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This article provides an overview of how internal models are used to calculate the Solvency Capital Requirement and the advantages and disadvantages of adopting this approach. It also highlights the use test, proxy techniques, and the development of full or partial internal models.

Under Solvency II companies can either use the Standard Formula or, if approved by their supervisor, their firm’s own internal model to calculate the Solvency Capital Requirement (SCR). A recent Solvency II readiness survey carried out by Moody’s Analytics confirmed that most large insurers in Europe have opted for a partial or full internal model.1 Even among smaller firms, the survey showed that 30% of the firms who currently use the Standard Formula are planning to upgrade to a partial or full internal model within the next three years.

The benefits of internal models

The survey results suggest that firms are mindful of the benefits of adopting an internal model, as they can use their own risk management structure and their own calibrations for the risk factors. The improvement in risk and capital management, which should be realized from implementing an internal model, is deemed to outweigh the significant effort in building and maintaining one. The internal model route is particularly advantageous for firms that already have an established enterprise risk management (ERM) system in place. For some insurers, adopting the Standard Formula is not a viable option. Using the Standard Formula would not be justifiable or defendable and, in doing so, they would risk a capital add-on (see articles 37 and 119 of the directive). By construction, an internal model should more accurately capture the risk profile of the entity. It also provides an opportunity for firms to take credit for any risk mitigation strategies that they have implemented (on the proviso that these are approved and documented).2

The burdens of internal models

A significant burden attached to internal models is the requirement to receive approval from the supervisor. The Solvency II Directive sets out the requirements that must be met, which include standards relating to statistical quality, calibration, validation, and documentation. Furthermore, there is the much talked about use test, which requires firms to demonstrate that their internal model is widely used in the business and plays an important role in the decision-making process. Interestingly, in the Moody’s Analytics Solvency II survey, some firms opting for the Standard Formula cited the use test requirement as a barrier to choosing the internal model route.

Developing advanced internal models

The delays to Solvency II have provided additional time for firms to develop more advanced internal models. The core of an internal model is the ability to use an insurer’s internal risk management structure and systems, and their own risk models and calibrations to determine the stresses and evaluate the SCR. However, internal models often now go further than that. The previously daunting challenge of producing a full probability distribution for economic capital is now achievable. Article 121 of the directive covering the statistical quality standards makes specific reference to the probability distribution forecast.3 Although no calculation method is specified, proxy techniques have been widely adopted. Proxy models (sometimes referred to as lite models) are an approximation to the actuarial cash flow model and techniques used in the industry, and include curve fitting and Least-Squares Monte Carlo (LSMC). Proxy functions provide a means of quickly valuing the assets and liabilities across the entire distribution. Larger firms are implementing a full Monte Carlo simulation-based internal model, making use of proxy models.

Proxy models: evaluating the SCR and beyond

The benefits of the simulation-based internal model extend beyond the primary objective of reading off the 99.5th percentile result to give the SCR – having a full distribution enables more transparent decision-making. Furthermore, proxy models can be used in the day-to-day management of the business, which helps with the fulfillment of the use test. The deferment of Solvency II has given insurers time to assess the quality of both their risk scenario generator, which defines the risk distributions and the quality of fit of the proxy models, and to implement improvements. Insurers still have to contend with the computational demands of running internal models and are looking to identify the optimal approach for a given computational budget. With this in mind, the technique of Least-Squares Monte Carlo (LSMC) is increasing in popularity as it provides a more efficient alternative to curve fitting when determining the proxy functions.

A simulation-based internal model, as described previously, contains numerous elements, including key technical components such as the marginal risk factor models, the proxy functions, and the dependency structure between risk factors. This approach overcomes the limitations of the simplistic “stress and correlate” aggregation approach found in the Standard Formula. In an internal model, the insurer has the scope to choose the form of the dependency structure and to apply company-specific aggregation rules. Under the Monte Carlo approach, this enables the capture of any non-linearity in the business and to more accurately model tail dependency.

Partial internal models

Under a full internal model approach, all risks are evaluated using the firm’s economic capital framework. However, not all large European insurers are going for a full internal model – indeed the Moody’s Analytics survey suggested an equal split between those going for a full internal model and those applying for a partial model. There are a wide variety of possible approaches to a partial internal model. The model may be “partial” in the sense that the internal model is only adopted for specific risk modules. For example, a Monte Carlo simulation-based approach may only be applied for the market risks with underwriting risks quantified using the Standard Formula stresses.

Alternatively, the “partial” may refer to when the internal model only applies to specified lines of business. The aggregation approach needs to be carefully considered when determining how to integrate the capital requirement for the internal model components with those calculated using the Standard Formula.

Interestingly, in the Moody’s Analytics Solvency II survey, some firms opting for the Standard Formula cited the use test requirement as a barrier to choosing the internal model route.

Internal model approval

Solvency II is scheduled to come into force on January 1, 2016. Companies intending to use an internal model will now be well established in the internal model approval process (IMAP) with their supervisor. The final compromise text of the Omnibus II details a phasing-in approach where supervisors will have the power to approve internal models from April 1, 2015. In the UK, an enhancement to the existing Individual Capital Assessment, known as ICA+, allows firms to use their Solvency II models as part of the ICA submission, which forms part of the current regulatory regime. Although ICA+ is optional, it provides a practical solution whereby the UK regulator, the Prudential Regulation Authority (PRA), combines their review of the ICA with the IMAP. For those firms opting to go down this route, ICA+ appears to be an essential part of IMAP. The PRA has emphasized the importance of firms keeping to their IMAP submission schedule and have made it clear that they will adopt a robust approach to internal model approval. In his speech on December 12, 2013, Julian Adams, Deputy Head of the PRA, stated that “models must meet the required tests and standards, capture all quantifiable risks, and deliver prudentially sound outcomes in a range of scenarios and over time”.4 The PRA expects firms to have contingency plans in place in case their model is not approved.

The delayed implementation of Solvency II (and to justify the significant costs spent on implementation) does offer the advantage that, when it does go live, insurers should have more advanced internal models that aim to more accurately quantify the risks they face. Another equally important consequence of the delay is that it has given time for a more thorough model validation to be carried out and, crucially, for senior management and the board to become more familiar with their internal models and the benefits which they can bring. With the complexity of creating and implementing internal models, this additional time may prove beneficial to insurance firms working toward meeting these regulations.

This article has highlighted the benefits and limitations of adopting Solvency II internal models. Although the first priority for many firms is to attain compliance, those firms that fully embrace the proper development of an internal model are more likely to obtain commercial and operational benefits from their investment. The improvement in risk and capital management realized from implementing an internal model seems to outweigh the significant effort in building and maintaining one.


1 Solvency II – A Field of Missed Opportunities, a survey by Moody’s Analytics. Of those firms surveyed, 86% of Tier 1 firms have opted for an internal model.

2 Directive of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (SOLVENCY II), February 2008.

3 Directive of the European Parliament and of the Council on the taking-up and pursuit of the business of Insurance and Reinsurance (SOLVENCY II), February 2008.

4 Julian Adams, Deputy Head of the Prudential Regulation Authority and Executive Director of Insurance, PRA Solvency II industry briefing, London, Solvency II – a turning point, December 12, 2013.

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