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Erschienen in:
Introductory Remarks Kapitel lesen Erstes Kapitel lesen

2018 | OriginalPaper | Buchkapitel

7. Credit Valuation Adjustments

verfasst von : Ioannis Akkizidis, Lampros Kalyvas

Erschienen in: Final Basel III Modelling

Verlag: Springer International Publishing

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Abstract

The derivative positions are subject to changes due to market volatility which changes the exposure to counterparty risk and the credit quality of the counterparty. Against this background, banks should keep aside additional capital, known as credit valuation adjustments (CVAs) capital charge, which stands for the difference between the risk-free and actual portfolio values which takes into account the default probability of a counterparty.
The CVA analysis is a critical element in pricing OTC derivatives. Since the changes in CVA are due to the market pricing of counterparty risk, the variability of the counterparty risk over time could be potentially more significant than the credit risk of the underlying position. Hence, the fair value of a financial derivative depends on the counterparty credit risk of the traded derivative.

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Vorheriges Kapitel Market Risk: Fundamental Review of the Trading Book (FRTB)
Nächstes Kapitel Revisions to Operational Risk
Fußnoten
1
From banks’ point of view.
 
2
The analysis of debt valuation adjustments, rising due to an institution’s default risk, is currently beyond the Basel regulatory market risk frameworks.
 
3
BCBS’s liquidity coverage ratio (LCR) and net stable funding ratio (NSFR).
 
4
Using futures to form the initial margin implies a “good faith” collateral assuming that the investor will satisfy the obligation of the contract.
 
5
A threshold of zero implies that any exposure is collateralised whilst a threshold of infinity is used to specify that one of the counterparties will not post collateral under any circumstances.
 
6
Intraday margining is common for vanilla products such as repos but other instruments such as swaps require a daily margin call frequency for the relevant valuations to be carried out.
 
7
In practice, collaterals are not delivered immediately; moreover, the portfolio is not settled and replaced immediately when the collateral is not posted. It may take several days for the bank to realise that the counterparty is defaulting; moreover, there is a grace period after the bank issues a notice of default. During this grace period the counterparty may still post a collateral; however, it may take a while to close out and replace complex trades.
 
8
Note that for margin agreements with daily or intra-daily exchange of margin the minimum MPoR is ten business days.
 
9
As opposed to the risk-neutral measures.
 
10
Each market scenario is a realisation of a set of price factors that affect the values of the trades in the portfolio, for example, FX rates, interest rates, equity prices, commodity prices, and credit spreads.
 
11
The use of discrete time intervals reduces the demand in computation resources.
 
12
Such as American/Bermudan and asset-settled derivatives.
 
13
For a single or a portfolio of transactions linked to a single counterparty.
 
14
The central peak is narrower, but the tails are significantly longer and fatter.
 
15
Also defined as a “credit-equivalent” or “loan-equivalent” exposure curve.
 
16
Implying, therefore, an absence of risk neutrality in volatilities and drifts for the diffusion processes of the risk factors.
 
17
International Financial Reporting Standards, Fair Value Measurement, entered into force on 1 January 2013. In estimating the accounting CVA exposure, institutions should be using risk-neutral drifts, calibrating both correlations and volatilities based on market data whenever information on market data is available and also defining the ten-business-day floor for the margin period of risk; see also IVSC (2013).
 
18
Risk-neutral probabilities assume the absence of arbitrage opportunities.
 
19
Assuming that not all assets will default at the same time in a well-structured portfolio.
 
20
Market participants have not always accepted and adopted the regulatory methodologies for estimating the fair value of derivative exposures as the most appropriate for the estimation of economic capital arising from the same exposures.
 
21
Based on the current supervisory standards, when a CDS is unavailable, banks “shall use a proxy spread that is appropriate taking into consideration the rating, industry and region of the counterparty” (BCBS, 2011).
 
22
Even though this process is not necessary and neither always the best practice to identify the default probability.
 
23
Whereas the value of the firm’s assets and liabilities at default determines the recovery rates in structural models.
 
24
Recovery rates usually take the form of a percentage of the expected value of the security at the time of default. Key elements of the recovery rate are (a) the amount of the recovery; and (b) the time interval between default and the recovery being realised. Generally, recovery rates are related to the seniority of the debt, which implies that in case the seniority of debt changes the recovery of the debt may change.
 
25
In addition, these models use the risk-neutral transition matrix, for example, rating agencies’ transition probabilities to determine the probability of default.
 
26
Discrete-time approximation of the Poisson process.
 
27
That is, the protection buyer, the protection seller, and the reference credit.
 
28
Filtration is a function with the purpose of filtering and controlling information propagation. In mathematical terms a filtration is a non-decreasing collection of σ algebras \( \left\{{\mathrm{\mathcal{M}}}_t\subseteq \mathrm{\Im}:\mathrm{t}\ge 0\right\} \) such that \( {\mathrm{\mathcal{M}}}_s\subseteq {\mathrm{\mathcal{M}}}_t \), for ∀s, t ≥ 0 with s ≤ t. Where \( {\mathrm{\mathcal{M}}}_t \) defines the information available at time t, assuming that this information is always kept and has been available as long as s ≤ t.
 
29
That is, the number of events per interval of time.
 
30
Proposed by Vasicek (1977); see reference list.
 
31
Alternatively, increasing k results in a large speed of mean reversion so the system will have less stochasticity for a given value of σ. Due to the positivity condition, an increasing θ will force an increase in k, whose effect will counterbalance the initial increase in σ.
 
32
Also called lifetime distributions.
 
33
Also known as “credit curve” due to its similarity to a yield curve.
 
34
Detailed description of calibration process and methodologies is beyond the scope of this book. For further reading the reader may refer to the books in the reference list of this chapter.
 
35
Although credit spreads must always be positive, interest rates can be negative under market stress conditions.
 
36
The correlation coefficient equals one or minus one. The former implies a perfect positive co-dependency (or co-movement) while the latter a negative co-dependency, that is, the variables move in the same or opposite directions, respectively. A correlation of less than one defines the degree of positive or negative strength in correlation. Correlations equal to zero implies no co-dependencies.
 
37
Based on UK Financial Service Authority (2010), CVA losses, during the financial crisis, increased in the UK five times the amounts of actual default losses.
 
38
In fact, banks permitted to employ and use both the VaR and the IMM modes have the obligation to implement the advanced CVA charge method.
 
39
Eligible hedges are single-name credit instruments that reference directly to counterparty and, under certain conditions, to CDS index hedges.
 
40
Not cleared through central counterparties.
 
41
Based on the external rating of the counterparty on the rating scale AAA, AA, A, BBB, BB, B, and CCC, the weights are 0.7%, 0.7%, 0.8%, 1%, 2%, 3%, 10%, respectively.
 
42
EAD is calculated following IMM or SA-CCR replacing the standardised and current exposure methods.
 
43
As since 2010, CVA (VaR) under BCBS (2011) has already been approached by the market, and extended description of this approach is beyond the scope of this book. This book focuses more on final Basel approaches referring to minimum capital requirements for the CVA risk framework (BCBS, 2017).
 
44
Based on the regulation, exposure profiles are used in the internal model method approval; moreover, if the IMM does not cover all transactions subject to the CVA risk charge and non-IMM transactions consist of a limited number of smaller portfolios, an institution can also be allowed to use the advanced approach for these portfolios.
 
45
It should be noted that LGDMKT, used as input in the calculation of the CVA capital charge, is different from the LGD that is determined under the IRBA and CCR default risk charge. LGDMKT is market assessment rather than an internal estimate. It is based on the provision of BCBS (2011) which mentions that “where market instrument of single counterparties should be driving the market-implied LGD or where a counterparty instrument is not available, [the estimation of the LGD should be] based on the proxy spread that is appropriate based on the rating, industry and region of the counterparty”.
 
46
The last financial crisis indicated that the majority of losses do not arise from counterparty defaults but rather from market variabilities of derivative portfolios.
 
47
The Basel II/Basel III market risk framework estimates the capital charge against only the actual variability in the derivatives’ market.
 
48
Note, however, that the CVA capital charge for both frameworks is calculated on a stand-alone basis, that is, interactions among the CVA book and trading book are not allowed.
 
49
MNS for the banks with supervisory approval to use IMM, see BCBS, 2006: 262–263 para 38, 39, excluding, however, the five-year cap in para 38. For those banks with no supervisory approval to use IMM, see BCBS, 2006: 75–76 para 320–323, excluding, however, the five-year cap in para 320.
 
50
The supervisory prescribed correlations rhc set as in the table below:
Single-name hedge h of counterparty c
Value of rhc
References counterparty c directly
100%
Has legal relation with counterparty c
80%
Shares sector and region with counterparty c
50%
 
51
Applying to the entire CVA book including eligible hedges.
 
52
The default value of mCVA set by the BCBS at 1.25; however, the supervisory authority may determine a higher degree based on the evaluation of the bank’s CVA model risk as well as the dependence on the counterparty’s credit quality and the bank’s exposure to the counterparty known as WWR (BCBS, 2017: 118 para 40).
 
53
Distinguished amongst maturities of 1 year, 2 years, 5 years, 10 years, and 30 years.
 
54
For the risk factors 1 year, 2 years, 5 years, 10 years, and 30 years, and inflation, the RWs are set to 1.59%, 1.33%, 1.06%, 1.06%, 1.06%, and 1.59%, respectively.
 
55
The proposed set of rules has set the correlations between the pairs of risk factors as in the table below:
Risk factor
1 year
2 years
5 years
10 years
30 years
Inflation
1 year
100%
91%
72%
55%
31%
40%
2 years
 
100%
87%
72%
45%
40%
5 years
  
100%
91%
68%
40%
10 years
   
100%
83%
40%
30 years
    
100%
40%
Inflation
     
100%
The first bucket associated to sectors (1 a) sovereigns including central banks, multilateral development banks; (1 b) local government, government-backed non-financials, education, and public administration; (2) financials including government-backed financials; (3) basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying; (4) consumer goods and services, transportation and storage, administrative and support service activities; (5) technology, telecommunications; (6) health care, utilities, professional and technical activities; (7) all other sectors.
 
56
The cross-bucket correlations of delta risk for counterparty credit spread are set in the table below:
Bucket
1
2
3
4
5
6
1
100%
10%
20%
25%
20%
15%
2
 
100%
5%
15%
20%
5%
3
  
100%
20%
25%
5%
4
   
100%
25%
5%
5
    
100%
5%
6
     
100%
 
57
The cross-bucket correlations across bucket 7 and another bucket are set to γbc = 0%.
 
58
Tenors are set at 0.5, 1, 3, 5, and 10 years.
 
59
The buckets 1 a), 1 b), 2, 3, 4, 5, 6, and 7 for investment grade (IG) receive the RWs of 0.5%, 1.0%, 5.0%, 3.0%, 3.0%, 2.0%, 1.5% and 5.0%, respectively; and, for high-yield/non-rated (HY/NR) the same buckets receive the RWs of 3.0%, 4.0%, 12.0%, 7.0%, 8.5%, 5.5%, 5.0%, and 12.0%, respectively.
 
60
Correlations between different tenors for the same entity are set to 90%; for unrelated entities of the same credit quality (IG and IG or HY/NR and HY/NR) correlations between the same tenors are set to 50% and between different tenors are set to 45%; for unrelated entities of different credit quality (IG and HY/NR) correlations between the same tenors are set to 40% and between different tenors are set to 36%; for entities that are legally related correlations between the same tenors are set to 90% and between different tenors are set to 81%.
 
61
The first two bucket groups contain six groups of sectors which are (1) sovereigns including central banks, multilateral development banks; (2) local government, government-backed non-financials, education, public administration; (3) financials including government-backed financials; (4) basic materials, energy, industrials, agriculture, manufacturing, mining and quarrying; (5) consumer goods and services, transportation and storage, administrative and support service activities; (6) technology, telecommunications; (7) health care, utilities, professional and technical activities. The third bucket group contains all other sectors.
 
62
The cross-bucket correlations of delta risk are set in the table below:
Bucket
1/8
2/9
3/10
4/11
5/12
6/13
7/14
1/8
100%
75%
10%
20%
25%
20%
15%
2/9
 
100%
5%
15%
20%
15%
10%
3/10
  
100%
5%
15%
20%
5%
4/11
   
100%
20%
25%
5%
5/12
    
100%
25%
5%
6/13
     
100%
5%
7/14
      
100%
 
63
Large size for the 1st eight buckets, small size for the 9th and 10th buckets, and not applicable size for the 11th bucket number.
 
64
Regions are classified as (a) emerging market economies associated to bucket numbers 1, 2, 3, 4, 9; and (b) advanced economies associated to bucket numbers 5, 6, 7, 8, and 10. Bucket number 11 is not associated to any region.
 
65
Buckets 1 and 5: consumer goods and services, transportation and storage, administrative and support service activities, health care, utilities; buckets 2 and 6: telecommunications, industrials; buckets 3 and 7: basic materials, energy, agriculture, manufacturing, mining and quarrying; buckets 4 and 8: financials including government-backed financials, real estate activities, technology; bucket 9: all sectors are described under bucket numbers 1 to 4; bucket 10: all sectors described under bucket numbers 5 to 8; bucket 11: other sectors.
 
66
The RWs for bucket numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 are set to 55%, 60%, 45%, 55%, 30%, 35%, 40%, 50%, 70%, 50%, and 70%, respectively.
 
67
The commodity group are assigned to 11 different buckets as follows: bucket 1: energy—solid combustibles; bucket 2: energy—liquid combustibles; bucket 3: energy—electricity and carbon trading; bucket 4: freight; bucket 5: metals—non-precious; bucket 6: gaseous combustibles; bucket 7: precious metals (including gold); bucket 8: grains and oilseed; bucket 9: livestock and dairy; bucket 10: softs and other agriculturals; bucket 11: other commodity group.
 
68
Based on the reference name’s bucket, the RWs assigned to buckets 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11 receive RWs of 30%, 35%, 60%, 80%, 40%, 45%, 20%, 35%, 25%, 35%, and 50%, respectively.
 
Literatur
Bluhm, C., Overbeck, L., & Wagner, C. (2010, June). Introduction to credit risk modelling, 2nd ed. Boca Raton: Chapman and Hall/CRC.
Cox, D. R. (1955). Some statistical methods connected with series of events. Journal of the Royal Statistical Society, 17(2), 129–164.
Cox, Ingersoll and Ross. (1985, March). A theory of the term structure of interest rates. Econometrica, 53(2), 385–407.CrossRef
Feller, W. (1951). Two singular diffusion problems. Annals of Mathematics, 54, 173–182.CrossRef
IASB (2012). IFRS 13: Fair value measurement. International Accounting Standards Board.
McNeil, A. J., Frey, R., & Embrechts, P. (2015). Quantitative risk management: Concepts, techniques and tools – Rev. ed. Princeton Series in Finance. Princeton: Princeton University Press.
Schönbucher, P. (2003). Credit derivatives pricing models: Models, pricing and implementation. Wiley Finance Series. Chichester; Hoboken, NJ: Wiley.
Uhlenbeck, G. E., & Ornstein, L. S. (1930). On the theory of Brownian motion. Physics Review, 36, 823–841.CrossRef
Vasicek. (1977). An equilibrium characterization of the term structure. Journal of Financial Economics, 5, 177–188.CrossRef
Metadaten
Titel
Credit Valuation Adjustments
verfasst von
Ioannis Akkizidis
Lampros Kalyvas
Copyright-Jahr
2018
Buch
Final Basel III Modelling

Print ISBN: 978-3-319-70424-1

Electronic ISBN: 978-3-319-70425-8

Copyright-Jahr: 2018

DOI
https://doi.org/10.1007/978-3-319-70425-8_7