
11%
Constant prepayment rate
2%
16%
Option pricing model
Inflation volatility
0%
8%
Interest rate volatility
0%
2%
IR - IR correlation
(10)%
95%
Hybrid correlation
(56)%
95%
Credit derivatives
556
603
Discounted cash flow
Credit spread (bps)
12
1,277
Recovery rate
15%
94%
Option pricing model
Credit volatility
5%
90%
Correlation pricing
model
Credit correlation
Equity derivatives
481
572
Option pricing model
Stock volatility
1%
101%
Index volatility
6%
17%
Index - index correlation
Stock - stock correlation
Stock Forwards
0%
5%
Index Forwards
0%
6%
FX derivatives
1,523
1,561
Option pricing model
Volatility
(9)%
57%
Quoted Vol
Discounted cash flow
Swap rate (bps)
(2)
100
Other derivatives
673
2891
Discounted cash flow
Credit spread (bps)
201
568
Option pricing model
Index volatility
0%
116%
Price
0%
677%
Commodity correlation
(22)%
98%
Total market values from
derivative
financial instruments
7,030
5,974
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, 2024
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 – Non-Derivative financial
instruments held at fair value:
Mortgage and other asset backed
securities held for trading:
Commercial mortgage-backed
securities
31
—
Price based
Price
0%
102%
Discounted cash flow
Credit spread (bps)
167
1,486
Mortgage- and other asset-
backed
securities
93
—
Price based
Price
0%
107%
Discounted cash flow
Credit spread (bps)
106
1,027
Recovery rate
60%
85%
Constant default rate
0%
4%
Constant prepayment rate
4%
18%
Total mortgage- and other asset-
backed
securities
124
—
Debt securities and other debt
obligations
4,379
4,537
Price based
Price
0%
300%
Held for trading
2,726
26
Discounted cash flow
Credit spread (bps)
9
651
Corporate, sovereign and
other
debt securities
2,726
Non-trading financial assets
mandatory at fair value through
profit or loss
1,499
Designated at fair value
through profit or loss
—
4,512
Financial assets at fair value
through other comprehensive
income
154
Equity securities
809
—
Market approach
Price per net asset value
0%
100%
Held for trading
114
—
Enterprise value/EBITDA
(multiple)
5
14
Enterprise value/Revenue
(multiple)
1
15
Non-trading financial assets
mandatory at fair value through
profit or loss
695
Discounted cash flow
Weighted average cost
capital
9%
20%
Designated at fair value
through profit or loss
—
Price based
Price
0%
100%
Loans
10,817
93
Price based
Price
0%
123%
Held for trading
5,931
93
Discounted cash flow
Credit spread (bps)
100
1,621
Non-trading financial assets
mandatory at fair value through
profit or loss
1,779
Designated at fair value
through profit or loss
—
—
Recovery rate
40%
84%
Financial assets at fair value
through other comprehensive
income
3,107
Loan commitments
—
6
Discounted cash flow
Credit spread (bps)
226
954
Recovery rate
40%
84%
Loan pricing model
Utilization
0%
100%
Other financial instruments
2,2082
513
Discounted cash flow
IRR
7%
13%
Repo rate (bps)
30
285
Total non-derivative financial
instruments held at fair value
18,336
4,688
1Valuation technique(s) and subsequently the significant unobservable input(s) relate to the respective total position
2Other financial assets include € 253 million of other trading assets, € 1.8 billion of other non-trading financial assets mandatory at fair value, and € 123 million other
financial assets at fair value through other comprehensive income
3Other financial liabilities include € 51 million of securities sold under repurchase agreements designated at fair value
Dec 31, 2024
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
5,218
5,207
Discounted cash flow
Swap rate (bps)
(4,176)
3,975
Inflation swap rate
0%
5%
Constant default rate
0%
12%
Constant prepayment rate
4%
16%
Option pricing model
Inflation volatility
0%
6%
Interest rate volatility
0%
3%
IR - IR correlation
(10)%
99%
Hybrid correlation
(70)%
55%
Credit derivatives
510
562
Discounted cash flow
Credit spread (bps)
15
1,148
Recovery rate
0%
40%
Correlation pricing
model
Credit correlation
0%
0%
Equity derivatives
642
1,201
Option pricing model
Stock volatility
2%
86%
Index volatility
9%
27%
Index - index correlation
0%
0%
Stock - stock correlation
0%
0%
Stock Forwards
0%
1%
Index Forwards
0%
1%
FX derivatives
995
1,470
Option pricing model
Volatility
(9)%
33%
Quoted Vol
0%
0%
Discounted cash flow
Swap rate (bps)
(3)
100
Other derivatives
580
2541
Discounted cash flow
Credit spread (bps)
286
626
Option pricing model
Index volatility
0%
160%
Price
17%
75%
Commodity correlation
0%
87%
Total market values from
derivative
financial instruments
7,945
8,694
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 solely due 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, 2025
Dec 31, 2024
Financial assets held at fair value:
Trading securities
38
113
Positive market values from derivative financial instruments
1,574
1,535
Other trading assets
(218)
(54)
Non-trading financial assets mandatory at fair value through profit or loss
93
57
Financial assets designated at fair value through profit or loss
—
—
Financial assets at fair value through other comprehensive income
—
(4)
Other financial assets at fair value
5
(3)
Total financial assets held at fair value
1,491
1,645
Financial liabilities held at fair value:
Trading securities
(1)
—
Negative market values from derivative financial instruments
(73)
(1,930)
Other trading liabilities
(1)
—
Financial liabilities designated at fair value through profit or loss
124
(104)
Other financial liabilities at fair value
(123)
(102)
Total financial liabilities held at fair value
(75)
(2,135)
Total
1,416
(490)
Recognition of trade date profit
If there are significant unobservable inputs used in a valuation technique on initial recognition, the financial instrument is
recognized at the transaction price and any trade date profit is deferred. The table below presents the movement during
the year 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.
2025
2024
Balance, beginning of year
691
577
New trades during the period
513
343
Amortization
(223)
(141)
Matured trades
(71)
(53)
Subsequent move to observability1
(38)
(36)2
Exchange rate changes
(5)
1
Balance, end of year
866
691
1This includes situations where an input remains unobservable but has become insignificant in relation to the deferred trade date profit in periods subsequent to the trade
date
2During the second quarter of 2024, the Group refined its methodology for the significance test of unobservable inputs subsequent to the trade date. This resulted in
release of € 15 million in the second quarter of 2024