Financial Instruments carried at Fair Value

 (unaudited)

Fair Value Hierarchy

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

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

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

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

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

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

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

Carrying value of the financial instruments held at fair value1

 

Mar 31, 2015

Dec 31, 2014

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)

1

Amounts in this table are generally presented on a gross basis, in line with the Group’s accounting policy regarding offsetting of financial instruments, as described in Note 1 “Significant Accounting Policies and Critical Accounting Estimates” of the Financial Report 2014.

2

Predominantly relates to derivatives qualifying for hedge accounting.

3

These are investment contracts where the policy terms and conditions result in their redemption value equaling fair value. See Note 41 “Insurance and Investment Contracts” of the Financial Report 2014 for more detail on these contracts.

4

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

Financial assets held at fair value:

 

 

 

 

 

 

Trading assets

88,074

110,563

13,548

82,020

100,505

13,155

Trading securities

87,529

97,376

9,078

81,789

86,894

8,957

Other trading assets

544

13,188

4,470

232

13,611

4,198

Positive market values from derivative financial instruments

8,498

726,430

11,155

5,439

614,960

9,559

Financial assets designated at fair value through profit or loss

10,061

110,452

5,297

8,826

104,307

4,152

Financial assets available for sale

42,098

25,621

4,616

36,272

23,597

4,427

Other financial assets at fair value

0

4,8232

0

0

4,3352

0

Total financial assets held at fair value

148,731

977,890

34,616

132,558

847,705

31,294

 

 

 

 

 

 

 

Financial liabilities held at fair value:

 

 

 

 

 

 

Trading liabilities

38,349

15,765

117

25,290

16,510

43

Trading securities

38,317

14,575

117

25,244

15,826

43

Other trading liabilities

32

1,190

0

46

685

0

Negative market values from derivative financial instruments

8,796

708,214

7,110

5,890

597,759

6,553

Financial liabilities designated at fair value through profit or loss

0

38,585

2,755

2

34,763

2,366

Investment contract liabilities3

0

9,654

0

0

8,523

0

Other financial liabilities at fair value

0

8,3962

(498)4

0

5,5612

(552)4

Total financial liabilities held at fair value

47,146

780,614

9,484

31,181

663,117

8,410

There have been no significant transfers of instruments between level 1 and level 2 of the fair value hierarchy.

Valuation Techniques

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

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

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

Where no reliable external pricing is available, ABS are valued, where applicable, using either relative value analysis which is performed based on similar transactions observable in the market, or industry standard valuation models incorporating available observable inputs. The industry standard external 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. The financial liabilities include structured note issuances, structured deposits, and other structured securities issued by consolidated vehicles, which may not be quoted in an active market. The fair value of these financial liabilities is determined by discounting the contractual cash flows using the relevant credit-adjusted yield curve. The market risk parameters are valued consistently to similar instruments held as assets, for example, any derivatives embedded within the structured notes are valued using the same methodology discussed in the “Over-The-Counter Derivative Financial Instruments” section above.

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

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

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

Some of the instruments 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 as gross assets and liabilities.

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 quarter was mainly due to a combination of mark-to-market gains and transfers between levels 2 and 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 customized CDO derivatives in which the underlying reference pool of corporate assets is not closely comparable to regularly market-traded indices; certain tranched index credit derivatives; 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 the quarter was mainly due to a combination of mark-to-market gains and transfers between levels 2 and 3 due to changes in the observability of input parameters used to value these instruments.

Other Trading Instruments classified in level 3 of the fair value hierarchy mainly consist of traded loans valued using valuation models based on one or more significant unobservable parameters. Level 3 loans comprise illiquid leveraged loans and illiquid residential and commercial mortgage loans. The increase in the quarter was primarily due to purchases and mark-to-market gains on the instruments.

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

In addition, certain hybrid debt issuances designated at fair value through profit or loss containing embedded derivatives are valued based on significant unobservable parameters. These unobservable parameters include single stock volatility correlations. The increase in assets during the period is primarily due to new issuances and mark-to-market gains on the instruments. For liabilities, the increase was driven by a combination of mark-to-market gains and transfers between levels 2 and 3 due to changes in the observability of input parameters used to value these instruments.

Financial Assets Available for Sale include non-performing loan portfolios where there is no trading intent and unlisted equity instruments where there is no close proxy and the market is very illiquid. The increase in assets during the period was primarily due to purchases and mark-to-market gains on the instruments.

Reconciliation of financial instruments classified in Level 3

 

Mar 31, 2015

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

1

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

2

Issuances 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.

3

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

4

Transfers 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.

5

Total gains and losses on available for sale include a gain of € 47 million recognized in other comprehensive income, net of tax, and a gain of € 10 million recognized in the income statement presented in net gains (losses) on financial assets available for sale.

6

This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a gain of € 716 million and for total financial liabilities held at fair value this is a gain of € 208 million. The effect of exchange rate changes is reported in other comprehensive income, net of tax.

7

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

Financial assets held at fair value:

 

 

 

 

 

 

 

 

 

 

Trading securities

8,957

0

773

468

(717)

0

(195)

916

(1,123)

9,078

Positive market values from derivative financial instruments

9,559

0

1,645

0

0

0

(293)

982

(738)

11,155

Other trading assets

4,198

0

398

344

(351)

94

(132)

213

(296)

4,470

Financial assets designated at fair value through profit or loss

4,152

0

496

195

0

820

(392)

58

(33)

5,297

Financial assets available for sale

4,427

0

2895

174

(100)

0

(214)

58

(18)

4,616

Other financial assets at fair value

0

0

0

0

0

0

0

0

0

0

Total financial assets held at fair value

31,294

0

3,6016,7

1,181

(1,168)

915

(1,225)

2,227

(2,208)

34,616

 

 

 

 

 

 

 

 

 

 

 

Financial liabilities held at fair value:

 

 

 

 

 

 

 

 

 

 

Trading securities

43

0

7

0

0

0

32

42

(6)

117

Negative market values from derivative financial instruments

6,553

0

981

0

0

0

(113)

669

(981)

7,110

Other trading liabilities

0

0

0

0

0

0

0

0

0

0

Financial liabilities designated at fair value through profit or loss

2,366

0

208

0

0

157

(67)

112

(22)

2,755

Other financial liabilities at fair value

(552)

0

(55)

0

0

0

64

31

14

(498)

Total financial liabilities held at fair value

8,410

0

1,1426,7

0

0

157

(84)

854

(996)

9,484

 

Mar 31, 2014

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

1

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

2

Issuances 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.

3

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

4

Transfers 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.

5

Total gains and losses on available for sale include a gain of € 10 million recognized in other comprehensive income, net of tax, and a gain of € 1 million recognized in the income statement presented in net gains (losses) on financial assets available for sale.

6

Represents assets held for sale related to BHF-BANK.

7

This amount includes the effect of exchange rate changes. For total financial assets held at fair value this effect is a gain of € 26 million and for total financial liabilities held at fair value this is a gain of € 3 million. The effect of exchange rate changes is reported in other comprehensive income, net of tax.

8

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

Financial assets held at fair value:

 

 

 

 

 

 

 

 

 

 

Trading securities

6,960

0

123

360

(783)

0

(146)

1,225

(1,224)

6,514

Positive market values from derivative financial instruments

10,556

0

(314)

0

0

0

(210)

1,031

(786)

10,277

Other trading assets

5,065

0

(16)

637

(720)

306

(70)

286

(639)

4,847

Financial assets designated at fair value through profit or loss

3,123

0

24

61

(9)

379

(431)

166

(76)

3,236

Financial assets available for sale

3,329

0

(56)5

93

(59)

0

(221)

148

(50)

3,183

Other financial assets at fair value6

1

(1)

0

0

0

0

0

0

0

0

Total financial assets held at fair value

29,033

(1)

(240)7,8

1,150

(1,572)

685

(1,078)

2,856

(2,775)

28,058

 

 

 

 

 

 

 

 

 

 

 

Financial liabilities held at fair value:

 

 

 

 

 

 

 

 

 

 

Trading securities

24

0

0

0

0

0

0

0

(2)

22

Negative market values from derivative financial instruments

8,321

0

(221)

0

0

0

(123)

571

(1,030)

7,517

Other trading liabilities

0

0

0

0

0

0

0

0

0

1

Financial liabilities designated at fair value through profit or loss

1,442

0

(102)

0

0

57

56

663

(51)

2,065

Other financial liabilities at fair value

(247)

0

8

0

0

0

(5)

0

191

(53)

Total financial liabilities held at fair value

9,539

0

(315)7,8

0

0

57

(71)

1,234

(892)

9,552

Sensitivity Analysis of Unobservable Parameters

Where the value of financial instruments is dependent on unobservable parameter inputs, the precise level for these parameters at the balance sheet date might be drawn from a range of reasonably possible alternatives. In preparing the financial statements, appropriate levels for these unobservable input parameters are chosen so that they are consistent with prevailing market evidence and in line with the Group’s approach to valuation control detailed above. Were the Group to have marked the financial instruments concerned using parameter values drawn from the extremes of the ranges of reasonably possible alternatives then as of March 31, 2015 it could have increased fair value by as much as € 3.4 billion or decreased fair value by as much as € 3.0 billion. As of December 31, 2014 it could have increased fair value by as much as € 3.3 billion or decreased fair value by as much as € 2.9 billion. In estimating these impacts, the Group either re-valued certain financial instruments using reasonably possible alternative parameter values, or used an approach based on its valuation adjustment methodology for bid-offer spread valuation adjustments. Bid-offer spread valuation adjustments reflect the amount that must be paid in order to close out a holding in an instrument or component risk and as such they reflect factors such as market illiquidity and uncertainty.

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

 

Mar 31, 2015

Dec 31, 2014

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

1

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

Securities:

 

 

 

 

Debt securities

795

721

833

725

Commercial mortgage-backed securities

30

23

57

47

Mortgage and other asset-backed securities

260

253

235

229

Sovereign and quasi sovereign debt obligations

53

53

63

37

Corporate debt securities and other debt obligations

451

392

478

412

Equity securities

124

214

124

224

Derivatives:

 

 

 

 

Credit

452

543

432

457

Equity

152

107

157

115

Interest related

396

207

392

184

Foreign exchange

6

6

4

2

Other

61

55

75

74

Loans:

 

 

 

 

Loans

1,291

1,107

1,175

988

Loan commitments

5

5

6

5

Other

72

67

79

79

Total

3,355

3,032

3,277

2,854

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 then the less liquid, non-performing positions which will have higher credit spreads. As Level 3 contains the less liquid fair value instruments, the wide ranges of parameters seen is to be expected, as there is a high degree of pricing differentiation within each exposure type to capture the relevant market dynamics. There follows a brief description of each of the principle parameter types, along with a commentary on significant interrelationships between them.

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

Interest rates, credit spreads, inflation rates, foreign exchange rates and equity prices are referenced in some option instruments, or other complex derivatives, where the payoff a holder of the derivative will receive is dependent upon the 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 (‘earnings before interest, tax, depreciation and amortization’) multiple approach can be used in the valuation of less liquid securities. Under this approach the enterprise value (‘EV’) of an entity can be estimated via identifying the ratio of the EV to EBITDA of a comparable observable entity and applying this ratio to the EBITDA of the entity for which a valuation is being estimated. Under this approach a liquidity adjustment is often applied due to the difference in liquidity between the generally listed comparable used and the company under valuation. A higher EV/EBITDA multiple will result in a higher fair value.

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

 

Mar 31, 2015

 

Fair value

 

 

 

 

in € m.
(unless stated otherwise)

Assets

Liabilities

Valuation technique(s)1

Significant unobservable input(s) (Level 3)

Range

1

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

2

Other financial assets include € 55 million of other trading assets, € 564 million of other financial assets designated at fair value and € 309 million other financial assets available for sale.

3

Other financial liabilities include € 1.2 billion of securities sold under repurchase agreements designated at fair value and € 116 million of other financial liabilities designated at fair value.

Financial instruments held at fair value – held for trading, designated at fair value and available-for-sale:

 

 

 

 

 

 

Mortgage- and other asset-backed securities

 

 

 

 

 

 

Commercial mortgage-backed securities

219

0

Price based

Price

0 %

107 %

 

 

 

Discounted cash flow

Credit spread (bps)

155

2,730

Mortgage- and other asset-backed securities

2,380

0

Price based

Price

0 %

184 %

 

 

 

Discounted cash flow

Credit spread (bps)

63

1,659

 

 

 

 

Recovery rate

0 %

83 %

 

 

 

 

Constant default rate

0 %

16 %

 

 

 

 

Constant prepayment rate

0 %

20 %

Total mortgage- and other asset-backed securities

2,599

0

 

 

 

 

Debt securities and other debt obligations

5,978

1,487

Price based

Price

0 %

345 %

Held for trading

5,545

117

Discounted cash flow

Credit spread (bps)

9

2,115

Sovereign and quasi sovereign obligations

812

 

 

 

 

 

Corporate debt securities and other debt obligations

4,734

 

 

 

 

 

Available-for-sale

433

 

 

 

 

 

Designated at fair value

0

1,370

 

 

 

 

Equity securities

1,885

0

Market approach

Price per net asset value

40 %

100 %

Held for trading

933

0

 

Enterprise value/EBITDA (multiple)

1

18

Designated at fair value

33

 

 

 

 

 

Available-for-sale

919

 

Discounted cash flow

Weighted average cost capital

8 %

13 %

Loans

12,071

0

Price based

Price

0 %

138 %

Held for trading

4,415

0

Discounted cash flow

Credit spread (bps)

40

3,040

Designated at fair value

4,700

 

 

Constant default rate

1 %

21 %

Available-for-sale

2,956

 

 

Recovery rate

0 %

67 %

Loan commitments

0

67

Discounted cash flow

Credit spread (bps)

3

900

 

 

 

 

Recovery rate

20 %

75 %

 

 

 

Loan pricing model

Utilization

0 %

100 %

Other financial instruments

9282

1,3183

Discounted cash flow

IRR

2 %

24 %

Total financial instruments held at fair value

23,461

2,872

 

 

 

 

 

Dec 31, 2014

 

Fair value

 

 

 

 

in € m.
(unless stated otherwise)

Assets

Liabilities

Valuation technique(s)1

Significant unobservable input(s) (Level 3)

Range

1

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

2

Other financial assets include € 50 million of other trading assets, € 405 million of other financial assets designated at fair value, € 293 million other financial assets available.

3

Other financial liabilities include € 1 billion of securities sold under repurchase agreements designated at fair value and € 104 million of other financial liabilities designated at fair value.

Financial instruments held at fair value – held for trading, designated at fair value and available-for-sale:

 

 

 

 

 

 

Mortgage- and other asset-backed securities

 

 

 

 

 

 

Commercial mortgage-backed securities

342

0

Price based

Price

0 %

106 %

 

 

 

Discounted cash flow

Credit spread (bps)

246

1,375

Mortgage- and other asset-backed securities

2,342

0

Price based

Price

0 %

184 %

 

 

 

Discounted cash flow

Credit spread (bps)

72

1,648

 

 

 

 

Recovery rate

0 %

97 %

 

 

 

 

Constant default rate

0 %

13 %

 

 

 

 

Constant prepayment rate

0 %

22 %

Total mortgage- and other asset-backed securities

2,684

0

 

 

 

 

Debt securities and other debt obligations

5,936

1,202

Price based

Price

0 %

286 %

Held for trading

5,477

43

Discounted cash flow

Credit spread (bps)

32

1,629

Sovereign and quasi sovereign obligations

835

 

 

 

 

 

Corporate debt securities and other debt obligations

4,643

 

 

 

 

 

Available-for-sale

459

 

 

 

 

 

Designated at fair value

0

1,159

 

 

 

 

Equity securities

1,719

0

Market approach

Price per net asset value

49 %

100 %

Held for trading

795

0

 

Enterprise value/EBITDA (multiple)

1

18

Designated at fair value

29

 

 

 

 

 

Available-for-sale

895

 

Discounted cash flow

Weighted average cost capital

6 %

13 %

Loans

10,648

0

Price based

Price

0 %

137 %

Held for trading

4,148

0

Discounted cash flow

Credit spread (bps)

95

3,040

Designated at fair value

3,719

 

 

Constant default rate

2 %

21 %

Available-for-sale

2,781

 

 

Recovery rate

0 %

67 %

Loan commitments

0

87

Discounted cash flow

Credit spread (bps)

115

1,000

 

 

 

 

Recovery rate

20 %

80 %

 

 

 

Loan pricing model

Utilization

0 %

100 %

Other financial instruments

7482

1,1213

Discounted cash flow

IRR

2 %

24 %

Total financial instruments held at fair value

21,735

2,409

 

 

 

 

 

Mar 31, 2015

 

Fair value

 

 

 

 

in € m.
(unless stated otherwise)

Assets

Liabilities

Valuation technique(s)

Significant unobservable input(s) (Level 3)

Range

1

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

Financial instruments held at fair value:

 

 

 

 

 

 

Market values from derivative financial instruments:

 

 

 

 

 

 

Interest rate derivatives

4,035

2,505

Discounted cash flow

Swap rate (bps)

4

2,242

 

 

 

 

Inflation swap rate

(1) %

7 %

 

 

 

 

Constant default rate

1 %

27 %

 

 

 

 

Constant prepayment rate

2 %

18 %

 

 

 

Option pricing model

Inflation volatility

0 %

8 %

 

 

 

 

Interest rate volatility

10 %

176 %

 

 

 

 

IR – IR correlation

(2) %

100 %

 

 

 

 

Hybrid correlation

(70) %

95 %

Credit derivatives

4,297

2,068

Discounted cash flow

Credit spread (bps)

2

15,048

 

 

 

 

Recovery rate

0 %

100 %

 

 

 

Correlation pricing model

Credit correlation

0 %

95 %

Equity derivatives

1,289

1,189

Option pricing model

Stock volatility

9 %

93 %

 

 

 

 

Index volatility

12 %

78 %

 

 

 

 

Index - index correlation

(4) %

98 %

 

 

 

 

Stock - stock correlation

9 %

97 %

FX derivatives

391

426

Option pricing model

Volatility

1 %

28 %

Other derivatives

1,142

4241

Discounted cash flow

Credit spread (bps)

350

1,500

 

 

 

Option pricing model

Index volatility

5 %

98 %

 

 

 

 

Commodity correlation

(30) %

90 %

Total market values from derivative financial instruments

11,155

6,612

 

 

 

 

 

Dec 31, 2014

 

Fair value

 

 

 

 

in € m.
(unless stated otherwise)

Assets

Liabilities

Valuation technique(s)

Significant unobservable input(s) (Level 3)

Range

1

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

Financial instruments held at fair value:

 

 

 

 

 

 

Market values from derivative financial instruments:

 

 

 

 

 

 

Interest rate derivatives

3,324

2,211

Discounted cash flow

Swap rate (bps)

42

2,418

 

 

 

 

Inflation swap rate

(1) %

8 %

 

 

 

 

Constant default rate

2 %

27 %

 

 

 

 

Constant prepayment rate

2 %

21 %

 

 

 

Option pricing model

Inflation volatility

0 %

8 %

 

 

 

 

Interest rate volatility

1 %

101 %

 

 

 

 

IR – IR correlation

(2) %

100 %

 

 

 

 

Hybrid correlation

(70) %

95 %

Credit derivatives

3,586

1,921

Discounted cash flow

Credit spread (bps)

155

9,480

 

 

 

 

Recovery rate

0 %

100 %

 

 

 

Correlation pricing model

Credit correlation

13 %

96 %

Equity derivatives

1,118

1,258

Option pricing model

Stock volatility

8 %

84 %

 

 

 

 

Index volatility

8 %

99 %

 

 

 

 

Index - index correlation

48 %

98 %

 

 

 

 

Stock - stock correlation

9 %

95 %

FX derivatives

264

242

Option pricing model

Volatility

6 %

26 %

Other derivatives

1,267

3681

Discounted cash flow

Credit spread (bps)

44

1,500

 

 

 

Option pricing model

Index volatility

7 %

138 %

 

 

 

 

Commodity correlation

(30) %

60 %

Total market values from derivative financial instruments

9,559

6,001

 

 

 

 

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

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

 

Three months ended

in € m.

Mar 31, 2015

Mar 31, 2014

Financial assets held at fair value:

 

 

Trading securities

655

216

Positive market values from derivative financial instruments

1,604

68

Other trading assets

264

37

Financial assets designated at fair value through profit or loss

342

66

Financial assets available for sale

201

20

Other financial assets at fair value

0

0

Total financial assets held at fair value

3,067

407

Financial liabilities held at fair value:

 

 

Trading securities

2

(2)

Negative market values from derivative financial instruments

(975)

106

Other trading liabilities

(1)

1

Financial liabilities designated at fair value through profit or loss

(94)

62

Other financial liabilities at fair value

60

(32)

Total financial liabilities held at fair value

(1,007)

136

Total

2,060

543

Recognition of Trade Date Profit

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

in € m.

Mar 31, 2015

Mar 31, 2014

Balance, beginning of year

973

796

New trades during the period

157

66

Amortization

(90)

(90)

Matured trades

(55)

(17)

Subsequent move to observability

(14)

(36)

Exchange rate changes

19

(1)

Balance, end of period

991

718