By Satinder Jandu and Dr Konstantinos Viglas

Thank you for your interest in our recent webinar "Implementing challenges of SA CVA - Aligning people, processes and technology", we received high attendance and excellent questions in the session. We were delighted with the interaction and wanted to give the questions the time and attention they deserve. For those queries we were unable to address in the webinar, we have followed up in this blog.

If you have any further questions or feedback, please feel free to comment below or to email NAG support.

Q: When can we expect regulators to specify technical requirements around e.g. leptokurtosis (fat tails) and wrong way risk?

• In the context of CVA, Wrong Way Risk (WWR) is understood as the correlation between EPEs and counterparty credit.
• In general, the counterparty survival probability is assumed deterministic in most CVA modelling approaches.
• Therefore, WWR is not captured.
• This is reflected in regulation where the c/p vega is omitted.
• The multiplier $$𝑚_{𝐶𝑉𝐴}$$, which is currently set to 1.25 is designed to capture WWR and may increase in the future.

Credit derivatives

• For credit derivatives there is an additional type of correlation that is not represented in models: the default correlation between c/p and reference credit.
• The reason is that if default correlation was modelled, c/p and reference default times should be generated with additional Monte Carlo, with a large number of paths (at least 1 million).

Q: Does a trading desk which traditionally hedges accounting CVA now have to do anything different to hedge Regulatory CVA and does hedging accounting CVA lead to hedging of Reg CVA?

• Strictly speaking hedging is always done with respect to the official risk neutral CVA calculation.
• The risk neutral CVA methodology cannot be prescribed. It must follow the mathematical principles of risk neutral pricing
• ... although there are some theoretical assumptions made, that usually follow the consensus practices across the street.
• One of these assumptions can be that there is no own default risk. CVA under this assumption is called ‘Unilateral CVA’.
• In the regulatory nomenclature ‘Unilateral CVA’ is called ‘Accounting CVA’. Unilateral/Accounting CVA often goes together with the assumption of no DVA.

Unilateral/Accounting CVA: $𝐶𝑉𝐴 = (1 − 𝑅){∫_0^𝑇}𝑒^{−{∫_0^𝑠} 𝑟_𝑢 𝑑𝑢} 𝐸𝑃𝐸_𝑠 \underbrace{(−𝑑𝑄_𝑠)}_{\substack{\text{Probability of} \\ \text{c/p default}}}$

Bilateral CVA: $𝐶𝑉𝐴 = (1 − 𝑅){∫_0^𝑇}𝑒^{−{∫_0^𝑠} 𝑟_𝑢 𝑑𝑢} 𝐸𝑃𝐸_𝑠 \underbrace{(−𝑑𝑄_𝑠)𝑄_𝑠^{𝑜𝑤𝑛}}_{\substack{\text{Probability of c/p} \\ \text{default GIVEN no} \\ \text{own default}}}$

• Traders will therefore continue to hedge Accounting CVA, the same way that they hedge the theoretical value of the trades themselves.
• However, any CVA capital charge methodology will potentially incentivise banks to adjust their trading so that they optimize their capital usage.
• This constitutes no change to current practice and applies to all types of capital charges, not just CVA capital charge.

Q: How are FX vega risks generated with respect to reporting currencies?

The FX vega for a pair of currencies where the basis is domestic currency, is prescribed by the regulation without ambiguity.

• The market implied volatility of all the instruments used in the calibration of the foreign-domestic FX process, is shifted by 1% relative to its current value and CVA is recalculated.
• The FX vega risk is then the difference between the CVA with the shifted volatility, divided by 1%.
• If there is an eligible hedge that is a volatility product itself, then its FX vega sensitivity is calculated in the analogous way.
• Remember that spot FX has no term structure (not to be confused with forward FX). However, there might be more than one implied FX volatilities to be shifted simultaneously, if the volatility model has a skew. This is not typical for XVA models, where usually FX is modelled as lognormal, but it could be the case for the hedge.

Example

Instrument: FX swap on EURUSD
Domestic currency: USD
Foreign currency: EUR

Calibration for CVA: EURUSD FX options

There is one implied Black volatility $$𝜎_{𝐸𝑈𝑅𝑈𝑆𝐷}$$ used for calibration. This is the implied spot volatility inferred from the FX market.

CVA sensitivity is then: $𝑆_{𝐸𝑈𝑅𝑈𝑆𝐷} = \frac{(𝐶𝑉𝐴(𝜎_{𝐸𝑈𝑅𝑈𝑆𝐷} + 0.01𝜎_{𝐸𝑈𝑅𝑈𝑆𝐷}) − 𝐶𝑉𝐴(𝜎_{𝐸𝑈𝑅𝑈𝑆𝐷}))}{0.01}$

Consider the example of EURGBP spot FX, denoted $$𝑋_{𝐺𝐵𝑃}^{𝐸𝑈𝑅}$$. The domestic currency is again USD.

Then, the foreign-foreign FX rate can be represented as: $𝑋_{𝐺𝐵𝑃}^{𝐸𝑈𝑅} = 𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}\cdot(𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃})^{−1}$

Regulation implies that the sensitivity of $$𝑋_{𝐺𝐵𝑃}^{𝐸𝑈𝑅}$$ must be obtained by a simultaneous 1% relative shift of the two domestic-based rates involved in the formula above.

Recall, that $$𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}$$ and $$𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}$$ will in general be correlated. If typically, spot FX is assumed lognormal, then one has to apply the volatility shifts in the quotient formula: $\frac{𝑑𝑋_{𝐺𝐵𝑃}^{𝐸𝑈𝑅}}{𝑋_{𝐺𝐵𝑃}^{𝐸𝑈𝑅}} = \frac{𝑑𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}}{𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}} − \frac{𝑑𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}{𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}} − \left\langle\frac{(𝑑𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}}{𝑋_{𝑈𝑆𝐷}^{𝐸𝑈𝑅}} \frac{𝑑𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}{𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}\right\rangle + \left\langle\frac{(𝑑𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}{𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}} \frac{(𝑑𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}{𝑋_{𝑈𝑆𝐷}^{𝐺𝐵𝑃}}\right\rangle$

Q: How will SA-CVA have an impact on measures like KVA?

This is an excellent question and provides a good opportunity to discuss something that may be one of the most complex challenges in terms of modelling.

What is KVA?

• KVA is the expected cost of capital for as long a trade exists.
• As an analogy, KVA is related to CVA of a trade the same way that MVA is related to the Initial Margin of a trade.

KVA on SA-CVA capital charge

• If an institution must calculate KVA on the SA-CVA charge in the future, this will be the most complex XVA to model.
• Let’s think of MVA for bilateral IM (i.e., ISDA SIMM), which also requires sensitivities. A risk neutral diffusion is generated and for each path, one has to obtain the sensitivities of the trade. This is already something computationally demanding.
• Now imagine that the exercise is to do something similar, but instead of having to calculate for each path the sensitivities of the trade, the task is to calculate the sensitivities of the CVA of the trade. It is in other words, MVA on CVA!
• Recall that CVA itself has more risk factors than the trade, as it is a volatility instrument.

KVA on SA-CVA capital charge will be an extremely complex calculation and is the typical domain of academic work with the purpose of establishing feasible approximate methods. KVA on BA-CVA (SA-CCR) would be far less complex, although itself among the most complex XVAs.

Q: Should regulator supplied models be model validated?

Model validation should be performed on all calculations that are deemed models according to the bank’s internal Model Risk Control policy. The definition of a model, in theory, can vary among different institutions, but in practice it is often in line with the SR11-7 definition. According to the SR11-7 definition, all conceivable regulatory capital calculations will fall under the definition of a model and therefore must be model validated.

It is worth mentioning that in modern Model Governance models are tiered according to attributes such as materiality, purpose and complexity. Traditionally, regulatory capital models are assessed to be of a lower tier because of their low complexity and the fact that they are not used to calculate PnL for books and records, or traded risk.

However, validating the actual regulatory calculation is often a very small part of the necessary validation and model governance work. The reason is that very often, substantial changes must be made in fundamental models that produce the data that feed the regulatory calculation.

Let us consider the example of SA-CVA. The aggregation formula probably will require validation for most banks. However, this is a relatively easy task because of its mathematical simplicity. On the other hand, most banks will need to implement many sensitivities that are already not implemented or improve the existing sensitivity calculation methodology. The model validation of these changes will constitute a huge task for model validation teams and will be one of the main challenges in implementing SA-CVA.

It is noted that modern Model Governance requires a whole lifecycle of actions, as opposed to a single validation review. More specifically the lifecycle of a model validation consists of the following stages:

• Risk assessment. The Model Validation Department risk assesses the model submitted for validation. Documentation, model owner testing and model risk tier are assessed before the review itself can start. At this stage Model Validation has the power to reject the proposed model, or request changes and/or additional documentation in advance of the review.
• Validation review. This will consist of theoretical review (“conceptual soundness”) and implementation review. Ideally, it will produce the most reliable documentation around the model.
• Formalising the results of the validation. This consists of the approval, conditional approval, or nonapproval of the model, by the relevant authority. This is also the stage where restrictions, ongoing monitoring and periodic review timing is agreed.

The last point should be stressed. Models are subject to periodic reviews, whereby validation must be re-done. The frequency of these periodic reviews is typically between two and five years. Furthermore, Model Validation/Governance departments are mandated with managing ongoing monitoring and restrictions and report model risk. Therefore, the new models (in this case mostly sensitivities) added to their model inventory, will impact Model Validation teams with permanent increases workload.

Q: What role can a vendor play in delivering regulatory change?

Vendors can play a key role in verifying your future state Target Operating Model (TOM) through independent verification of calculations, scalable data storage and HPC (GPU, AD for SA-CVA sensitivities) and orchestration of key data inputs driving regulatory calculations. No matter what you decide on your “Build vs. buy” decision, a vendor can help you meet that regulatory deadline quicker.

Q: Does Agile work in delivering regulatory change?

By Agile we mean using SAFE or SCRUM methodologies for delivering large and complex regulatory change. We know of several banks who successfully use Agile methodology to deliver the capital calculators for Basel III regulations, two banks in particular have used SAFE for FRTB. We would still advise the generation of a good central Business Requirement Document (BRD) that can be used to build the backlog in Jira or drive inner stakeholders who provide input to your capital calculator. In addition, Agile is used outside of IT such as Agile Audits.