Simulation-based capital models: testing, justifying and communicating choices. A report from the life aggregation and simulation techniques working party

Abstract

The development of an economic capital model requires a decision to be made regarding how to aggregate capital requirements for the individual risk factors while taking into account the effects of diversification. Under the Individual Capital Adequacy Standards framework, UK life insurers have commonly adopted a correlation matrix approach due to its simplicity and ease in communication to the stakeholders involved, adjusting the result, where appropriate, to allow for non-linear interactions. The regulatory requirements of Solvency II have been one of the principal drivers leading to an increased use of more sophisticated aggregation techniques in economic capital models. This paper focusses on a simulation-based approach to the aggregation of capital requirements using copulas and proxy models. It describes the practical challenges in parameterising a copula including how allowance may be made for tail dependence. It also covers the challenges associated with fitting and validating a proxy model. In particular, the paper outlines how insurers could test, communicate and justify the choices made through the use of some examples.

Eliminating proxy errors from capital estimates by targeted exact computation

“…Within the life insurance industry, it is common practice to replace the asset and liability functions of risk factors with simpler and faster-to-calculate approximations called proxy models or simply "proxies" (Robinson & Elliott, 2014). Androschuck et al (2017) discuss several approximation techniques that have been motivated by their practical usefulness, including curve fitting, replicating portfolios, and Least Squares Monte Carlo.…”

“…The main challenge in the introduction and use of proxy models is in demonstrating that they reflect the loss distribution and the capital requirements accurately. Androschuck et al (2017) discuss that this is a design, validation and communication challenge. They highlight the importance of resolving whether fitting errors resulting from the use of proxy models are material and the importance of making suitable adjustments to mitigate the effects of these errors in the capital modelling.…”

“…Proxy design within life insurance capital applications is discussed in Caroll & Hursey (2011), Hursey (2012), and Hursey et al (2014. Androschuck et al (2017) suggest during design and validation to consider, amongst other measures, the maximum absolute error amongst in and out-of-sample testing across the whole distribution. Under this approach, prudent choices of error bounds are larger than the maximum error observed.…”

Selecting Bivariate Copula Models Using Image Recognition

“…A further property of bivariate copulas relates to the extent that observations are concentrated in the four corners of the unit box, even when correlation is low, leading to spider-like pattern. This property, which distinguishes, for example, a t from a Gaussian copula model, is termed arachnitude in Shaw et al (2010), see also Androschuck et al (2017), Genest et al (2019. We measure arachnitude in the way proposed by Shaw et al (2010), that is, as…”

Copula model selection using image recognition

“…A further property of bivariate copulas relates to the extent that observations are concentrated in the four corners of the unit box, even when correlation is low, leading to spider-like pattern. This property, which distinguishes, e.g., a t from a Gaussian copula model, is termed arachnitude in Shaw et al (2010), see also Androschuck et al (2017), Genest et al (2019. We measure arachnitude in the way proposed by Shaw et al (2010), that is, as…”