Under the European Union’s Solvency II regulations, insurance firms are required to use a one-year VaR (Value at Risk) approach. This involves a one-year projection of the balance sheet and requires sufficient capital to be solvent in 99.5% of outcomes. The Solvency II Internal Model risk calibrations require annual changes in market indices/term structure/transitions for the estimation of the risk distribution for each of the Internal Model risk drivers.

Transition and default risk are typically modelled using transition matrices. To model this risk requires a model of transition matrices and how these can change from year to year. In this paper, four such models have been investigated and compared to the raw data they are calibrated to. The models investigated are:

• A bootstrapping approach – sampling from an historical data set with replacement.

• The Vašíček model was calibrated using the Belkin approach.

• The K-means model – a new non-parametric model produced using the K-means clustering algorithm.

• A two-factor model – a new parametric model, using two factors (instead of a single factor with the Vašíček) to represent each matrix.

The models are compared in several ways:

1. 1. A principal components analysis (PCA) approach that compares how closely the models move compared to the raw data.

2. 2. A backtesting approach that compares how each model’s extreme percentile compares to regulatory backtesting requirements.

3. 3. A commentary on the amount of expert judgement in each model.

4. 4. Model simplicity and breadth of uses are also commented on.

This paper sets out the working party’s view that for a defined benefit pension scheme’s commutation rate the appropriate starting point should be to set it in line with the scheme’s cash equivalent transfer value basis. We recognise that there may be several reasons why an actuary in their advice may deviate from that starting point and we explore these in detail, giving our views on when deviation is and is not justified, noting that many common reasons used such as selection risk are often used without (in our view) adequate justification. We also cover frequency of review – our view is that commutation rates should be reviewed at least every 3 years and actuaries should consider performing a high-level review of commutation rates annually. We suggest that actuaries should consider proposing market-related commutation rates especially in periods of volatile market conditions. In terms of timing, there are good arguments to review commutation terms either following or during a valuation. Finally, we set out some considerations on how actuaries should present their advice, such as clearly setting out all the information required to take key decisions, following up with any actuarial certification in writing (if necessary) and illustrating the impact on members for changing commutation rates.

Fertility, particularly at its current low level in many developed countries and high level in some less developed countries, is a key factor driving demographic, economic, and societal changes at local, national, and global levels. Population ageing due to low fertility and increasing longevity represents one of the most significant global megatrends and risks. Many countries are already experiencing population decline and rapid growth of their elderly populations, with implications for workforce size, economic development, health and pension schemes, and social security arrangements. Actuaries are well known for their work on mortality and morbidity, but they have rarely considered fertility and its proximate determinants, despite their demographic and economic effects. This paper explores key explanations and outcomes of past and projected future fertility trends, and the implications for actuaries and for political and economic decision-makers.

In this paper, we explore potential surplus modelling improvements by investigating how well the available models describe an insurance risk process. To this end, we obtain and analyse a real-life data set that is provided by an anonymous insurer. Based on our analysis, we discover that both the purchasing process and the corresponding claim process have seasonal fluctuations. Some special events, such as public holidays, also have impact on these processes. In the existing literature, the seasonality is often stressed in the claim process, while the cash inflow usually assumes simple forms. We further suggest a possible way of modelling the dependence between these two processes. A preliminary analysis of the impact of these patterns on the surplus process is also conducted. As a result, we propose a surplus process model which utilises a non-homogeneous Poisson process for premium counts and a Cox process for claim counts that reflect the specific features of the data.