v3.26.1
Financial Instruments carried at fair value
 6 Months Ended
Jun. 30, 2026
Financial Instruments carried at Fair Value [Abstract]  
Financial instruments carried at fair value Financial instruments carried at fair value
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 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 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 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 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 carried at fair value
Jun 30, 2026
Dec 31, 2025
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
71,176
93,621
11,792
64,552
78,554
10,705
Trading securities
68,093
81,646
4,340
62,958
63,987
3,635
Other trading assets
3,083
11,975
7,452
1,593
14,567
7,070
Positive market values from derivative
financial instruments
2,955
265,368
7,570
1,273
233,373
7,008
Non-trading financial assets mandatory
at fair value through profit or loss
1,707
135,771
4,912
1,570
117,244
5,681
Financial assets designated at fair value
through profit or loss
—
—
—
—
—
—
Financial assets at fair value through
other comprehensive income
25,609
20,240
2,691
25,262
16,034
2,348
Other financial assets at fair value
1,592
(1,378)1
22
1,594
(821)1
22
Total financial assets held at fair value
103,039
513,621
26,988
94,250
444,384
25,764
Financial liabilities held at fair value:
Trading liabilities
36,277
11,618
54
33,727
9,127
25
Trading securities
36,276
9,547
22
33,727
7,391
23
Other trading liabilities
—
2,071
32
—
1,735
2
Negative market values from derivative
financial instruments
4,184
250,497
5,489
2,770
217,119
5,938
Financial liabilities designated at fair
value through profit or loss
938
138,848
4,647
154
109,354
5,547
Investment contract liabilities
—
512
—
—
469
—
Other financial liabilities at fair value
418
5261
862
375
(193)1
362
Total financial liabilities held at fair value
41,817
402,001
10,277
37,025
335,875
11,547
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 six months ended June 30, 2026, transfers in trading securities and non-trading financial assets from Level 1
to Level 2 amounted to € 6.0 billion of assets and € 1.5 billion of liabilities; transfers from Level 2 to Level 1 amounted to
€ 5.7 billion of assets and € 2.2 billion of 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, gains 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 and settlements.
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 increase in assets during the period are driven by settlements, gains 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. 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 gains 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 assets during the period is
driven by issuances, purchases, net transfers between Level 2 and Level 3 due to changes in the observability of input
parameters used to value these instruments and gains partially offset by sales and settlements.
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 predominantly 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 settlements, sales 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, gains 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 as level 3 in
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 decrease in liabilities during 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 and settlements partially offset by issuances 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 increase in the period is driven by issuances, purchases and gains
partially offset by settlements, sales and net transfers between Level 2 and Level 3 due to changes in the observability of
input parameters used to value these instruments.
Reconciliation of financial instruments classified in Level 3
Reconciliation of financial instruments classified in Level 3
Jun 30, 2026
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
period
Financial assets held at fair value:
Trading securities
3,635
—
278
1,531
(955)
—
(179)
531
(500)
4,340
Positive market values from derivative financial instruments
7,008
—
383
609
1,497
(1,927)
7,570
Other trading assets
7,070
—
(18)
1,130
(2,242)
2,145
(1,167)
765
(231)
7,452
Non-trading financial assets mandatory at fair value through profit or loss
5,681
—
299
1,585
(357)
167
(2,176)
69
(356)
4,912
Financial assets designated at fair value through profit or loss
—
—
—
—
—
—
—
—
—
—
Financial assets at fair value through other comprehensive income
2,348
—
505
484
(116)
1,297
(1,360)
64
(75)
2,691
Other financial assets at fair value
22
—
3
—
—
—
—
(3)
22
Total financial assets held at fair value
25,764
—
9946,7
4,729
(3,670)
3,610
(4,274)
2,926
(3,093)
26,988
Financial liabilities held at fair value:
Trading securities
23
—
(1)
—
—
—
22
Negative market values from derivative financial instruments
5,938
—
(40)
285
1,150
(1,844)
5,489
Other trading liabilities
2
—
(2)
15
19
(2)
32
Financial liabilities designated at fair value through profit or loss
5,547
—
35
2,034
(669)
425
(2,725)
4,647
Other financial liabilities at fair value
36
—
18
(23)
78
(22)
86
Total financial liabilities held at fair value
11,547
—
106,7
—
—
2,034
(391)
1,671
(4,593)
10,277
1Total gains and losses predominantly relate to net gains (losses) on financial assets/liabilities at fair value through profit or loss reported in the interim 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 € 7 million recognized in other comprehensive income, net of tax and a gain of € 2 million recognized in the income statement presented in net gain (losses)
6This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a gain of € 170 million and for total financial liabilities held at fair value this is a loss of € 10 million
7For assets, positive balances represent gains, negative balances represent losses. For liabilities, positive balances represent losses, negative balances represent gains
Jun 30, 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
period
Financial assets held at fair value:
Trading securities
2,964
—
(23)
991
(864)
—
(130)
697
(465)
3,170
Positive market values from derivative financial instruments
7,933
—
1,230
(162)
1,788
(2,596)
8,193
Other trading assets
6,184
—
(389)
680
(1,201)
1,017
(974)
664
(300)
5,682
Non-trading financial assets mandatory at fair value through profit or loss
5,805
—
(247)
893
(47)
375
(522)
90
(427)
5,920
Financial assets designated at fair value through profit or loss
—
—
—
—
—
—
—
—
—
—
Financial assets at fair value through other comprehensive income
3,383
—
(235)5
445
(157)
311
(483)
376
(479)
3,161
Other financial assets at fair value
12
—
(10)
—
—
—
20
—
22
Total financial assets held at fair value
26,281
—
3266,7
3,008
(2,269)
1,703
(2,271)
3,634
(4,266)
26,148
Financial liabilities held at fair value:
Trading securities
26
—
(6)
—
5
—
25
Negative market values from derivative financial instruments
8,707
—
18
(233)
1,471
(2,635)
7,328
Other trading liabilities
93
—
—
(93)
—
—
—
Financial liabilities designated at fair value through profit or loss
4,569
—
(203)
2,099
(649)
759
(1,302)
5,273
Other financial liabilities at fair value
(13)
—
49
(1)
(12)
(29)
(5)
Total financial liabilities held at fair value
13,382
—
(141)6,7
—
—
2,099
(976)
2,223
(3,965)
12,621
1Total gains and losses predominantly relate to net gains (losses) on financial assets/liabilities at fair value through profit or loss reported in the interim 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 loss of € 1 million recognized in other comprehensive income, net of tax and a gain of € 2 million recognized in the income statement presented in net gain (losses)
6This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a loss of € 749 million and for total financial liabilities held at fair value this is a gain of € 158 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 June 30, 2026 it could have increased fair value by as much as € 2.2 billion or
decreased fair value by as much as € 1.3 billion. 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.
The changes in sensitive amounts from December 31, 2025, to June 30, 2026, were an increase in positive fair value
movement of € 77 million, and an increase in negative fair value movement of € 51 million.
The change in positive fair value movements from December 31, 2025, to June 30, 2026, represents a 4% increase and
the change in negative fair value movements represents a 4% increase. 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
Jun 30, 2026
Dec 31, 2025
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
167
144
237
219
Commercial mortgage-backed securities
15
15
13
13
Mortgage and other asset-backed securities
14
14
10
9
Corporate, sovereign and other debt securities
138
115
214
197
Equity securities
109
81
102
74
Derivatives:
Credit
275
159
261
127
Equity
116
56
74
36
Interest related
763
416
660
339
Foreign Exchange
76
43
64
46
Other
239
84
222
61
Loans
426
364
475
394
Other
—
—
—
—
Total
2,171
1,346
2,094
1,294
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
Jun 30, 2026
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
55
Price based
Price
0%
101%
Discounted cash
flow
Credit spread (bps)
109
881
Mortgage- and other asset-backed
securities
84
Price based
Price
0%
105%
Discounted cash
flow
Credit spread (bps)
67
877
Recovery rate
20%
85%
Constant default rate
0%
4%
Constant prepayment
rate
1%
30%
Total mortgage- and other asset-backed
securities
139
—
Debt securities and other debt
obligations
5,950
4,662
Price based
Price
0%
1007%
Held for trading
4,125
19
Discounted cash
flow
Credit spread (bps)
52
452
Corporate, sovereign and other
debt securities
4,125
Non-trading financial assets mandatory
at fair value through profit or loss
1,362
Designated at fair value through profit or
loss
—
4,644
Financial assets at fair value through
other comprehensive income
462
Equity securities
725
3
Market approach
Price per net asset
value
0%
100%
Held for trading
76
3
Enterprise value/
EBITDA
(multiple)
1
14
Enterprise value/
Revenue (multiple)
4
8
Non-trading financial assets mandatory
at fair value through profit or loss
649
Discounted cash
flow
Weighted average cost
capital
9%
20%
Price based
Price
0%
75%
Loans
11,436
32
Price based
Price
0%
167%
Held for trading
7,317
32
Discounted cash
flow
Credit spread (bps)
10
3,115
Non-trading financial assets mandatory
at fair value through profit or loss
1,917
Designated at fair value through profit or
loss
—
Recovery rate
40%
84%
Financial assets at fair value through
other comprehensive income
2,202
Loan commitments
4
Discounted cash
flow
Credit spread (bps)
157
984
Recovery rate
70%
84%
Loan pricing model
Utilization
0%
100%
Other financial instruments
1,1462
—
Discounted cash
flow
IRR
7%
13%
Repo rate (bps.)
0
350
Total non-derivative financial
instruments held at fair value
19,396
4,701
1Valuation technique(s) and subsequently the significant unobservable input(s) relate to the respective total position
2Other financial assets include € 135 million of other trading assets, € 984 million of other non-trading financial assets mandatory at fair value and € 27 million other
financial assets at fair value through other comprehensive income
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
—
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%
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
—
—
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
1Valuation 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
Jun 30, 2026
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
4,187
2,872
Discounted
cash flow
Swap rate (bps)
(1,245)
4,085
Inflation swap rate
0%
9%
Constant default rate
2%
5%
Constant prepayment
rate
3%
7%
Option pricing
model
Inflation volatility
0%
7%
Interest rate volatility
0%
3%
IR - IR correlation
(25%)
96%
Hybrid correlation
(56%)
95%
Credit derivatives
706
611
Discounted
cash flow
Credit spread (bps)
1
3,095
Recovery rate
15%
82%
Option pricing
model
Credit volatility
5%
90%
Correlation
pricing
model
Credit correlation
Equity derivatives
484
619
Option pricing
model
Stock volatility
46%
68%
Index volatility
2%
49%
Index - index
correlation
Stock - stock
correlation
Stock Forwards
0%
1%
Index Forwards
0%
10%
FX derivatives
1,519
1,107
Option pricing
model
Volatility
(15%)
47%
Quoted Vol
Discounted
cash flow
Swap rate (bps)
(14)
100
Other derivatives
696
3671
Discounted
cash flow
Credit spread (bps)
230
717
Option pricing
model
Index volatility
1%
110%
Price
Commodity correlation
42%
87%
Total market values from derivative
financial instruments
7,592
5,576
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, 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
0%
0%
Equity derivatives
481
572
Option pricing
model
Stock volatility
1%
101%
Index volatility
6%
17%
Index - index
correlation
0%
0%
Stock - stock
correlation
0%
0%
Stock Forwards
0%
5%
Index Forwards
0%
6%
FX derivatives
1,523
1,561
Option pricing
model
Volatility
(9%)
57%
Quoted Vol
0%
0%
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
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.
Six months ended
in € m.
Jun 30, 2026
Jun 30, 2025
Financial assets held at fair value:
Trading securities
191
34
Positive market values from derivative financial instruments
633
1,725
Other trading assets
(5)
(189)
Non-trading financial assets mandatory at fair value through profit or loss
107
(7)
Financial assets designated at fair value through profit or loss
—
—
Financial assets at fair value through other comprehensive income
1
—
Other financial assets at fair value
(2)
9
Total financial assets held at fair value
925
1,572
Financial liabilities held at fair value:
Trading securities
1
6
Negative market values from derivative financial instruments
(375)
(761)
Other trading liabilities
2
—
Financial liabilities designated at fair value through profit or loss
(34)
200
Other financial liabilities at fair value
(19)
(54)
Total financial liabilities held at fair value
(425)
(610)
Total
500
962
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 six months ended for 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.
Jun 30, 2026
Jun 30, 2025
Balance, beginning of year
866
691
New trades during the period
268
215
Amortization
(147)
(118)
Matured trades
(101)
(35)
Subsequent move to observability1
(69)
(26)
Exchange rate changes
1
(5)
Balance, end of period
818
723
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