3.1.1 Definition of Fair Value

IFRS 13 defines fair value (see Figure 3.2) as “the price that would be received to sell an asset or paid to transfer a liability in an orderly transaction between market participants at the measurement date”. This definition of fair value emphasises that it is a market-based measurement, not an entity-specific measurement. When measuring fair value, an entity uses the assumptions that market participants would use when pricing the asset or liability under current market conditions, including assumptions about risk. As a result, an entity's intention to hold an asset or to settle or otherwise fulfil a liability is not relevant when measuring fair value.

Principal Market versus Most Advantageous Market

Under IFRS 13, management determines fair value based on a hypothetical transaction that would take place in the principal market or, in its absence, the most advantageous market, for the asset or liability (see Figure 3.3). In most cases, these two markets would be the same. In evaluating principal or most advantageous markets, IFRS 13 restricts the eligible markets to those that the entity can access at the measurement date. Although an entity must be able to access the market, it does not need to be able to sell the particular asset or transfer the particular liability on the measurement date to be able to measure fair value on the basis of the price in that market.

The principal market is the market with the greatest volume and level of activity for the asset or liability, even if the prices in other markets are more advantageous. In the absence of evidence to the contrary, the market in which an entity normally transacts is presumed to be the principal market or the most advantageous market in the absence of a principal market.

The most advantageous market is the market that maximises the amount that would be received to sell the asset or minimises the amount that would be paid to transfer the liability, after taking into account transaction costs and transport costs.

3.1.2 Fair Value Hierarchy

To increase consistency and comparability in fair value measurements and related disclosures, IFRS establishes a fair value hierarchy. IFRS 13 carries over the three-level fair value hierarchy disclosures from IFRS 7, requiring an entity to distinguish between financial asset and financial liability fair values based on how observable the inputs to the fair value measurement are. The hierarchy categorises the inputs used in valuation techniques into three levels: level 1, level 2 and level 3. A fair value measurement is categorised within the hierarchy based on the lowest-level input that has a significant effect on the measure.

3.1.3 Level 1 Financial Instruments

If an entity holds a position in a single asset or liability and the asset or liability is traded in an active market for identical assets or liabilities that the entity can access at the measurement date, the fair value of the asset or liability is measured within level 1.

A quoted market price in an active market provides the most reliable evidence of fair value and is used without adjustment to measure fair value whenever available, with limited exceptions.

Level 1 financial instruments include high-liquidity government bonds and derivative, equity and cash products traded on high-liquidity exchanges.

The fair value is measured (see Figure 3.4) as the product of (i) the quoted price for the individual asset or liability and (ii) the quantity held by the entity, even if the market's normal daily trading volume is not sufficient to absorb the quantity held and placing orders to buy/sell the position in a single transaction might affect the quoted price.

3.1.4 Level 2 Financial Instruments

Level 2 financial instruments are valued with valuation techniques where all significant inputs into the valuation are based on observable market data, or where the fair value can be determined by reference to similar instruments trading in active markets.

Level 2 inputs include:

• Quoted prices for similar assets or liabilities in active markets.
• Quoted prices for identical or similar assets or liabilities in markets that are not active. Instruments include, for example, poorly liquid equities.
• Inputs other than quoted prices that are observable for the asset or liability, for example interest rates and yield curves observable at commonly quoted intervals, implied volatilities and credit spreads. Instruments include most interest rate swaps, FX forwards, cross-currency swaps, FX and interest rate options, and market quoted credit default swaps (CDSs).

Level 2 and level 3 financial derivatives are valued using a valuation model. The output of a valuation model is always an estimate or approximation of a fair value that cannot be measured with complete certainty. As a result, valuations are adjusted (see Figure 3.5), where appropriate, to reflect close-out costs, credit exposure, model-driven valuation uncertainty, trading restrictions and other factors, when such factors would be considered by market participants in measuring fair value.

In the case of derivatives, entities typically start by calculating a mid-market fair valuation (i.e., a valuation using mid-market rate and/or price curves) that assumes no counterparty credit risk, and then the entity applies different adjustments to this valuation. In the case of a level 2 derivative recognised as an asset (see Figure 3.6) these adjustments reduce the mid-market fair value of the derivative by deducting other elements that would be taken into account by market participants were the entity to sell the derivative in the market (i.e., its exit price). These adjustments typically include:

• mid-market to bid, or to offer, adjustment;
• non-performance adjustment (CVA or DVA); and
• funding value adjustment (FVA).

In the case of a level 2 liability derivative, the adjustment to the credit risk-free mid-market fair valuation would commonly include the elements shown in Figure 3.7. The non-performance adjustment is termed “debit valuation adjustment”, and reduces the absolute value of the liability. Other adjustments would increase the value of the liability.

3.1.5 Level 3 Financial Instruments

Financial instruments are classified as level 3 if their valuation incorporates significant inputs that are not based on observable market data (unobservable inputs). A valuation input is considered observable if it can be directly observed from transactions in an active market, or if there is compelling external evidence demonstrating an executable exit price. In other words, the fair valuation of the financial asset/liability requires the estimation of at least one input variable that has a significant impact on the valuation, because such variable price/rate is unobservable in the market. IFRS 13 does not specify when an input is deemed to be significant, but market practice assumes that an input variable is significant if it contributes more than 10% to the valuation of a financial instrument. An entity develops unobservable inputs using the best information available in the circumstances, which might include the entity's own data, taking into account all information about market participant assumptions that is reasonably available.

Level 3 financial instruments typically include correlation-based instruments (e.g., basket and spread options) for which the underlying correlation is unobservable, illiquid bonds and illiquid loans, and CDSs for which credit spreads are unobservable. Interest swaps, cross-currency swaps, inflation swaps, FX forwards and options with very long-dated maturities may also be level 3 financial instruments.

Similarly to level 2 derivatives, the fair value of a level 3 asset derivative is calculated by adjusting its credit risk-free mid-market fair valuation, but adding an additional adjusting element, as shown in Figure 3.8 for an asset derivative. This element addresses the inherent valuation uncertainty associated with the forecasting process, primarily uncertainty in estimating unobservable valuation input parameters and uncertainty in the output provided by the valuation model.

3.1.6 Mid-to-Bid and Mid-to-Offer Adjustments

As a principle of IFRS 13, where an asset or a liability measured at fair value has a bid and an ask price, the entity must use the price within the bid–ask spread that is most representative of fair value. Mid-market pricing or other pricing conventions can be used as a practical expedient for fair value measurements within a bid–ask spread if these conventions do not contravene the principle.

Regarding level 2 and level 3 derivatives, the use of bid prices for long positions and ask prices for short positions is generally required because this is usually more representative of fair value than the practical expedient of using mid-market prices.

Any premium or discount applied must be consistent with the characteristics of the derivative asset or liability. However, no block discounts (i.e., a downward adjustment to a quoted price that would occur if a market participant were to sell a large holding of derivatives in one or a few transactions) are applied.

3.1.7 Credit and Debit Valuation Adjustment

An important element of IFRS 9 is the requirement, when determining the fair value of a financial derivative, to include non-performance risk (i.e. the risk that the counterparty to the financial derivative or the entity will default before the maturity/expiration of the transaction and will be unable to meet all contractual payments, thereby resulting in a loss for the entity or the counterparty).

Suppose that an entity bought a 6-month option and paid an up-front premium. The option was, therefore, recognised as an asset. The entity was exposed to the credit risk of the counterparty to the option during the option's 6-month term. When fair valuing the option, the entity was required to adjust the option's fair value to incorporate the risk that the counterparty to the option could default before its expiration. This adjustment is referred to as credit valuation adjustment, and it is based on the rationale that a market participant would include it when determining the price it would pay to acquire the option. This valuation adjustment for credit reflects the estimated fair value of protection required to hedge the counterparty credit risk embedded in such instrument.

Conversely, let us assume that an entity sold a 6-month option and received an up-front premium. The option would be recognised as a liability. The counterparty to the option would be exposed to the credit risk of the entity during the next 6 months. When fair valuing the option, the entity would be required to adjust the option's fair value to incorporate the risk that the entity will default before its expiration. This adjustment is referred to as debit valuation adjustment.

IFRS 9 does not provide guidance on how CVA or DVA is to be calculated beyond requiring that the resulting fair value must reflect the credit quality of the instrument. Quantifying CVAs is a complex exercise due to the substantial number of assumptions involved and the interaction among these assumptions. There are a variety of ways to determine CVA, and judgement is required to assess the appropriateness of the method used.

3.1.8 Funding Valuation Adjustment

Imagine an uncollateralised swap between ABC (our entity) and Megabank in which the fair value (excluding FVA) was a EUR 10 million unrealised loss from ABC's perspective (i.e., the derivative was recognised in ABC's statement of financial position as a liability). As the derivatives agreement between ABC and Megabank was uncollateralised, ABC was not required to post any collateral to reduce Megabank's credit exposure to ABC. As a result, were ABC to become insolvent, Megabank would suffer a EUR 10 million loss.

Imagine further that, in turn, Megabank hedged its market risk exposure by entering into another derivative that mirrored the terms of our derivative with another bank (Hedgebank) with which a cash collateral agreement was in place (see Figure 3.9). As a result, Megabank had to post EUR 10 million in cash collateral to mitigate Hedgebank's exposure to Megabank, incurring a funding cost stemming from the financing of such cash collateral.

Alternatively, had the derivative between ABC and Megabank showed a EUR 10 million unrealised gain, Hedgebank would have posted EUR 10 million cash collateral with Megabank. Megabank would have placed that cash, earning a yield or reducing its funding needs.

Therefore, when Megabank quoted the derivative pricing to ABC on trade date, it should have taken into account the potential funding costs stemming from future potential favourable movements (from Megabank's perspective) in the derivative's fair value. Additionally, Megabank should have incorporated in the pricing the potential funding benefits stemming from future potential unfavourable movements in the derivative's fair value. The net adjustment is what is termed a funding valuation adjustment.

Thus, FVA incorporates the cost or benefit of unsecured funding into the fair valuation of a derivative to ensure an accurate exit price.

3.1.9 Model Uncertainty Adjustment

Uncertainties associated with the use of model-based valuations are incorporated into the measurement of fair value through the use of model reserves. These reserves reflect the amounts that an entity estimates should be deducted from valuations produced directly by models to incorporate uncertainties in the relevant modelling assumptions, in the model and market inputs used, or in the calibration of the model output to adjust for known model deficiencies. Model valuation adjustments are dependent on the size of portfolio, complexity of the model, whether the model is market standard and to what extent it incorporates all known risk factors. In arriving at these estimates, an entity considers a range of market practices, including how it believes market participants would assess these uncertainties. Model reserves should be reassessed periodically in light of information from market transactions, consensus pricing services and other relevant sources.

3.1.10 Day 1 Profit (or Loss)

For new transactions resulting in a financial derivative classified as level 2 or level 3, the financial instrument is initially recognised at the transaction price. Suppose that an option was bought from a client in exchange for the payment of an up-front premium of EUR 11 million. On the trading day the option was revalued using the entity's valuation model for options of that type. Suppose that the valuation indicated that the option was worth EUR 13 million. The EUR 2 million difference between the transaction price and the valuation price represented the transaction's initial profit. Initial gains or losses result from the difference between the model valuation and the initial transaction price. IFRS 9 permits gains or losses to be recognised at inception only when fair value is evidenced by observable market data (i.e., level 1 and level 2 instruments). Thus, entities are required to defer initial gains and losses for financial instruments with fair values that are based on significant unobservable inputs (i.e., level 3 instruments). In our example, the recognition of the transaction's initial profit was as follows (see Figure 3.9):

• For a derivative classified as a level 1 or level 2 instrument, the initial profit was recognised immediately in profit or loss. In this case, the entity recognised a EUR 2 million gain in profit or loss at the end of trade date and, in theory, the counterparty to the option recognised a EUR 2 million loss.
• For a derivative classified as a level 3 instrument, the initial profit was not recognised, but rather deferred. The initial profit for level 3 derivatives is termed day 1 profit. The counterparty to the derivative would recognise a day 1 loss.

In the case of assets, deferred day 1 profit is amortised (typically on a straight-line basis) over the term of the transaction and recognised as a liability. The amounts deferred may subsequently be recognised to the extent that factors change in such a way that the input is now observable to the market participants setting the price, or if the financial instrument in question is closed out.

3.2.1 Simple One-Period Model of Default

A simple example of the calculation of CVAs is a cash flow – an “exposure at default” (EAD) – of 100 that is expected to be received in 1 year. Denote the probability that the counterparty will default over the next year by PD. If the counterparty does default, let us assume that it pays a recovery rate R, which is a fixed percentage of the cash flow amount. We further assume that this recovery is paid at the cash flow date. The expected cash flow amount can be estimated using a simple single-period binomial tree, as shown in Figure 3.10, where the credit adjusted value of the cash flow, CFAdjusted, is the expected payoff discounted off the risk-free curve. This gives:

If the 1-year probability of default is 0.75%, the recovery rate R is assumed to be 60%, and the 1-year risk-free rate r is 5%, the CVA value of the cash flow is given by:

Without the CVA, the present value of the cash flow would be:

Thus, the CVA is 0.2857 ( = 95.2381 – 94.9524). This amount may alternatively be calculated as follows:

The factor 1 – R is referred to as loss given default (LGD). Therefore, the CVA may be formulated as well as follows:

3.2.2 Working Example of CVA in a Swap

Suppose that on 1 July 20X0 ABC issued a EUR 100 million 5-year floating rate debt linked to 6-month Euribor and, in order to fix the interest expense, entered into a 5-year swap with Megabank (on an uncollateralised basis) in which on a semiannual basis it paid a fixed rate of 3.20% and received 6-month Euribor on a EUR 100 million notional, as follows:

On 1 July 20X3 (i.e., 2 years before maturity) ABC revalued the swap. On that date, the 2-year mid-market swap rate was 3.41% and ABC estimated based on market quotes that the bid-to-mid spread would be 1 basis point (i.e., 0.01%), resulting in a 2-year bid swap rate of 3.40%. The credit risk-free valuation, before CVA and FVA, was EUR 390,000, calculated as follows:

Notes:

(1) <589,000> = 100 mn × (2% × 182 days/360 – 3.20% × 182 days/360)

(2) 0.9900 = 1/(1 + 2% × 182 days/360)

(3) <583,000> = <589,000> × 0.9900

(4) 0.9751 = 0.9900 × [1/(1 + 3% × 183 days/360)]

The expected first two negative settlement amounts (<589,000> and <75,000>) meant that ABC was expected to pay those amounts at their settlement date (31-Dec-X3 and 30-Jun-X4, respectively), and as a result, that Megabank would be exposed to ABC's credit risk (see Figure 3.11).

The positive expected last two settlement amounts (422,000 and 688,000) meant that ABC was supposed to receive those amounts at their settlement date (31-Dec-X4 and 30-Jun-X5, respectively), and as a result, that ABC would be exposed to Megabank's credit risk (see Figure 3.11).

The first step in calculating the DVA/CVA is to define a time grid (i.e., to divide into time buckets the period in which the derivative exposes either party to credit risk). In our example, the swap exposed either party until its maturity on 30 June 20X5. ABC decided to divide the term into four semiannual periods, coinciding with the swap interest periods (e.g., the first period from 1 July 20X3 to 31 December 20X3).

The second step encompassed calculating the present value (PV) of the EAD at each time bucket. The EAD represented the credit risk-free valuation of the swap at a certain point of time, or in other words, the exposure were one of the two counterparties to default at such moment. One “simple” way is to assume that rates will behave as expected by the market. In our case, the exposures during each time bucket had an upward sloping profile during the first three buckets (see Figure 3.12). The PV of the EAD for a bucket was calculated as the average of the bucket's start and end exposures, as shown in the following table:

The start exposure at bucket 1 was the credit risk-free valuation as of 1 July 20X3, or 390,000. The end exposure corresponding to bucket 1 was the derivative's credit risk-free valuation as of 31 December 20X3 just prior to the <589,000> settlement amount:

Notes:

(1) 0.9850 = 1/(1 + 3% × 183 days/360)

(2) <74,000> = <75,000> × 0.9850

The exposure at the start of bucket 2 was 982,000 (=393,000 – (–589,000)) calculated as (i) the exposure at the end of bucket 1 minus (ii) <589,000>. The end exposure corresponding to bucket 2 was the credit risk-free valuation as of 31 December 20X4 just prior to the <75,000> settlement amount, as shown in the next table:

Notes:

(1) 0.9802 = 1/(1 + 4% × 182 days/360)

(2) 414,000 = 422,000 × 0.9802

The exposures at buckets 3 and 4 were calculated similarly and have been omitted to avoid excessive repetition.

The third step encompassed calculating the probability of default. As illustrated in Figure 3.12, all the EADs were positive (i.e., ABC was exposed to Megabank's credit risk) and as a result each EAD was subject to the PD of Megabank.

Suppose that CDSs on Megabank were trading at 30, 40, 45 and 50 basis points for 6-, 12-, 18- and 24-month protection tenors, respectively. The probability of default from today until the settlement date can be approximated using the following expression:

where CDS is the credit default swap spread to obtain protection on the name that creates the credit exposure, Maturity is the time in years to the cash flow, and LGD is the loss given default. ABC assumed that Megabank's LGD was 40%.

The expression above provides the probability of default from today to the end date of the bucket (i.e., the cumulative PD). The PD for a specific time bucket (i.e., the probability of default from the start date to the end date of the bucket) is calculated as (i) the cumulative PD for the bucket minus (ii) the cumulative PD for the previous bucket, as follows:

Notes:

(1) 1.67% = 1 – exp(–0.45% × 1.5/40%)

(2) 0.67% = 1.67% – 1.00%

Based on the method above, the CVA for a certain EAD can be calculated as the present value of the expected loss amount at the time of default:

The expected loss amount is calculated by multiplying the probability of default, the loss given default and the present value of the exposure at default at the time of default:

Therefore the CVA was EUR 8,000, representing just 2% of the EUR 390,000 credit risk-free valuation.

3.2.3 Debit Valuation Adjustments

Similarly to derivatives on the asset side, when determining the fair value of a derivative on the liability side, IFRS 9 requires an adjustment to take into account the credit risk associated to the derivative. This adjustment is referred to as debit valuation adjustment. It represents the theoretical cost to counterparties of hedging, or the credit risk reserve that a counterparty could reasonably be expected to hold, against their credit risk exposure to the entity.

As noted above, the DVA reduces the value of a liability derivative (see Figure 3.13). The requisite of recognising a “lower loss” when an entity's own creditworthiness deteriorates is arguably somewhat fictitious, especially as it would be difficult to realise such a profit when closing out or transferring the derivative. Moreover, this requirement may lead to significant volatility in profit or loss in periods of credit market turmoil.

The mechanics of calculating DVAs are identical to those of CVAs, but incorporating the PD of the entity. The counterparty to the derivative would hold a financial asset and would be including a CVA that takes into account the credit risk of the entity.

3.2.4 Combining CVA and DVA

In our previous example, all EADs were positive, meaning that it was expected that, at all times during the life of the swap, ABC was exposed to Megabank's credit risk, while Megabank was not expected to be exposed to ABC's credit risk. There could be, however, situations in which positive EADs (subject to the PD of Megabank) and negative EADs (subject to the PD of ABC) are both present.

For example, let us imagine an EAD profile (as shown in Figure 3.14) in which the expected EADs (in present value terms) for buckets 1 and 2 were negative amounts (<300,000> and <230,000>, respectively). The first time bucket amount meant that, were ABC to default during the period corresponding to such time bucket, Megabank would be exposed to 300,000 being owed by ABC. Megabank's expected loss would be calculated incorporating ABC's probability of defaulting during time bucket 1 and ABC's loss given default, as 300,000 × PD_ABC × LGD_ABC. This amount would represent a DVA.

Conversely, imagine the expected EADs (in present value terms) for buckets 3 and 4 were positive amounts (150,000 and 220,000, respectively). The third time bucket amount meant that, were Megabank to default during the period corresponding to such time bucket, ABC would be exposed to 150,000 being owed by Megabank. ABC's expected loss would be calculated as 150,000 × PD_Megabank × LGD_Megabank, PD_Megabank being Megabank's PD during the period corresponding to time bucket 3 and LGD_Megabank being Megabank's LGD in such a situation. This amount would represent a CVA.

Therefore, the CVA/DVA calculation of the fair value of the derivative would be the following sum (the DVAs are likely to exceed the CVAs):

3.2.5 Calculating CVA and DVA Using Monte Carlo Simulation

The previous example was relatively straightforward, as it assumed that:

• only one derivative was outstanding between ABC and Megabank;
• the derivative was uncollateralised;
• interest rates going forward will behave as expected by the market on valuation date; and
• both ABC and Megabank had observable CDS spreads.

Simulation of the EAD Profile – Monte Carlo Simulation Method

In our previous example, the EAD calculation for each time bucket assumed that interest rates during the life of the derivative will perform as expected on the valuation date. However, in practice it is unlikely that realised interest rates move exactly as expected.

Entities with significant resources may develop processes to calculate CVA/DVA in a more accurate manner. These entities are typically banks or corporates that either developed their own models or bought simulation packages from third party vendors. The process of calculating CVA/DVA can be divided into five steps (see Figure 3.15).

First Step: Collecting Netting Set Data

In a first step, the relevant data relating to a netting set is collected (see Figure 3.16). A netting set is a group of derivatives, and their related collateral, with a single counterparty to which the entity is credit exposed on a net basis from a legal perspective. In our previous example, all the outstanding derivatives and the collateral posted/received to secure these derivatives under the same ISDA agreement between ABC and Megabank constituted a netting set.

Also in this first step, all the market variables (commonly referred to as market factors) that affect the fair valuation of the derivatives in the netting set are identified. In our previous example, the swap was linked to the 6-month Euribor rate. In the netting set other market factors may be identified. Imagine that another swap in the netting set was linked to USD Libor 3-month rate. That second swap would bring two other market factors: the USD Libor 3-month rate and the EUR–USD FX rate.

Finally, the period from the valuation date until the maturity of the last derivative in the netting set is divided into time buckets (commonly referred to as the time grid). It is relatively common to divide the time period into quarterly time buckets.

Second Step: Simulating Market Factors

In a second step, the market factors identified in the previous step are simulated: a large number of paths of future behaviour of the market factors are generated along the time grid. The simulation is often generated using a Monte Carlo simulation method which can simulate forward in time thousands of potential paths of movements of a market factor, based on a suitably chosen stochastic process for that market factor. This is the most complex part of the simulation process, especially when several market factors affect the netting set. The parameters of this process are calibrated based on historical market data (several years of history). The latest daily close of market values form the starting point of the simulation, and their volatilities and assumed correlations are added as inputs as well.

In our previous example, there was only a market factor (the Euribor 6-month rate). ABC would have also incorporated the term structure of volatilities of this interest rate using market cap and floor volatility information. The starting point of the Euribor 6-month rate would be its market level on valuation date (2% in our case). The result would be a large number of paths of future movement of the Euribor 6-month rate, as illustrated in Figure 3.17.

Third Step: Calculating Exposure at Default Profile

In a third step, the netting set's exposure at default profile is determined. In a first task within the third step, the credit risk-free fair value – or mark-to-market (MtM) – of each derivative in the netting set is calculated for each time bucket across each path of market factors. Each MtM represents the claim owed by (a positive MtM) or to (a negative MtM) the counterparty, were one of the two parties to the derivative default. The MtM calculation takes into account credit mitigants such as collateral and break clauses. In our case, each path of Euribor 6-month rates generated a path of MtMs of the swap, each MtM path starting at EUR 390,000 and ending at nil (see Figure 3.18).

The next task within the third step is to divide the paths of MtMs into two groups: a first group of positive MtMs and a second group of negative MtMs (see Figure 3.19). A positive MtM means that the entity is exposed to the counterparty's credit risk. Conversely, a negative MtM means that the counterparty is exposed to the entity's credit risk.

The third task within the third step is, for each group, to determine the EAD at each time bucket. A time bucket's EAD is calculated as the arithmetic average of the group's MtMs at such time bucket, as illustrated in Figure 3.20 for the group encompassing positive MtMs. The end outcome of the third step is the EAD profile for each group, as illustrated in Figure 3.21.

Fourth Step: Calculating the CVA/DVA

In a fourth step, the probability of default of the counterparty and the entity at each time bucket is calculated. The basis for the calculation of the PD is the CDS of the entity (or the counterparty's CDS as the case may be). If no CDS is trading in the market, PDs are calculated from other alternative sources. Figure 3.22 shows my own pecking order regarding the use of alternative sources when calculating the entity's (or the counterparty's) PDs:

• yields may be available for publicly traded bonds issued by the entity;
• CDSs may be available for competitors with a financial situation (i.e., rating) similar to that of the entity;
• CDSs may be available for an index of companies in the entity's industry, region and rating;
• PDs may be available for the entity's external ratings from the reports published by the rating agencies (e.g., Moody's); or
• the entity's banks may have rated the entity using an internal rating system for which an equivalent external rating may be inferred. The PD would be calculated using the method mentioned in Section 3.2.2.

Additionally, a loss given default is estimated for each time bucket for both the entity and the counterparty. Normally a constant LGD is assumed across all time buckets.

Next, the CVA/DVA is calculated as the sum of CVA and DVA. Because the amounts have opposite signs, there is a partial (or total) offset between them:

The CVA would be calculated as the sum of the expected loss at each time bucket of group 1. The expected loss corresponding to a time bucket would be determined by multiplying for each time bucket (i) the present value of the EAD, (ii) the counterparty's PD and (iii) the counterparty's LGD:

The DVA results in a negative amount, reducing the effect of the CVA. Similarly to the CVA calculation, the DVA would be calculated taking into account the present value of the EAD, the entity's PDs and LGDs:

The overall CVA/DVA has been calculated for the portfolio of derivatives being part of the netting set. The final step in this process is to allocate the resulting CVA/DVA to the derivatives being part of the netting set.

When the derivative instruments are presented in a single line in the statement of financial position (e.g. because they are all assets or all liabilities or both but presented net) and they are not designated separately in a hedging relationship, disaggregating the single adjustment may not be necessary. However, in all other cases it will be necessary to allocate the net portfolio adjustment to the individual derivatives in the netting set. Whilst neither IFRS 13 nor IFRS 9 provides guidance on how to perform the allocation, IFRS 13 requires this allocation to be done on a reasonable and consistent basis. Two approaches are commonly used:

• A relative fair value approach. The overall CVA/DVA is allocated to either the individual asset derivatives or the individual liability derivatives. When the CVA amount exceeds the DVA amount, resulting in a positive amount, the overall CVA/DVA is referred to as just CVA and it is allocated only to individual asset derivatives based on the relative credit risk-free fair value of each asset derivative. Thus, in that case, liability derivatives would not be allocated any CVA. Conversely, when the DVA amount exceeds the CVA amount, resulting in a negative amount, the overall CVA/DVA is referred to as just DVA and it is allocated only to individual liability derivatives based on the relative credit risk-free fair value of each liability derivative. Figure 3.23 illustrates how a 54,000 CVA (a positive overall CVA/DVA amount) is allocated among three asset derivatives in a netting set according to their credit risk-free valuation.
• A relative credit adjustment approach. The overall CVA/DVA is allocated to each derivative (both assets and liabilities) based on their contribution to the CVA/DVA amount. This approach requires keeping track of the contribution of each derivative to the EAD profile. This method is theoretically sounder than the previous one, but in my opinion adds an operational complexity that is difficult to justify.