ML models

ML models study a dataset and use the knowledge gained to make predictions for other datapoints. An ML model consists of an ML algorithm and one or more hyperparameters. ML algorithms study a dataset to make predictions, where hyperparameters determine the settings of the ML algorithm. The studying of a dataset is known as the training of the ML algorithm. Most ML algorithms have hyperparameters that need to be set by the user prior to the training. The trained algorithm, together with the calibrated set of hyperparameters, form the ML model.

ML models have different forms and shapes, and even more purposes. For selecting an appropriate ML model, a deeper understanding of the various types of ML that are available and how they work is required. Three types of ML can be distinguished:

• Supervised learning.
• Unsupervised learning.
• Semi-supervised learning.

The main difference between these types is the data that is required and the purpose of the model. The data that is fed into an ML model is split into two categories: the features (independent variables) and the labels/targets (dependent variables, for example, to predict a person’s height – label/target – it could be useful to look at the features: age, sex, and weight). Some types of machine learning models need both as an input, while others only require features. Each of the three types of machine learning is shortly introduced below.

Supervised learning

Supervised learning is the training of an ML algorithm on a dataset where both the features and the labels are available. The ML algorithm uses the features and the labels as an input to map the connection between features and labels. When the model is trained, labels can be generated by the model by only providing the features. A mapping function is used to provide the label belonging to the features. The performance of the model is assessed by comparing the label that the model provides with the actual label.

Unsupervised learning

In unsupervised learning there is no dependent variable (or label) in the dataset. Unsupervised ML algorithms search for patterns within a dataset. The algorithm links certain observations to others by looking at similar features. This makes an unsupervised learning algorithm suitable for, among other tasks, clustering (i.e. the task of dividing a dataset into subsets). This is done in such a manner that an observation within a group is more like other observations within the subset than an observation that is not in the same group. A disadvantage of unsupervised learning is that the model is (often) a black box.

Semi-supervised learning

Semi-supervised learning uses a combination of labeled and unlabeled data. It is common that the dataset used for semi-supervised learning consist of mostly unlabeled data. Manually labeling all the data within a dataset can be very time consuming and semi-supervised learning offers a solution for this problem. With semi-supervised learning a small, labeled subset is used to make a better prediction for the complete data set.

The training of a semi-supervised learning algorithm consists of two steps. To label the unlabeled observations from the original dataset, the complete set is first clustered using unsupervised learning. The clusters that are formed are then labeled by the algorithm, based on their originally labeled parts. The resulting fully labeled data set is used to train a supervised ML algorithm. The downside of semi-supervised learning is that it is not certain the labels are 100% correct.

Setting up the model

In most ML implementations, the data gathering, integration and pre-processing usually takes more time than the actual training of the algorithm. It is an iterative process of training a model, evaluating the results, modifying hyperparameters and repeating, rather than just a single process of data preparation and training. After the training is performed and the hyperparameters have been calibrated, the ML model is ready to make predictions.

Machine learning in financial risk management

ML can add value to financial risk management applications, but the type of model should suit the problem and the available data. For some applications, like challenger models, it is not required to completely explain the model you are using. This makes, for example, an unsupervised black box model suitable as a challenger model. In other cases, explainability of model results is a critical condition while choosing an ML model. Here, it might not be suitable to use a black box model.

In the next section we present some examples where ML models can be of added value in financial risk management.

Data quality analysis

All modeling challenges start with data. In line with the ‘garbage in, garbage out’ maxim, if the quality of a dataset is insufficient then an ML model will also not perform well. It is quite common that during the development of an ML model, a lot of time is spent on improving the data quality. As ML algorithms learn directly from the data, the performance of the resulting model will increase if the data quality increases. ML can be used to improve data quality before this data is used for modeling. For example, the data quality can be improved by removing/replacing outliers and replacing missing values with likely alternatives.

An example of insufficient data quality is the presence of large or numerous outliers. An outlier is an observation that significantly deviates from the other observations in the data, which might indicate it is incorrect. Outlier detection can easily be performed by a data scientist for univariate outliers, but multivariate outliers are a lot harder to identify. When outliers have been detected, or if there are missing values in a dataset, it might be useful to substitute some of these outliers or impute for missing values. Popular imputation methods are the mean, median or most frequent methods. Another option is to look for more suitable values; and ML techniques could help to improve the data quality here.

Multiple ML models can be combined to improve data quality. First, an ML model can be used to detect outliers, then another model can be used to impute missing data or substitute outliers by a more likely value. The outlier detection can either be done using clustering algorithms or by specialized outlier detection techniques.

Loan approval

A bank’s core business is lending money to consumers and companies. The biggest risk for a bank is the credit risk that a borrower will not be able to fully repay the borrowed amount. Adequate loan approval can minimize this credit risk. To determine whether a bank should provide a loan, it is important to estimate the probability of default for that new loan application.

Established banks already have an extensive record of loans and defaults at their disposal. Together with contract details, this can form a valuable basis for an ML-based loan approval model. Here, the contract characteristics are the features, and the label is the variable indicating if the consumer/company defaulted or not. The features could be extended with other sources of information regarding the borrower.

Supervised learning algorithms can be used to classify the application of the potential borrower as either approved or rejected, based on their probability of a future default on the loan. One of the suitable ML model types would be classification algorithms, which split the dataset into either the ‘default’ or ‘non-default’ category, based on their features.

Challenger models

When there is already a model in place, it can be helpful to challenge this model. The model in use can be compared to a challenger model to evaluate differences in performance. Furthermore, the challenger model can identify possible effects in the data that are not captured yet in the model in use. Such analysis can be performed as a review of the model in use or before taking the model into production as a part of a model validation.

The aim of a challenger model is to challenge the model in use. As it is usually not feasible to design another sophisticated model, mostly simpler models are selected as challenger model. ML models can be useful to create more advanced challenger models within a relatively limited amount of time.

Challenger models do not necessarily have to be explainable, as they will not be used in practice, but only as a comparison for the model in use. This makes all ML models suitable as challenger models, even black box models such as neural networks.

Segmentation

Segmentation concerns dividing a full data set into subsets based on certain characteristics. These subsets are also referred to as segments. Often segmentation is performed to create a model per segment to better capture the segment’s specific behavior. Creating a model per segment can lower the error of the estimations and increase the overall model accuracy, compared to a single model for all segments combined.

Segmentation can, among other uses, be applied in credit rating models, prepayment models and marketing. For these purposes, segmentation is sometimes based on expert judgement and not on a data-driven model. ML models could help to change this and provide quantitative evidence for a segmentation.

There are two approaches in which ML models can be used to create a data-driven segmentation.  One approach is that observations can be placed into a certain segment with similar observations based on their features, for example by applying a clustering or classification algorithm. Another approach to segment observations is to evaluate the output of a target variable or label. This approach assumes that observations in the same segment have the same kind of behavior regarding this target variable or label.

In the latter approach, creating a segment itself is not the goal, but optimizing the estimation of the target variable or classifying the right label is. For example, all clients in a segment ‘A’ could be modeled by function ‘a’, where clients in segment ‘B’ would be modeled by function ‘b’. Functions ‘a’ and ‘b’ could be regression models based on the features of the individual clients and/or macro variables that give a prediction for the actual target variable.

Credit scoring

Companies and/or debt instruments can receive a credit rating from a credit rating agency. There are a few well-known rating agencies providing these credit ratings, which reflects their assessment of the probability of default of the company or debt instrument. Besides these rating agencies, financial institutions also use internal credit scoring models to determine a credit score. Credit scores also provide an expectation on the creditworthiness of a company, debt instrument or individual.

Supervised ML models are suitable for credit scoring, as the training of the ML model can be done on historical data. For historical data, the label (‘defaulted’ or ‘not defaulted’) can be observed and extensive financial data (the features) is mostly available. Supervised ML models can be used to determine reliable credit scores in a transparent way as an alternative to traditional credit scoring models. Alternatively, credit scoring models based on ML can also act as challenger models for traditional credit scoring models. In this case, explainability is not a key requirement for the selected ML model.

Conclusion

ML can add value to, or replace, models applied in financial risk management. It can be used in many different model types and in many different manners. A few examples have been provided in this article, but there are many more.

ML models learn directly from the data, but there are still some choices to be made by the model user. The user can select the model type and must determine how to calibrate the hyperparameters. There is no ‘one size fits all’ solution to calibrate a ML model. Therefore, ML is sometimes referred to as an art, rather than a science.

When applying ML models, one should always be careful and understand what is happening ‘under the hood’. As with all modeling activities, every method has its pitfalls. Most ML models will come up with a solution, even if it is suboptimal. Common sense is always required when modeling. In the right hands though, ML can be a powerful tool to improve modeling in financial risk management.

Working with ML models has given us valuable insights (see the box below). Every application of ML led to valuable lessons on what to expect from ML models, when to use them and what the pitfalls are.

Machine learning and Zanders

Zanders already encountered several projects and research questions where ML could be applied. In some cases, the use of ML was indeed beneficial; in other cases, traditional models turned out to be the better solution.

During these projects, most time was spent on data collection and data pre-processing. Based on these experiences, an ML based dataset validation tool was developed. In another case, a model was adapted to handle missing data by using an alternative available feature of the observation.

ML was also used to challenge a Zanders internal credit rating model. This resulted in useful insights on potential model improvements. For example, the ML model provided more insight in variable importance and segmentation. These insights are useful for the further development of Zanders’ credit rating models. Besides the insights what could be done better, the ML model also emphasized the advantages of classical models over the ML-based versions. The ML model was not able to provide more sensible ratings than the traditional credit rating model.

In another case, we investigated whether it would be sensible and feasible to use ML for transaction screening and anomaly detection. The outcome of this project once more highlighted that data is key for ML models. The available data was numerous, but of low quality. Therefore, the used ML models were not able to provide a helpful insight into the payments, or to consistently detect divergent payment behavior on a large scale.

Besides the projects where ML was used to deliver a solution, we investigated the explainability of several ML models. During this process we gained knowledge on techniques to provide more insights into otherwise hardly understandable (black box) models.

Business margin protection

ARF can be a very efficient hedging instrument when the business margin needs to be protected, namely in the following business scenarios:

• Budgeted sales revenue or budgeted costs of goods sold are incurred with reliable regularity and spread evenly in time. This exposure needs to be hedged against the functional currency.
• The business is run in separate books with different functional currencies, FX exposure is determined and hedged against the respective functional currency of these books. Resulting margin can be budgeted with high degree of reliability and stability, is relatively small and needs to be hedged from the currency of the respective business book to the functional currency of the reporting entity.

Increased complexity

Hedging such FX exposure with conventional FX forwards would lead to a very high number of transactions, as well as data on the side of underlying FX exposure determination, resulting in a data flood and high administrative effort. A hedge accounting according the IFRS 9 rules is almost impossible due to high number of hedge relationships to manage. The complexity increases even more if treasury operations are centralized and the FX exposure has to be concentrated via intercompany FX transactions in the group treasury first.

If the ARF instruments are not directly supported by the used treasury management system (TMS), the users have to resort to replicating the single external ARF deal with a series of conventional FX forwards, creating individual FX forwards for each fixation date of the observation period. As the observation periods are usually long (at least 30 days) and rate fixation periodicity is usually daily, this workaround leads to a high count of fictitious deals with relatively small nominal, leading to an administrative burden described above. Moreover, this workaround prevents automated creation of deals via an interface from a trading platform and automated correspondence exchange based on SWIFT MT3xx messages, resulting in a low automation level of treasury operations.

Add-on for SAP TRM

Currently, the ARF instruments are not supported in SAP Treasury and Risk management system (SAP TRM). In order to bridge the gap and to help the centralized treasury organizations to further streamline their operations, Zanders has developed an add-on for SAP TRM to manage the fixing of the average rate over the observation period, as well as to correctly calculate the fair value of the deals with partially fixed average rate.

The solution consists of dedicated average rate FX forward collective processing report, covering:

• Particular information related to ARF deals, including start and end of the fixation period, currently fixed average rate, fixed portion (percentage), locked-in result for the fixed portion of the deal in the settlement currency.
• Specific functions needed to manage this type of deals: creation, change, display of rate fixation schedule, as well as creating final fixation of the FX deal, once the average rate is fully calculated through the observation period.

Figure 1 Zanders FX Average Rate Forwards Cockpit and the ARF specific key figures

The solution builds on the standard SAP functionality available for FX deal management, meaning all other proven functionalities are available, such as payments, posting via treasury accounting subledger, correspondence, EMIR reporting, calculation of fair value for month-end evaluation and reporting. Through an enhancement, the solution is fully integrated into market risk, credit risk and, if needed, portfolio analyser too. Therefore, correct mark-to-market is always calculated for both the fixed and unfixed portion of the deal.

Figure 2 Integration of Zanders ARF solution into SAP Treasury Transaction manager process flow

The solution builds on the standard SAP functionality available for FX deal management, meaning all other proven functionalities are available, such as payments, posting via treasury accounting subledger, correspondence, EMIR reporting, calculation of fair value for month-end evaluation and reporting. Through an enhancement, the solution is fully integrated into market risk, credit risk and, if needed, portfolio analyser too. Therefore, correct mark-to-market is always calculated for both the fixed and unfixed portion of the deal.

Zanders can support you with the integration of ARF forwards into your FX exposure management process. For more information do not hesitate to contact Michal Šárnik.

This exemption has been applied in a diverse way by supervisors and therefore, the treatment of Structural FX risk has been updated in recent regulatory publications. In this article we discuss these publications and market practice around Structural FX risk based on an analysis of the policies applied by the top 25 banks in Europe.

Based on the 1996 amendment to the Capital Accord, banks that apply for the exemption of Structural FX positions can exclude these positions from the Pillar 1 capital requirement for market risk. This exemption was introduced to allow international banks with subsidiaries in currencies different from the reporting currency to employ a strategy to hedge the capital ratio from adverse movements in the FX rate. In principle a bank can apply one of two strategies in managing its FX risk.

1. In the first strategy, the bank aims to stabilize the value of its equity from movements in the FX rate. This strategy requires banks to maintain a matched currency position, which will effectively protect the bank from losses related to FX rate changes. Changes in the FX rate will not impact the equity of a bank with e.g. a consolidated balance sheet in Euro and a matched USD position. The value of the Risk-Weighted Assets (RWAs) is however impacted. As a result, although the overall balance sheet of the bank is protected from FX losses, changes in the EUR/USD exchange rate can have an adverse impact on the capital ratio.
2. In the alternative strategy, the objective of the bank is to protect the capital adequacy ratio from changes in the FX rate. To do so, the bank deliberately maintains a long, open currency position, such that it matches the capital ratio. In this way, both the equity and the RWAs of the bank are impacted in a similar way by changes in the EUR/USD rate, thereby mitigating the impact on the capital ratio. Because an open position is maintained, FX rate changes can result in losses for the bank. Without the exemption of Structural FX positions, the bank would be required to hold a significant amount of capital for these potential losses, effectively turning this strategy irrelevant.

As can also be seen in the exhibit below, the FX scenario that has an adverse impact on the bank differs between both strategies. In strategy 1, an appreciation of the currency will result in a decrease of the capital ratio, while in the second strategy the value of the equity will increase if the currency appreciates. The scenario with an adverse impact on the bank in strategy 2 is when the foreign currency depreciates.

Until now, only limited guidance has been available on e.g. the risk management framework, (number of) currencies that can be in scope of the exemption and the maximum open exposure that can be exempted. As a result, the practical implementation of the Structural FX exemption varies significantly across banks. Recent regulatory publications aim to enhance regulatory guidance to ensure a more standardized application of the exemption.

Regulatory Changes

With the publication of the Fundamental Review of the Trading Book (FRTB) in January 2019, the exemption of Structural FX risk was further clarified. The conditions from the 1996 amendment were complemented to a total of seven conditions related to the policy framework required for FX risk and the maximum and type of exposure that can be in scope of the exemption. Within Europe, this exemption is covered in the Capital Requirements Regulation under article 352(2).

To process the changes introduced in the FRTB and to further strengthen the regulatory guidelines related to Structural FX, the EBA has issued a consultation paper in October 2019. A final version of these guidelines was published in July 2020. The date of application was pushed back one year compared to the consultation paper and is now set for January 2022.

The guidelines introduced by EBA can be split in three main topics:

1. Definition of Structural FX.
   The guidelines provide a definition of positions of a structural nature and positions that are eligible to be exempted from capital. Positions of a structural nature are investments in a subsidiary with a reporting currency different from that of the parent (also referred to as Type A), or positions that are related to the cross-border nature of the institution that are stable over time (Type B). A more elaborate justification is required for Type B positions and the final guidelines include some high-level conditions for this.
2. Management of Structural FX.
   Banks are required to document the appetite, risk management procedures and processes in relation to Structural FX in a policy. Furthermore, the risk appetite should include specific statements on the maximum acceptable loss resulting from the open FX position, on the target sensitivity of the capital ratios and the management action that will be applied when thresholds are crossed. It is moreover clarified that the exemption can in principle only be applied to the five largest structural currency exposures of the bank.
3. Measurement of Structural FX.
   The guidelines include requirements on the type and the size of the positions that can be in scope of the exemption. This includes specific formulas on the calculation of the maximum open position that can be in scope of the exemption and the sensitivity of the capital ratio. In addition, banks will need to report the structural open position, maximum open position, and the sensitivity of the capital ratio, to the regulator on a quarterly basis.

One of the reasons presented by the EBA to publish these additional guidelines is a growing interest in the application of the Structural FX exemption in the market.

Market Practice

To understand the current policy applied by banks, a review of the 2019 annual reports of the top 25 European banks was conducted. Our review shows that almost all banks identify Structural FX as part of their risk identification process and over three quarters of the banks apply a strategy to hedge the CET1 ratio, for which an exemption has been approved by the ECB. While most of the banks apply the exemption for Structural FX, there is a vast difference in practices applied in measurement and disclosure. Only 44% of the banks publish quantitative information on Structural FX risk, ranging from the open currency exposure, 10-day VaR losses, stress losses or Economic Capital allocated.

The guideline that will have a significant impact on Structural FX management within the bigger banks of Europe is the limit to include only the top five open currency positions in the exemption: of the banks that disclose the currencies in scope of the Structural FX position, 60% has more than 5 and up to 20 currencies in scope. Reducing that to a maximum of five will either increase the capital requirements of those banks significantly or require banks to move back to maintaining a matched position for those currencies, which would increase the capital ratio volatility.

Conclusion

The EBA guidelines on Structural FX that will to go live by January 2022 are expected to have quite an impact on the way banks manage their Structural FX exposures. Although the Structural FX policy is well developed in most banks, the measurement and steering of these positions will require significant updates. It will also limit the number of currencies that banks can identify as Structural FX position. This will make it less favourable for international banks to maintain subsidiaries in different currencies, which will increase the cost of capital and/or the capital ratio volatility.

Finally, a topic that is still ambiguous in the guidelines is the treatment of Structural FX in a Pillar 2 or ICAAP context. Currently, 20% of the banks state to include an internal capital charge for open structural FX positions and a similar amount states to not include an internal capital charge. Including such a capital charge, however, is not obvious. Although an open FX position will present FX losses for a bank which would favour an internal capital charge, the appetite related to internal capital and to the sensitivity of the capital ratio can counteract, resulting in the need for undesirable FX hedges.

The new guidelines therefore present clarifications in many areas but will also require banks to rework a large part of their Structural FX policies in the middle of a (COVID-19) crisis period that already presents many challenges.

Alternatives for a calculating compounded SARON

After explaining in the previous article the use of compounded SARON as a term alternative to CHF LIBOR, the Swiss National Working Group (NWG) published several options as to how a compounded SARON could be used as a benchmark in banking products, such as loans or mortgages, and financial instruments (e.g. capital market instruments). Underlying these options is the question of how to best mitigate uncertainty about future cash flows, a factor that is inherent in the compounding approach. In general, it is possible to separate the type of certainty regarding future interest payments in three categories . The market participant has:

• an aversion to variable future interest payments (i.e. payments ex-ante unknown). Buying fixed-rate products is best, where future cash flows are known for all periods from inception. No benchmark is required due to cash flow certainty over the lifetime of the product.
• a preference for floating-rate products, where the next cash flow must be known at the beginning of each period. The option ‘in advance’ is applicable, where cash flow certainty exists for a single period.
• a preference for floating-rate products with interest rate payments only close to the end of the period are tolerated. The option ‘in arrears’ is suitable, where cash flow certainty only close to the end of each period exists.

Based on the Financial Stability Board (FSB) user’s guide, the Swiss NWG recommends considering six different options to calculate a compounded risk-free rate (RFR). Each financial institution should assess these options and is recommended to define an action plan with respect to its product strategy. The compounding options can be segregated into options where the future interest rate payments can be categorized as in arrears, in advance or hybrid. The difference in interest rate payments between ‘in arrears’ and ‘in advance’ conventions will mainly depend on the steepness of the yield curve. The naming of the compounding options can be slightly different among countries, but the technique behind those is generally the same. For more information regarding the available options, see Figure 1.

Moreover, for each compounding technique, an example calculation of the 1-month compounded SARON is provided. In this example, the start date is set to 1 February 2019 (shown as today in Figure 1) and the payment date is 1 March 2019. Appendix I provides details on the example calculations.

Figure 1: Overview of alternative techniques for calculating compounded SARON. Source: Financial Stability Board (2019).

0) Plain (in arrears): The observation period is identical to the interest period. The notional is paid at the start of the period and repaid on the last day of the contract period together with the last interest payment. Moreover, a Plain (in arrears) structure reflects the movement in interest rates over the full interest period and the payment is made on the day that it would naturally be due. On the other hand, given publication timing for most RFRs (T+1), the requiring payment is on the same day (T+1) that the final payment amount is known (T+1). An exception is SARON, as SARON is published one business day (T+0) before the overnight loan is repaid (T+1).

Example: the 1-month compounded SARON based on the Plain technique is like the example explained in the previous article, but has a different start date (1 February 2019). The resulting 1-month compounded SARON is equal to -0.7340% and it is known one day before the payment date (i.e. known on 28 February 2019).

1) Payment Delay (in arrears): Interest rate payments are delayed by X days after the end of an interest period. The idea is to provide more time for operational cash flow management. If X is set to 2 days, the cash flow of the loan matches the cash flow of most OIS swaps. This allows perfect hedging of the loan. On the other hand, the payment in the last period is due after the payback of the notional, which leads to a mismatch of cash flows and a potential increase in credit risk.

Example: the 1-month compounded SARON is equal to -0.7340% and like the one calculated using the Plain (in arrears) technique. The only difference is that the payment date shifts by X days, from 1 March 2019 to e.g. 4 March 2019. In this case X is equal to 3 days.

2) Lockout Period (in arrears): The RFR is no longer updated, i.e. frozen, for X days prior to the end of an interest rate period (lockout period). During this period, the RFR on the day prior to the start of the lockout is applied for the remaining days of the interest period. This technique is used for SOFR-based Floating Rate Notes (FRNs), where a lockout period of 2-5 days is mostly used in SOFR FRNs. Nevertheless, the calculation of the interest rate might be considered less transparent for clients and more complex for product providers to be implemented. It also results in interest rate risk that is difficult to hedge due to potential changes in the RFR during the lockout period. The longer the lockout period, the more difficult interest rate risk can be hedged during the lockout period.

Example: the 1-month compounded SARON with a lockout period equal to 3 days (i.e. X equals 3 days) is equal to -0.7337% and known 3 days in advance of the payment date.

3) Lookback (in arrears): The observation period for the interest rate calculation starts and ends X days prior to the interest period. Therefore, the interest payments can be calculated prior to the end of the interest period. This technique is predominately used for SONIA-based FRNs with a delay period of X equal to 5 days. An increase in interest rate risk due to changes in yield curve is observed over the lifetime of the product. This is expected to make it more difficult to hedge interest rate risk.

Example: assuming X is equal to 3 days, the 1-month compounded SARON would start in advance, on January 29, 2019 (i.e. today minus 3 days). This technique results in a compounded 1-month SARON equal to -0.7335%, known on 25 February 2019 and payable on 1 March 2019.

4) Last Reset (in advance): Interest payments are based on compounded RFR of the previous period. It is possible to ensure that the present value is equivalent to the Plain (in arrears) case, thanks to a constant mark-up added to the compounded RFR. The mark-up compensates the effects of the period shift over the full life of the product and can be priced by the OIS curve. In case of a decreasing yield curve, the mark-up would be negative. With this technique, the product is more complex, but the interest payments are known at the start of the interest period, as a LIBOR-based product. For this reason, the mark-up can be perceived as the price that a borrower is willing to pay due to the preference to know the next payment in advance.

Example: the interest rate payment on 1 March 2019 is already known at the start date and equal to -0.7328% (without mark-up).

5) Last Recent (in advance): A single RFR or a compounded RFR for a short number of days (e.g. 5 days) is applied for the entire interest period. Given the short observation period, the interest payment is already known in advance at the start of each interest period and due on the last day of that period. As a consequence, the volatility of a single RFR is higher than a compounded RFR. Therefore, interest rate risk cannot be properly hedged with currently existing derivatives instruments.

Example: a 5-day average is used to calculate the compounded SARON in advance. On the start date, the compounded SARON is equal to -0.7339% (known in advance) that will be paid on 1 March 2020.

6) Interest Rollover (hybrid): This technique combines a first payment (installment payment) known at the beginning of the interest rate period with an adjustment payment known at the end of the period. Like Last Recent (in advance), a single RFR or a compounded RFR for a short number of days is fixed for the whole interest period (installment payment known at the beginning). At the end of the period, an adjustment payment is calculated from the differential between the installment payment and the compounded RFR realized during the interest period. This adjustment payment is paid (by either party) at the end of the interest period (or a few days later) or rolled over into the payment for the next interest period. In short, part of the interest payment is known already at the start of the period. Early termination of contracts becomes more complex and a compensation mechanism is needed.

Example: similar to Last Recent (in advance), a 5-day compounded SARON can be considered as installment payment before the starting date. On the starting date, the 5-day compounded SARON rate is equal to -0.7339% and is known to be paid on 1 March 2019 (payment date). On the payment date, an adjustment payment is calculated as the delta between the realized 1-month compounded SARON, equal to -0.7340% based on Plain (in arrears), and -0.7339%.

There is a trade-off between knowing the cash flows in advance and the desire for a payment structure that is fully hedgeable against realized interest rate risk. Instruments in the derivatives market currently use ‘in arrears’ payment structures. As a result, the more the option used for a cash product deviates from ‘in arrears’, the less efficient the hedge for such a cash product will be. In order to use one or more of these options for cash products, operational cash management (infrastructure) systems need to be updated. For more details about the calculation of the compounded SARON using the alternative techniques, please refer to Table 1 and Table 2 in the Appendix I. The compounding formula used in the calculation is explained in the previous article.

Overall, market participants are recommended to consider and assess all the options above. Moreover, the financial institutions should individually define action plans with respect to their own product strategies.

Conclusions

The transition from IBOR to alternative reference rates affects all financial institutions from a wide operational perspective, including how products are created. Existing LIBOR-based cash products need to be replaced with SARON-based products as the mortgages contract. In the next installment, IBOR Reform in Switzerland – Part III, the latest information from the Swiss National Working Group (NWG) and market developments on the compounded SARON will be explained in more detail.

Appendix I – II

Contact

For more information about the challenges and latest developments on SARON, please contact Martijn Wycisk or Davide Mastromarco of Zanders’ Swiss office: +41 44 577 70 10.

The other articles on this subject: 

Transition from CHF LIBOR to SARON, IBOR Reform in Switzerland, Part I
Compounded SARON and Swiss Market Development, IBOR Reform in Switzerland, Part III
Fallback provisions as safety net, IBOR Reform in Switzerland, Part IV

References

1. Mastromarco, D. Transition from CHF LIBOR to SARON, IBOR Reform in Switzerland – Part I. February 2020.
2. National Working Group on Swiss Franc Reference Rates. Discussion paper on SARON Floating Rate Notes. July 2019.
3. National Working Group on Swiss Franc Reference Rates. Executive summary of the 12 November 2019 meeting of the National Working Group on Swiss Franc Reference Rates. Press release November 2019.
4. National Working Group on Swiss Franc Reference Rates. Starter pack: LIBOR transition in Switzerland. December 2019.
5. Financial Stability Board (FSB). Overnight Risk-Free Rates: A User’s Guide. June 2019.
6. ISDA. Supplement number 60 to the 2006 ISDA Definitions. October 2019.
7. ISDA. Interbank Offered Rate (IBOR) Fallbacks for 2006 ISDA Definitions. December 2019.
8. National Working Group on Swiss Franc Reference Rates. Executive summary of the 7 May 2020 meeting of the National Working Group on Swiss Franc Reference Rates. Press release May 2020

Two building blocks

The appropriate approach and level of complexity in the mortgage valuation depend on the underlying purpose. Examples of valuation purposes are: regulatory, accounting, risk or sales of the mortgage portfolio. For example BCBS, IRRBB, Solvency, IFRS and the EBA ask for (specific) valuation methods of mortgages. The two building blocks for a ‘fair value’ calculation of mortgages are expected cash flows and a discount curve.

The market value is the sum of the expected cash flows at the moment of valuation, which are derived by discounting future expected cash flows with an appropriate curve. For both building block models, choices have to be made resulting in a tradeoff between the accuracy level and the computational effort.

Figure 1: Constructing the expected cash flows from the contractual cash flows for a loan with an annuity repayment type.

Cash flow schedule

The contractual cash flows are projected cash flows, including repayments. These can be derived based on the contractually agreed loan components, such as the interest rate, the contractual maturity and the redemption type.

The three most commonly used redemption types in the mortgage market are:

• Bullet: interest only payments, no contractual repayment cash flows except at maturity
• Linear: interest (decreasing monthly) and constant contractual repayment cash flows
• Annuity: fixed cash flows, consisting of an interest and contractual repayment part

However, the expected cash flows will most likely differ from this contractually agreed pattern due to additional prepayments. Especially in the current low interest rate environment, borrowers frequently make prepayments on top of the scheduled repayments.

Figure 1 shows how to calculate an expected cash flow schedule by adding the prepayment cash flows to the contractual cash flow. There are two methods to derive : client behavior dependent on interest rates and client behavior independent of interest rates. The independent method uses an historical analysis, indicating a backward looking element. This historical analysis can include a dependency on certain contract characteristics.

On the other hand, the interest rate dependent behavior is forward looking and depends on the expected level of the interest rates. Monte Carlow simulations can model interest dependent behavior.

Another important factor in client behavior are penalties paid in case of a prepayment above a contractually agreed threshold. These costs are country and product specific. In Italy, for example, these extra costs do not exist, which could currently result in high prepayments rates.

Discount curve

The curve used for cash flow discounting is always a zero curve. The zero curve is constructed from observed interest rates which are mapped on zero-coupon bonds to maturities across time. There are three approaches to derive the rates of this discount curve: the top down-approach, the bottom-up approach or the negotiation approach. The first two methods are the most relevant and common.

In theory, an all-in discount curve consists of a riskfree rate and several spread components. The ‘base’ interest curve concerns the risk-free interest rate term structure in the market at the valuation date with the applicable currency and interest fixing frequency (or use ccy- and basis-spreads). The spreads included depend on the purpose of the valuation. For a fair value calculation, the following spreads are added: liquidity spread, credit spread, operational cost, option cost, cost of capital and profit margin. An example of spreads included for other valuation purposes are offerings costs and origination fee.

Top-down versus Bottom-up

The chosen calculation approach depends on the available data, the ability to determine spread components, preferences and the purpose of the valuation.

A top-down method derives the applied rates of the discount curve from all-in mortgage rates on a portfolio level. Different rates should be used to construct a discount curve per mortgage type and LTV level, and should take into account the national guaranteed amount (NHG in the Netherlands). Subtract all-in mortgage rates spreads that should not part of the discount curve, such as the offering costs. Use this top-down approach when limited knowledge or tools are available to derive all the individual spread components. The all-in rates can be obtained from the following sources: mortgage rates in the market, own mortgage rates or by designing a mortgage pricing model.

Figure 2

The bottom-up approach constructs the applied discount curve by adding all applicable spreads on top of the zero curve at a contract level. This method requires that several spread components can be calculated separately. The top-down approach is quicker, but less precise than the bottom-up approach, which is more accurate but also computationally heavy. Additionally, the bottom-up method is only possible if the appropriate spreads are known or can be derived. One example of a derivation of a spread component is credit spreads determined from expected losses based on an historical analysis and current market conditions.

In short

A fair value calculation performed by a discounted cash flow method consists of two building blocks: the expected cash flows and a discount curve. This requires several model choices before calculating a fair value of a mortgage (portfolio).

The expected cash flow model is based on the contractual cash flows and any additional prepayments. The mortgage prepayments can be modeled by assuming interest dependent or interest independent client behavior.

To construct the discount curve, the relevant spreads should be added to the risk-free curve. The decision for a top-down or bottom-up approach depends on the available data, the ability to determine spread components, preferences and the purpose of the valuation.

These important choices do not only apply for fair value calculations but are applicable for many other mortgage valuation purposes.

 Zanders Valuation Desk

Independent, high quality, market practice and accounting standard proof are the main drivers of our Valuation Desk. For example, we ensure a high quality and professionalism with a strict, complete and automated check on the market data from our market data provider on a daily basis. Furthermore, we have increased our independence by implementing the F3 solution from FINCAD in our current valuation models. This permits us to value a larger range of financial instruments with a high level of quality, accuracy and wider complexity.

For more information or questions concerning valuation issues, please contact Pierre Wernert: p.wernert@zanders.eu.

The standard model, as defined by IFRS 17, of measuring the value of insurance contracts is the ‘building blocks approach’. In this approach, the value of the contract is measured as the sum of the following components:

• Block 1: Sum of the future cash flows that relate directly to the fulfilment of the contractual  obligations.
• Block 2: Time value of the future cash flows. The discount rates used to determine the time value reflect the characteristics of the insurance contract.
• Block 3: Risk adjustment, representing the compensation that the insurer requires for bearing the uncertainty in the amount and timing of the cash flows.
• Block 4: Contractual service margin (CSM), representing the amount available for overhead and profit on the insurance contract. The purpose  of the CSM is to prevent a gain at initiation of the contract.

Risk adjustment vs risk margin

IFRS 17 does not provide full guidance on how the risk adjustment should be calculated. In theory, the compensation required by the insurer for bearing the risk of the contract would be equal to the cost of the needed capital. As most insurers within the IFRS jurisdiction capitalize based on Solvency II (SII) standards, it is likely that they will leverage on their past experience. In fact, there are many similarities between the risk adjustment and the SII risk margin.

The risk margin represents the compensation required for non-hedgeable risks by a third party that would take over the insurance liabilities. However, in practice, this is calculated using the capital models of the insurer itself. Therefore, it seems likely that the risk margin and risk adjustment will align. Differences can be expected though. For example, SII allows insurers to include operational risk in the risk margin, while this is not allowed under IFRS 17.

Liability adequacy test

Determining the impact of IFRS 17 is not straightforward: the current IFRS accounting standard leaves a lot of flexibility to determine the reserve value for insurance liabilities (one of the reasons for introducing IFRS 17). The reserve value reported under current IFRS is usually grandfathered from earlier accounting standards, such as Dutch GAAP. In general, these reserves can be defined as the present value of future benefits, where the technical interest rate and the assumptions for mortality are locked-in at pricing.

However, insurers are required to perform liability adequacy testing (LAT), where they compare the reserve values with the future cash flows calculated with ‘market consistent’ assumptions. As part of the market consistent valuation, insurers are allowed to include a compensation for bearing risk, such as the risk adjustment. Therefore, the biggest impact on the reserve value is expected from the introduction of the CSM.

The IASB has defined a hierarchy for the approach to measure the CSM at transition date. The preferred method is the ‘full retrospective application’. Under this approach, the insurer is required to measure the insurance contract as if the standard had always applied. Hence, the value of the insurance contract needs to be determined at the date of initial recognition and consecutive changes need to be determined all the way to transition date. This process is outlined in the following case study.

A case study

The impact of the new IFRS standards is analyzed for the following policy:

• The policy covers the risk that a mortgage owner deceases before the maturity of the loan. If this event occurs, the policy pays the remaining notional of the loan.
• The mortgage is issued on 31 December 2015 and has an initial notional value of € 200,000 that is amortized in 20 years. The interest percentage is set at 3 per cent.
• The policy pays an annual premium of € 150. The annual estimated costs of the policy are equal to 10 per cent of the premium.

In the case of this policy, an insurer needs to capitalize for the risk that the policy holder’s life expectancy decreases and the risk that expenses will increase (e.g. due to higher than expected inflation). We assume that the insurer applies the SII standard formula, where the total capital is the sum of the capital for the individual risk types, based on 99.5 per cent VaR approach, taking diversification into account.

The cost of capital would then be calculated as follows:

• Capital for mortality risk is based on an increase of 15 per cent of the mortality rates.
• Capital for expense risk is based on an increase of 10 per cent in expense amount combined with an increase of 1 per cent in the inflation.
• The diversification between these risk types is assumed to be 25 per cent.
• Future capital levels are assumed to be equal to the current capital levels, scaled for the decrease in outstanding policies and insurance coverage.
• The cost-of-capital rate equals 6 per cent.

At initiation (i.e. 2015 Q4), the value of the contract under the new standards equals the sum of:

• Block 1: € 482
• Block 2: minus € 81
• Block 3: minus € 147
• Block 4: minus € 254

Consecutive changes

The insurer will measure the sum of blocks 1, 2 and 3 (which we refer to as the fulfilment cash flows) and the remaining amount of the CSM at each reporting date. The amounts typically change over time, in particular when expectations about future mortality and interest rates are updated. We distinguish four different factors that will lead to a change in the building blocks:

Step 1. Time effect
Over time, both the fulfilment cash flows and the CSM are fully amortized. The amortization profile of both components can be different, leading to a difference in the reserve value.

Step 2. Realized mortality is lower than expected
In our case study, the realized mortality is about 10 per cent lower than expected. This difference is recognized in P&L, leading to a higher profit in the first year. The effect on the fulfilment cash flows and CSM is limited. Consequently, the reserve value will remain roughly the same.

Step 3. Update of mortality assumptions
Updates of the mortality assumptions affect the fulfilment cash flows, which is simultaneously recognized in the CSM. The offset between the fulfilment cash flows and the CSM will lead to a very limited impact on the reserve value. In this case study, the update of the life table results in higher expected mortality and increased future cash outflows.

Step 4. Decrease in interest rates
Updates of the interest rate curve result in a change in the fulfilment cash flows. This change is not offset in the CSM, but is recognized in the other comprehensive income. Therefore a decrease in the discount curve will result in a significant change in the insurance liability. Our case study assumes a decrease in interest rates from 2 per cent to 1 per cent. As a result, the fulfilment cash flows increase, which is immediately reflected by an increase in the reserve value.

The impact of each step on the reserve value and underlying blocks is illustrated below.

Onwards

The policy will evolve over time as expected, meaning that mortality will be realized as expected and discount rates do not change anymore. The reserve value and P&L over time will evolve as illustrated below.

The profit gradually decreases over time in line with the insurance coverage (i.e. outstanding notional of the mortgage). The relatively high profit in 2016 is (mainly) the result of the realized mortality that was lower than expected (step 2 described above).

As described before, under the full retrospective application, the insurer would be required to go all the way back to the initial recognition to measure the CSM and all consecutive changes. This would require insurers to deep-dive back into their policy administration systems. This has been acknowledged by the IASB by allowing insurers to implement the standards three years after final publication. Insurers will have to undertake a huge amount of operational effort and have already started with their impact analyses. In particular, the risk adjustment seems a challenging topic that requires an understanding of the capital models of the insurer.

Zanders can support in these qualitative analyses and can rely on its past experience with the implementation of Solvency II.