PwC Actuarial Services Newsletter Issue 3 Key points in brief: • Topic 1: Help! We are getting older… • Topic 2: ALM in a solvency driven world • Topic 3: Model validation – Being your own toughest critic

Topic 1: Help! We are getting older… We are getting older. However, we do not know exactly how much older. The impact of an update in mortality projections on life insurers and pension funds may be dramatic. Insurers and pension funds are seeking ways to mitigate the impact of new updates in mortality projections on their liabilities. This article provides an introduction to new ways to manage longevity risks.

Insurers and pension funds seek ways to mitigate longevity risks In the past, actuaries and demographers have repeatedly underestimated mortality. As a result, insurers and pension funds were confronted with significant and unexpected increases in liabilities due to updates in mortality projections. Newly developed mortality models are better able to explain historical mortality, and (hopefully) provide more accurate mortality projections. Nevertheless, there is still great uncertainty in the development of mortality: • Medical breakthroughs may cause mortality rates to improve (much) faster than expected; • If bacteria become resistant against antibiotics, mortality rates may improve slower than expected, or they may even deteriorate. To cover unexpected developments in mortality, insurers and pension funds are required to hold risk capital for longevity risk. In addition, there is an increased focus by insurers and pension funds on governance of risks and the risk appetite towards different types of risk. However, there are still many insurers and pension funds that are unaware of the potential impact on their liabilities from new developments in mortality, and how large their longevity exposure is.

An example of required risk capital is the SCR Longevity risk that insurers have to hold under Solvency II. The risk capital requirement based on the Standard Formula is an instantaneous 20% downward shock on mortality.1 As a result, both insurers and pension funds are looking for ways to mitigate longevity risk. In the UK, for example, buy-ins, buy-outs and longevity swaps are used for many pension plans to mitigate the uncertainty in mortality projections and to secure payments to their policyholders. These approaches can be classified as classical reinsurance in which longevity risk is transferred to a counterparty. Another way to reduce the (financial) exposure to longevity risk is through derivatives. In the Netherlands, four longevity derivatives have been closed by life insurers to lower their longevity risk exposure. Longevity reinsurance and derivatives have different characteristics. The remainder of this article will discuss the pros and cons of these two ways to mitigate longevity risk. - Insurers may (after supervisory approval) use an internal model to model the longevity shock. 1

Transfer of longevity risk through reinsurance Though payments from a pension fund or insurer to its policyholders are uncertain, the insurer or pension fund can determine its best estimate for these cash flows. If the insurer wants to get rid of the longevity risk associated with these payments, it can consider an (at-the-money) reinsurance contract. In such a reinsurance contract, the insurer or pension fund agrees to pay a fixed leg that consists of the best estimate projection at inception of the payments plus a risk premium (the fixed leg). In return, the reinsurer will pay the actual payments for the remaining policyholders in the underlying portfolio (the floating leg). This structure is illustrated in Figure 1. The advantage of a reinsurance contract is that the longevity risk of a portfolio is transferred and the related volatility in P&L results is significantly reduced. The (financial) impact of new mortality prognoses will be carried by the reinsurer. The valuation of a reinsurance contract is straightforward, and the structure of the contract is easy to explain. Since benefit payments are reinsured, a reinsurance contract is ideal for a block of pensions that is already in payment. A disadvantage is that reinsurers will only take over uncertainty after a thorough due diligence. Data requirements are stringent, because sufficient years of quality data are needed for the reinsurer to perform due diligence. In addition, if the reinsurance contract is calibrated ‘at-the-money’, the risk premium will be substantial.

Fig. 1 Cash flows in a reinsurance contract

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Reducing longevity exposure using innovative derivatives Several life insurers in the Netherlands have reduced their longevity risk exposure using customized longevity derivatives. These derivate products provide the insurer with a benefit at some future date if mortality rates improve more than expected. The longevity derivatives are inspired by Solvency II regulation. Risk capital needs to be held for a given shock in mortality, but what if an insurer has a product (derivative) that generates a payment in the same shocked scenario?

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Example: Figure 2 shows a (fictitious) payoff structure. At inception of the contract, the insurer determines the distribution of its liabilities (dependent on mortality improvements). Based on this distribution, the insurer determines the often-called attachment point (AP) and detachment point (DP): • IIf the liabilities over a certain period are less than AP, the payoff is zero; • If the liabilities are between AP and DP, the payoff is between zero and the notional; • If the liabilities are above DP, the payoff is equal to the notional. The AP and DP are chosen somewhere between the 50th and the 99.5th percentile to ensure there is a payment in the shocked longevity scenario (in the example above: AP = 11 and DP = 11.5). As a result, the risk capital requirement (SCR) for longevity risk and the risk margin both decrease, thereby improving the solvency ratio of the insurer. A longevity derivative mitigates the effect of a new mortality update: when the liabilities increase as a result of new mortality prognoses, the value of the derivative increases as well. The valuation of such a longevity derivative, however, is complex and the structure is more difficult to understand than a traditional reinsurance contract. Further, the longevity risk is not completely transferred. Only the SCR and risk margin as required under Solvency II decrease. For pension funds there is no ‘regulatory incentive’, and therefore longevity derivatives are unlikely to be of interest for pension funds.

The main advantage of a longevity derivative is that all parameters can be chosen flexibly, and this enables the insurer to decrease the required risk capital for longevity risk at a reasonable price. Further, these derivatives are based on synthetic portfolios, and as a result there are few data requirements. Longevity derivatives provide an innovative way for life insurers to free up risk capital, thus increasing own funds that can be used e.g. to attract new business.

Wrap up Longevity risk can be reduced in several ways. Which type of product fits best for a pension fund or insurer depends on the specific situation. The following questions may help to assess whether or not it is beneficial to consider reinsurance or a derivative to reduce longevity risk: 1. What is your exposure to/ appetite for longevity risk? and is the risk currently within acceptable boundaries; 2. What are the portfolios where you would benefit from mitigating longevity risk? 3. Is the objective to reduce longevity risk and P&L volatility, or to improve the solvency position by lowering regulatory capital requirements? 4. What are you willing to pay to reduce longevity risk? Live longer, reduce risk!

Topic 2: ALM in a solvency driven world Asset liability management (ALM) is to an insurance company what diplomacy is between countries. The goal is to align the asset side with the liability side, or at least to enhance the understanding between the two. This has proven to be a difficult task, with different approaches followed by asset management and risk management.

In the meantime, on the risk management side, various solvency models have been introduced.

Solvency regime calls for a change We have observed that many large insurance companies implicitly have two ALM departments, one on the asset management side and one on the risk side. Asset managers are still prone to use historical data within the CAPM framework to find the optimal strategic asset allocation, whereas risk managers today use an economic scenario generator (ESG) to model the potential future outcomes of the portfolio held, including intricate options and guarantees within the portfolios. There is a mismatch between the techniques used and this impacts insurance business today. The new solvency regimes (Solvency II, SST) have not made the situation easier. One approach we find promising is to base ALM on solvency models, as this is currently the model that captures the specificities of the insurance company best. Some simplifications might be necessary; for example, assuming that insurance risk does not change on a daily basis should not pose any problems. Basically, only market risk changes and thus the modelling can be simplified and optimized. Below we show the new CAPM view that would enable better ALM for insurers.

New modelling techniques The graph below combines two worlds, and provides both a CRO view and a CIO view in an efficient solvency frontier. On the y-axis we have the expected return as calculated using the ESG and our example portfolio of assets (A1, A2) and liabilities (L1, L2). On the x-axis, market risk is calculated using the solvency model. Here, a bond cash flow is modelled with zero coupon bonds (ZCB) and liability cash flows with ZCB with a negative sign. In this way, a replicating portfolio could be modelled simultaneously alongside the assets. Only when combining both assets and liabilities in the calculation can a true ALM be achieved. The assumptions for the forward looking economic scenarios come from asset management. Here, asset management would have the opportunity to tweak the assumptions away from historical averages for internal steering purposes. Hence, these can be tuned to adapt to changes in the economic outlook. This is a crucial assumption as it integrates asset management in the solvency discussion and enables a better strategic view for asset allocation. Also, this would replace the backward-looking CAPM framework. This approach allows the company to investigate any current or potential asset allocation from a risk and return strategy perspective. As shown in the graph, two alternative positions would provide the same or even more return but at a lower risk. This view would also be easily presentable for upper management and could form an integral part of the risk committee meetings. Such a model can be constructed by using the output from the market risk module of any insurance company with an internal model or a model based on economic scenarios. The modelling allows for constraints, thus

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On the asset management side the CAPM framework is the governing approach. ALM is primarily based on the matching of cash flows, perhaps including some sensitivities. The introduction of replicating portfolios, while a fast and pragmatic approach, did not enhance asset management’s understanding of the liabilities, because the assets they use are often synthetic and not available in the market. A Least Square Monte Carlo (LSMC) approach may provide a better solution, however lacks the ease of explanation.

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avoiding an undiversified portfolio. Also, since liabilities are included, an optimal matching will be one of the outcomes of the model. Here, a replicating portfolio or LSMC can be used. The techniques needed are standard optimisation methods with constraints, which are readily available in most statistical software packages such as R.

Conclusion Following the market turmoil since the beginning of the financial crisis, a need for a bilateral understanding of the various regimes such as IFRS, Statutory and Solvency has increased. With the proposed technique, two diverse worlds are combined and the discussions between asset and risk management enhanced. It also provides an understanding of the impact on risk and return of the current asset allocation, allowing a comparison of different options and the calculation of sensitivities. This provides a stronger foundation for management decisions and through alignment, helps reduce the number of competing metrics present in the industry. Going forward this could be the starting point for any ALM discussion and market risk reporting.

Topic 3: Model validation – Being your own toughest critic Every model is only as good as its validation. More regulatory requirements and an increased risk awareness drive the need for high-quality model results and thus more thorough model validation. The relevance of models in insurance companies is growing, not just because of new dimensions of data and modelling performance capabilities, but also the tendency towards analytics-driven decision making. Model validation needs to be seen as a useful exercise to gain a better understanding of models throughout the company as well as a chance to strengthen one’s model through honest and critical feedback. A number of approaches for the various potential aspects of model validation have been established. Both the tools and the mindset with which insurance companies conduct validations need to be challenged and monitored. An important key in responding to the challenges is to find the balance between thoroughness and efficiency. In this article, we have limited our scope to regulatory model validation to address the most pressing issues faced by our clients today.

Regulatory perspective According to Article 264 of the Delegated Acts, insurers need to validate the calculation of technical provisions at least once a year. The article stipulates the aspects of the calculations that are to be assessed during the validation exercise, including data, groupings, approximations, assumptions, methods and level of the technical provisions. In addition, the regulation requires assessing the impact of changes in the assumptions on future management actions.

EIOPA and local regulators make further specifications on the coordination and the execution of model validation2. The question of who needs to carry out the validations remains a decision by the insurance company, while ensuring that conflicts of interest are avoided and the independence of validations is upheld. The Actuarial Function does not need carry out the validations itself, but it needs to assess the validations conducted. The Actuarial Function ensures that the validation approaches cover both quantitative and qualitative aspects (including controls, documentation, and the interpretation and communication of results), are appropriate for the characteristics of the insurance liabilities. The approaches must also be proportionate considering the significance of the impact of assumptions, approximations, and methodologies on the value of technical provisions. The Actuarial Function also defines and follows a regular and dynamic process in which it periodically refines validation approaches and makes recommendations on changes to the model based on past experience. - EIOPA-BoS-14/166 EN: Guidelines on the valuation of technical provisions; ‚Auslegungs­ entscheidung zur versicherungsmathematischen Funktion in Versicherungsunternehmen’, BaFin, 21 December 2015 2

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• What models are used and what are their limitations? • Are the models verified, documented and tested regularly? • How is the confidence and reliability of the models’ results ensured?

Models Aspects of validation

• Which data is used and where does it come from? • Are data limitations documented and considered? Data • Do the data sets correspond to the model needs?

Assumptions

• What assumptions underlie and are they transparent? • Are the assumptions derived and applied appropriately?

Scope of the validation The validation should focus on the three main categories: Data, Assumptions and Models. Each comes with a different set of questions (see graphic). While these categories need to be dealt with individually, the interdependencies between them should not be ignored. How valuable are strong data sets that are not leveraged to their full capacity? How sound are assumptions derived from data that we don’t trust completely? How good is a model that relies on assumptions that are not in sync with what the models tries to achieve? Assessing models in a holistic way can help to address both individual issues and interdependencies. Insurance companies have to encourage and ensure that models are built on an appropriate functional foundation and with transparent goal setting. Powerful and reliable models use data, assumptions and methods in coordinated fashion. They also allow for a controlled and comprehensive validation process that includes documentation tests and controls.

Approaches to assess actuarial models The main goal of the model validation exercise is to confirm the appropriateness, completeness and accuracy of the methods and models used. Models need to be assessed against product and business characteristics as well as regulatory requirements. Finding the right model validation approach means including both qualitative and quantitative methods. A classic qualitative approach is the review of the model documentation. This should allow for explanations of the underlying assumptions and situations for which the model reaches its limits (typically scenario analysis). The checks for model completeness include an assessment whether all relevant product features, all cash in- and

out-flows, and all material risks associated with the products are depicted in their entirety; the rationale for decisions not to model certain risks should be documented. Incorporating benchmarks of methods and assumptions into the validation framework provides additional confidence through comparison with the market. Furthermore, an estimation whether management actions and policyholder behaviour are modelled properly. A number of quantitative approaches have proven effective and may provide information regarding the significance, reliability, comprehensibility, robustness or sensitivity of the model: • Back-testing and reverse stress testing approaches use historic input data to compare the model output with actual historic results. • Statistical tests provide quantitative indications on the goodness of fit, although require sufficient available data. • Automated tests for checks of completeness, consistency and credibility are available and recommended. • Applying the model on an individual contract level can indicate whether products are depicted reasonably. • Stress and scenario analyses to assess model robustness and sensitivity are also common practice. Effective risk management requires an ability to step back from model details to ask bigger questions related to common model risks: • Is the right model applied? (conceptual risk) • Is the model implemented and used correctly? (implementation risk) • Are the results meaningful? (output risk) • Are the results complete and correct? (disclosure risk).

Industry view The insurance industry has begun to address the topic of validation in the recent years. Working with our clients on these or adjacent topics, the experience suggests a key starting point to developing an effective and efficient model validation framework is beginning with a model inventory and categorisation. A comprehensive inventory ensures a clear picture of the component models needed to produce results. The categorisation requires an assessment of each model’s risk be made using expert judgement. Models may be high risk because of the relative contribution of their output to the final results but also due to uncertainty of assumptions, quality of data, or complexity and risk of error. Solvency II regulation sets no explicit materiality rules, but the principle of proportionality suggests that approaches used should reflect the nature, scale and complexity of the business being modelled. Defining one’s own materiality provides the basis for determining the appropriate scope and depth of validation activities and requires a thorough examination of risk appetite, tolerance for variability, and assessment of capital capacity. Insurers that take the time to develop a vision for proportionality early are likely to reap the benefits of clear and efficient validations in the long run.

Further we note three key challenge areas all companies face when establishing model validation processes: 1. Resources and independence 2. Breadth of technical actuarial knowledge 3. Validation skills Resources are an issue in two ways. First, few companies have the capacity to free up resources from existing staff to work on model validation in addition to daily business. In addition to knowledgeable actuaries, model validation requires individuals who consider IT processes, governance and control procedures. For the actuaries, those performing the validation must also be independent of the models being tested. While hiring additional resources can address these issues, most companies are working to control costs and the validation work may not need full-time employees. Even if the number of resources has been addressed, the next challenge is ensuring that validation resources have the technical skills to adequately challenge the various models. While the experience of a certain topic will certainly vary, sufficient core subject matter knowledge and experience drives effective challenge and review.

Finally, validation itself is a learned skill. While technical capability is one requirement, understanding review techniques and principles drive superior results. In addition to actuarial methods a challenge to validation scope, documentation quality, communication and processes are needed. Certainly these skills can be learned, but are not a given in today’s organisations. Each of these points tends to become more critical for smaller companies, especially since they often have less experience with complex models and yet have the same subject matter areas to consider (e.g. IFRS4, Embedded Value, or ALM). Regardless of the size of the insurance company, it is critical to approach these topics head-on. Model validation is more than a necessary chore, as it can spark valuable communication between departments to challenge views, as well as to sharpen and further develop modelling capabilities. By applying the four-eye principle it establishes clear responsibilities and helps to avoid errors or restatements, increasing the confidence stakeholders have in the models. Ultimately, model validation provides a higher level of assurance in the insurance industry by limiting a source of controllable uncertainty and allowing companies to manage the unavoidable uncertainties.

Actuarial Services – Your Contacts Switzerland

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Thomas Hull Tel: +41 58 792 2510 [email protected]

Dr. Clemens Frey Tel: +49 89 579 06236 [email protected]

Jan-HuugLobregt Tel: +31 88 792 7463 [email protected]

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