Tradeable credit assets are vulnerable to two varieties of credit risk: default risk (which manifests itself as a binary outcome) and spread risk (which arises as spreads change continuously). Current (2017) regulatory credit risk rules require banks to hold capital for both these risks. Aggregating these capital amounts is non-trivial.

The aim was to implement the bubble value at risk (buVaR) approach, proposed by Wong (

The principal setting for the study was the South African credit market which represents a developing market. Previous work by Wong (

Using South African data, closed form solutions were derived for free parameters of Wong’s formulation, and the relationship between the spread level and the response function was developed and calibrated.

The results indicate that the original calibrations and assumptions made by Wong (

The application of buVaR to South African government bond credit default swaps spreads highlighted the metric’s countercyclical properties that would potentially have countered bubble developments had they been implemented during the credit crisis of 2008/2009. Regulatory authorities should take this important metric into account when allocating South African bank’s credit risk capital.

Credit losses experienced in the financial crisis of 2008–2009 emphasised the complexities surrounding tradeable credit instruments. In their fundamental review of the trading book, the Basel Committee on Banking Supervision (BCBS

A 2013 global survey conducted by the Joint Forum on Banking Firms and Supervisors revealed that since the crisis banks have improved governance and risk reporting and that risk aggregation has become far more sophisticated (BCBS ^{1}

In the trading book, tradeable credit instruments are associated with two sources of risk. Firstly, default risk in which there is a probability that the underlying issuer may forfeit its obligation through contractual non-compliance (Brown & Moles

Procyclicality – defined as those economic quantities that are positively correlated with the overall state of the economy (Van Vuuren

Value at risk (VaR) has been the preferred market risk measurement tool since 1994 (BCBS

Applying conventional VaR to tradeable credit instruments poses challenges, as all the risks pertaining to these instruments are not adequately captured in the measurement (Amato & Remolona

The remainder of this article proceeds as follows: the ‘Literature study’ section explores tradeable credit instruments and the regulatory treatment thereof. The section also highlights difficulties in the measurement of credit risk under regulatory recommendations. The choice of data and relevance thereof is explained in ‘Data and methodology’ section along with the mathematics of the metrics being assessed. The logic behind Wong’s (

Conventionally, a bank’s trading book is predominantly affected by market risk, with the banking book being mostly susceptible to credit risk (BCBS

Institutions holding portfolios of debt securities or derivatives to hedge risk stemming from their securities, face several forms of risk. Spread movements is one such risk, while the possibility of issuer defaults of tradeable credit instruments is another. Correlated defaults between issuers of securities pose further risk to banks and financial institutions (Wong

Spread risk is traditionally modelled using historical simulations and applying a VaR approach. Simulated returns are generated from the spread variable over an observation period – between 1 and 3 years under the Basel formulation. The return vector is

In what has been informally labelled Basel IV, the BCBS have suggested changes to the trading book/banking book boundary by addressing issues such as the trading book definition, trading book components and ineligible trading book instruments (BCBS

Boundary definitions of Basel II and Basel IV trading book.

Definition | Current intent-based boundary | Revised boundary |
---|---|---|

Trading book definition | Mostly self-determined by banks. | Instruments must be included in the trading book if certain criteria are met. |

Contents of the trading book | None prior to the trading book review. | Guidance for appropriate trading book instruments include:
Accounting trading assets and liabilities Instruments resulting from market making and underwriting activities Listed equities, equity investments in funds, options All short positions in cash instruments |

Guidance for instruments that do not qualify | Only one footnote. | Any unutilised equity. |

Boundary permeability | Switching between trading and banking book is allowed. | Only under exceptional circumstances which do not include market conditions. |

Capital arbitrage mitigation | N/A | Reduced capital charges stemming from the rare instances where portfolio switching is allowed will not be enjoyed. |

Supervisory authority to re-designate | N/A | If assets are improperly designated supervisors can switch between trading and banking book. |

Valuation requirements | Use readily available closed out prices for daily valuation. | All trading book instruments must be fair valued daily through the profit and loss statement. |

Reporting to ease boundary supervision | N/A | Banks must have comprehensive reports on the decision-making regarding boundary determination. |

N/A, not applicable.

Because entities only default once, an historical simulation approach is impossible since there is no time series of observable default history available. Monte Carlo simulations are used instead. Possible occurrences of ratings migration (of which default is a special case) are generated over a 1-year simulation horizon. The Monte Carlo simulation assumes that credit default driver follows a particular distribution: simulated values are mapped to an end-state rating (upgrades, downgrades or a default). The probabilities of these trajectories from the current rating to the end-state ratings (including default) are embedded within the rating transition matrix. These matrices are populated with single-year transition rates assembled by credit rating agencies using empirical historical statistics of defaults and upgrades or downgrades in selected benchmark sectors. The portfolio positions are mapped to relevant sectors before the simulation begins. Correlation coefficients are determined independently and used to capture correlation risk between the sectors. Regulatory capital rules require that the VaR of this distribution is determined at a 99.9% confidence level and a time horizon of 1 year – this is known as credit VaR. Crouhy, Galai and Mark (

The responses received by the BCBS from commentators mostly suggested that integrating the default component of the trading book into market risk models, presents several challenges and complexities. The BCBS thus decided that the total credit risk capital charge for both the standardised and models-based approaches would comprise two components: an integrated credit spread risk capital risk charge and an incremental default risk (IDR) charge (BCBS

The complex relationship between market and credit risk gives way to aggregation issues including the inability to clearly identify diversification issues and related compounding effects. This challenge also fuelled the perception that adding separately estimated risk components for market and credit risk will most certainly be conservative, due to not all diversification possibilities being considered. However, the BCBS suggests from the financial crisis learnings that non-linear interactions between market and credit risk may reinforce each other and lead to even more severe losses. The BCBS further suggests that under a top-down aggregation approach (as commonly used in practice) diversification benefits should be approached with caution (indeed, the BCBS now restricts the use of negative correlations in portfolio assembly and construction, BCBS

Adding independently estimated risk measurements in a top-down approach is flawed in that it assumes that perfect correlations between market and credit risks exist. Since both risk forms are affected by the same economic factors, ^{2}

Diversification benefits are, however, not unobtainable and the BCBS highlights this by showing the interactions between interest rates and credit risk in the banking book. Creating a hypothetical bank, Drehmann, Sorensen and Stringa (

Diversification benefits are not guaranteed when using VaR, since the market risk measure is neither coherent nor sub-additive. Coherent risk measures such as ES guarantee the diversification benefits if an integrated measurement of total risk is measured. If separate measurements are done for market and credit risk, diversification benefits cannot be guaranteed even if coherent measurements are used. The choice of metric is not the only challenge related to integrated risk measurement. The metrics used in credit and market risk are not entirely comparable. For example, market risk models capture complete return distributions whereas credit risk models account mostly for losses stemming from defaults and ignore gains. A further challenge emerges in the different horizons that the risks are measured in, despite credit risk becoming more tradeable in the 21st century because of financial innovations such as securitisation.

The BCBS conclude that although integrated risk models have high data and technological demands, the aggregation and integrated measurement of market and credit risk should be done consistently in such a way that a common horizon is imposed, and all income, profits and losses are accounted for. However, the challenges mentioned, as well as the fact that a top-down approach is favoured by most banks with these approaches involving simple correlations ignoring non-linear interactions, suggest that even under integrated measurements diversifications benefits are not guaranteed.

The data employed in the credit buVaR risk metric were daily credit spreads for 5-year and 10-year South African government CDSs, from January 2000 to November 2016. South African credit ratings were obtained from Fitch ratings (Fitch Ratings

Credit buVaR combines both spread and default risk and Wong (

Compared with conventional default risk measures, the way in which default risk in the credit buVaR model is accounted for contrasts with spread VaR. The reliance on slow-reacting, backward-looking rating transition matrices is entirely replaced by the derivation of the cap on the spread level used in the subsequent inflator. This inflator imposed on the spread VaR measurement ensures a forward-looking, all-in credit loss measurement.

The credit buVaR model allows for credit and market risks in a diversifiable manner while solely relying on credit spread data. Wong (

This straightforward method using an historical simulation approach does not produce a statistically precise method, but neither do other VaR approaches (Wong

Credit buVaR’s ability to account for both default and spread risk in one regulatory capital calculation is made feasible when the calculation metric aims to detect widening of the issuer’s credit spreads. Wong (_{+}) is used to increase the VaR measure as required.

Since increased spreads precede defaults, long positions incur losses due to these changes while negative changes in spreads cause losses for short positions. However, defaults only affect long positions and thus the inflator is only applied to the positive side of the distribution. To incorporate the inflator the original return distribution undergoes a transformation when the returns are positive as shown in

In _{+}) is always greater than 1, so it amplifies the positive returns (positive returns in this case represent an

_{1} and _{2} are free parameters. A pricing function is used to cap the inflator as spreads cannot widen indefinitely without the benchmark bond entering default at some stage. Wong (

To calculate the spread cap, _{cap}, Wong (

_{defaulted} is the yield of the bond at the point of default. Wong (_{+}) as an adjustment that will inflate two standard deviations of spread returns up to the percentage loss at the point of default, calculated as _{cap}. This two standard deviation in

However, _{cap} satisfies

Substituting into

_{2} which must be calibrated. Wong (_{2} = 0.5 is the most suitable as it produces an inflator that increases rapidly to penalise RSW; however, it decreases in such a way that the spread inflated through the inflator will never exceed _{cap}. This ensures that the holder of the bond will never lose more than the principal amount, less the recovery amount. An advantage of _{2} as a free parameter is that it can be adjusted and calibrated as required by a regulator, depending on the requisite level of conservatism.

The credit buVaR model relies integrally on the simulation of _{cap} indicating the moment of default. This is fundamental to the model as it enables the aggregation of spread and default risk. Central to _{cap} is the risk-free rate of the market as well as the assumed bond recovery rate in the event of default. Firstly, compared with the US, South Africa is a high interest rate environment and thus the risk-free rate used to calibrate _{cap} is considerably elevated. JIBAR (November 2016) is used as the risk-free rate for calibration. In addition, the lack of CDS data for the South African market complicates the assumption of a recovery rate, since no noteworthy government or corporate bonds for which there are CDS data defaulted in the analysis period.

_{2} = 0.5 as that of Wong (

Credit risk measures on 5-year credit default swap spreads using standard deviation as a measure of volatility (risk-free rate = 7.00%, bond recovery rate = 10%, _{2} = 0.5).

The uncalibrated buVaR output in

Wong (

The bond recovery rate assumption is implemented first as it is based on empirical market data and insight, whereas the free parameter _{2} is calibrated to a suitable level and chosen at the discretion of the user. A _{2} of 1.0 (c.f. Wong _{2} = 0.5) reduces the increase of buVaR over conventional VaR to levels that may be acceptable to banks: between 1.0 and 2.5.

Credit risk measures on five-year credit default swap spreads using standard deviation as a measure of volatility (risk-free rate = 7.00%, bond recovery rate = 50%, _{2} = 1.0).

Assuming better bond recovery rates and applying a larger _{2} produces results that are still elevated – but more sensible using buVaR – as shown in ^{3}

Credit risk measures on five-year credit default swap spreads using standard deviation as a measure of volatility in the months preceding the credit crisis. Arrows indicate focus regions.

The choice of volatility measure may influence buVaR’s suitability. It is well known that better, more reactive measures of volatility are frequently used in practice, such as generalized autoregressive conditional heteroskedasticit (GARCH) and exponentially weighted moving average (EWMA) models.

Credit risk measures on five-year credit default swap spreads using the EWMA approach as a measure of volatility (_{2} = 1.0, _{EWMA} = 0.95).

The EWMA approach in

The choice of VaR measure may also influence buVaR’s suitability. Despite VaR being widely used in finance, the BCBS has decided to replace it with ES or ‘conditional VaR’ (BCBS

Credit bubble value at risk using value at risk and expected shortfall.

_{2} (= 1.0) remains identical to that chosen for five-year South African government bond CDS spreads as this value produces similar capital retention levels (c.f.

Credit buVaR for 10-year credit default swap spreads (risk-free rate = 7.00%, bond recovery rate = 50%, _{2} = 1.0).

_{+}. Each line represents Δ_{+} versus _{2} values (these _{2} values are the numbers on the graph at the maximum value of Δ_{+} for each fixed _{2}). _{+} versus the current spread,

(a) The effect of the spread level, _{+} (as well as an indication of the maximum ∆_{+} for different levels of _{2} and (b) the effect of spread level, _{2}.

The first derivative of _{+} with respect to _{+} is a maximum (i.e. the open circles in

Lower _{2} values generate inflators which elevate spreads early, that is, far from levels at which the bond would default. Wong (_{+} should penalise excessive growth as soon as possible and thus applies an _{2} = 0.5. Higher _{2} values elevate spreads more slowly than lower _{2} values, so excess growth is only penalised severely enough at spread levels close to those that would result in a bond default.

_{+} for various levels of _{2} and

Surface plot showing the impact of _{2} and spread level, _{+}.

_{2} value of 0.5 would apply too harsh a capital requirement for institutions as buVaR is five times higher than spread VaR during crisis periods. This quantity of capital retention would be too punitive for most institutions. At low _{2} values, the inflator imposes severe liquidity constraints on institutions. A higher _{2} is thus preferred in this study. Using

_{+} (its first derivative) with respect to

First derivative of ∆_{+} with respect to spread level,

The rate of change of Δ_{+} is considerably elevated in the pre-crisis period. This highlights the model’s ability to anticipate market bubbles and subsequently elevate buVaR through Δ_{+} to potentially retard or halt the bubble’s development.

_{f}_{ }, and the assumed bond recovery rate on _{cap}.

Impact of (a) the risk-free rate on the inflator as a function of _{cap}.

An increase in _{f} increases _{cap} as well as the value of _{+} experiences a maximum. Using _{f} increases, the yield at default, _{defaulted}, increases at a faster rate, so _{cap} = _{defaulted} − _{f} increases. This influence is trivial compared with the impact of the recovery rate on _{cap} (_{cap}.

Denzlera et al. (

Market-implied probabilities of default (using

South Africa’s credit rating is currently (November 2016) just above junk and has a negative outlook (Moody’s Investor Service

Implementation of a buVaR-like model in the banking environment would require significant cooperation between the regulator and regulated institutions. Bubble VaR models effectively attempt to replace the BCBS countercyclical buffer and thus thresholds and parameters would have to be tested and agreed upon. What would be an evident advantage of such a model is that it would not be burdened by complicated timing issues regarding the retention and release of capital buffers. These timing issues under the current BCBS formulation would be a key focus area, as they would have to be analysed and compared with continuous capital estimates under buVaR models.

Initial research between regulators and banks could focus on the optimal value for _{2}, as a comparison of this work with Wong’s (

Regulatory capital recommendations for financial markets are constantly evolving. A combination of several BCBS publications^{4}

Bubble VaR results using Wong’s (_{2} produces more feasible estimates. Applying buVaR to 5 and 10-year South African government bond CDS spreads produced results showing that buVaR is more responsive and conservative prior to periods of severe CDS spread increases. This highlights the metric’s countercyclical properties that would potentially have countered bubble developments. Depicting buVaR results on the same timescale as market-implied PDs and the South African credit rating shows that buVaR does ramp up significantly in the pre-crisis bubble development period. However, the model is robust when shocks occur such as the removal of the Minister of Finance in late 2015.

A tractable solution is provided in _{2}. Within any jurisdiction, institutions and policymakers will have local knowledge of bond recovery and risk-free rates which, in turn, determine _{cap} Using this information in conjunction with the results from _{2} and, thus, the associated increase in capital can be ascertained. This can be used as a guide for regulatory and institutional capital calibration.

The procyclical nature of financial markets and the way in which its participants react to fuelling this phenomenon are well documented. The BCBS proposed the implementation of a CCB, but this has raised concerns regarding uncertainty whether the right data are used for estimation: the credit-to-GDP ratio may not be optimal for jurisdictions with unique markets (Drehmann & Tsatsaronis

Future research opportunities include the optimal calibration of the free parameter _{2}. This parameter has a significant impact on the buVaR model and appropriate guidance is required if it is to be implemented. Research on the parameter would include analysis across multiple economies, markets and scenarios to ensure suitable implementation guidelines are created. Further research may also include investigation on the relationship between model outputs, CDS spreads and actual credit ratings as it was not the central focus of this study. Finally, as capital requirements for tradeable credit instruments arise both from default and spread risk, further research may analyse combined capital requirements from separate conventional models to that of aggregating buVaR-like models.

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

D.V. was the principal author and analyst and G.v.V. responsible for model design and implementation of the article.

First derivative of

This function = 0 (since when _{+}) where:

The trading and banking books are accounting terms that refer to assets held by a bank that are regularly traded and the bank’s balance sheet assets expected to be held to maturity respectively.

The interaction of market and credit risk (IMCR) working group established by the BCBS give several examples where this can occur.

South African credit ratings relative to spreads and buVaR are provided in

Basel IV comprises: BCBS 306, BCBS 319, BCBS 347, BCBS 362, BCBS 303, BCBS 279, BCBS 352, BCBS 355, BCBS 325, BCBS 349 (PWC