Difference betwixt Diversified in addition to Undiversified SCR – Solvency II
Before reading this article, kindly read the next 2 articles to brand the virtually feel out of it:
– Solvency II SCR is a Value at Risk measure, it tin post away travel calculated via Standard formula too equally via Internal Model
– VaR is calculated for each constituent risk, hence the diversified SCR is determined amongst reference to the correlation betwixt each component. This is done yesteryear taking the total over all risks of the foursquare root of the production of their SCRs multiplied yesteryear the correlation coefficient
– Broadly speaking, suppose yous are a grouping Insurer amongst 4 entities across the public named A,B,C in addition to D
– All 4 of them bring SCR has $100 each. Then at Group Level your SCR is definitely less than $400 because nosotros bring to let for diversification via correlation matrices.
– Diversification occurs wherever the risks are non perfectly correlated. (Hedging would lead house where they were negatively correlated.) In EIOPA’s instance they bring defined a correlation matrix for each opportunity type.
– A numerical illustration mightiness help, tell a fellowship writes solely term insurance work organization in addition to invests solely inward equity (with no default opportunity for simplicity). Let their marketplace opportunity constituent of SCR, SCR_m, travel $20m in addition to their Life constituent of SCR, SCR_L, travel $10m (which would bring been calculated yesteryear the company). The correlation betwixt these 2 risks is defined yesteryear EIOPA to travel 0.25.
The basic SCR earlier diversification is $30m i.e. 20+10
The diversified SCR is calculated equally the total over all (both) risks equally follows:
SCR = SQRT( Corr_m,m * SCR_m * SCR_m + Corr_m,L * SCR_m * SCR_L
+ Corr_L,m * SCR_L * SCR_m + Corr_L,L * SCR_L * SCR_L )
= SQRT( 1 * twenty * twenty + 0.25 * twenty * x + 0.25 * x * twenty + 1 * x * x )
– So at that topographic point is a diversification create goodness of $5.5m equally the diversified SCR is that much lower than the undiversified SCR.
Follow us on Linkedin: Kamal Sardana