Solutions for Life Insights banner

Alongside the introduction of the Solvency II capital regime regulators are increasingly interested in the solvency position of insurance companies looking to realise significant diversification benefits through merger or acquisition. This is of particular relevance where the transaction involves one or two firms which have or are seeking internal model approval, where insurers are looking to retain the full diversification benefit modelled by their internal model post transaction.

In 2016 Willis Towers Watson was engaged to advise two UK insurers in matters relating to a merger of their two businesses, recognising that our unique combination of M&A and reconstruction experience, deep industry capital and internal model technical expertise, and modelling capability would make us ideal advisors. As part of the engagement, Willis Towers Watson was asked to model the capital position of the combined business and in particular analyse the effects of diversification benefits arising from the merger, and this aspect is described below.


The modelling needed to satisfy the following requirements:

  1. Results were needed quickly. To help the two boards understand any showstoppers to the merger, initial results were required within one month after project inception.
  2. The model needed to be flexible to consider the various business structures proposed for the merged company.
  3. To fully realise diversification benefits the model needed to consider a joint and consistent set of risks affecting both companies, but also consider that risks arise for and affect the two businesses in different ways.
  4. The results needed to be consistent with those produced by models already in place at both companies.
  5. The model needed to produce stress tests and updates, to aid understanding of the resilience of the combined structure under stresses and to roll forward or project capital positions into future times.

A model of the joint business was created within Willis Towers Watson’s economic capital model, RiskAgility EC. The model takes a stochastic approach to the modelling of capital requirements, based on a joint universe of risks affecting the would-be merged entity. In this way, capital requirements could be derived from consistently generated scenarios representing the “states of the world” which would affect the joint business.

Faced with a tight deadline and a wide variety of what-ifs to consider, the flexibility and modularity of RiskAgility EC proved to be the ideal solution.


The process undertaken to construct the model and produce results was as follows:

  1. We undertook analysis to understand the risks affecting the two businesses. Wherever possible, risk factors consistent between the two entities were mapped to each other, (e.g. market risks such as equity and property returns), but we also recognised that some risks are unique to each business, and therefore should not be combined (e.g. where mortality or expense experience may be different).
  2. We built the structure of the business in the model at a granular level, in recognition of potentially having to remodel the structure of the entities if the proposed structure were to change.
  3. We chose calibrations to model how the risks evolve over the model’s time horizon. This included the marginal distributions of the risks, as well as correlations imposing joint movements of the risks together. The two companies naturally had different views as to the behaviour of the risks affecting both entities and in some cases calibration benchmarking presented a third view. A reconciliation process was carried out to understand the most appropriate calibration to take in each case.
  4. We constructed proxy models used to estimate the joint entity’s losses as a function of how the risks have evolved. One of the companies was already using a proxy model approach to the modelling of capital requirements and these were transferred directly to the joint model. The other company had used a replicating portfolio approach to model a component of its business, and for this component we constructed an empirical proxy model directly using the outputs of the replicating portfolio.
  5. RiskAgility EC was set to generate a large number (2 million) of joint states of the world in which the merged company would operate. In each state of the world, the proxy models were used to approximate the company’s balance sheet positions at a granular level. Losses were then aggregated across different levels within the business, and capital requirements were produced from the aggregated losses. Because the model’s structure was flexible, we were able to generate a number of reports which showed capital requirements at different levels and with different aggregation criteria.
  6. We were able to reconcile the capital requirements of the two individual entities with results which had already been produced by the companies’ own models. The capital requirement at the group level within the model showed us how much diversification benefit would be obtained through the merger.
  7. Using the model which had been built we were able to undertake a series of further analyses to help both clients understand how the diversification benefits would arise in the joint entity.


Faced with a tight deadline and a wide variety of what-ifs to consider, the flexibility and modularity of RiskAgility EC proved to be the ideal solution – providing a flexible and fast platform to build a joint group capital model where assumptions and structures could be changed quickly. Within just one month we were able to produce the results required to inform a go/ no go decision. The availability of existing inputs from both companies to feed into the model, plus data from our annual Risk Collaboration Survey for assumption setting, also played a key role in delivering the final results in a short timeframe