A common problem in capital modelling involves dealing with volatility assumptions that are inconsistent with the exposure assumptions from which they were originally derived, for example when rolling parameters forward from year to year, due to timing constraints in the capital modelling process, or when performing sensitivity or scenario testing. To obtain meaningful results from modelled output, it is important to use parameters that reflect the business being modelled as accurately as possible. The purpose of this session is to outline a simple formula that capital modellers can use to adjust volatility parameters based on changes in volume. We will show that, based on historical data, the relationship between reserve volume and volatility of reserve movements is well described by a power law formula. The data suggest that suitable values for the exponent parameter fall in the range 0.12 to 0.31, and we suggest 0.22 as a suitable value for a typical use case. In addition, we note that benchmark survey data collected indicates that capital modelling practitioners typically make less allowance for the sensitivity of volatility to volume than is indicated by historical data. Volumes larger than around USD $50 million may therefore have CoVs that are overstated, and volumes smaller than this may have CoVs that are understated.

Speakers Neil Gedalla FIA, Principal, LCP Adam Smylie AIA, Associate Consultant, LCP Jade Lagrue AIA, Associate Consultant, LCP