# Definition of SCR and SF Model

Discussion in 'SA3' started by vidhya36, May 22, 2020.

1. ### vidhya36Very Active Member

SCR definition is calibrated to the Value at Risk of Basic Own Funds at 99.5% confidence level over a one-year time horizon.

How do I verify this definition in the Standard Formula Model? I do see certain Risk Parameters flowing in for modules such as P&R and CAT modules. But had little luck in understanding the intuition behind certain multipliers. For example, the Premium and Reserve Risk module uses a multiplier of 3. Why?

Can somebody guide me how the calculation of SCR as per the SF model ties up to the definition we have above, please. I understand we have various modules of Risk charge calculations coming through together aggregated using a prescribed correlation coefficients which utilizes the BSCR formula to flow towards the final aggregated figure. Why Square root? What's the intuition behind taking a square-root of the components and multiplying with a correlation coefficient? These are some of the queries that's currently surfacing my mind.

Any direction would be great.

Thanks
KV

Duc Thinh Vu likes this.
2. Hi Vidhya36,

General comment: my advice would be to develop the intuition behind the concepts underlying the standard formula. The SF is designed to capture the average risk profile of firms / jurisdictions bound by Solvency II. The final calibrations / approach will almost certainly have had a political overlay. In other words, the 'intuition' at times could have been "change [x] or I won't support the overall package" . You may find the final CEIOPs calibration paper: https://www.eiopa.europa.eu/mwg-int...zZjg0U9SlG_SgiuT7fvkThULidFMpxmFBVNbjvUIY,&dl a useful resource.

Premium & Reserve multiplier: The SF appears to be assuming that the underlying P&R distribution is lognormal. Multiplying the standard deviation by 3 is approximately equivalent to a 99.5% VaR. See page 188 of the attached link.

Use of square root: The 'intuition' is akin to why you'd take the square root of the sum of covariances between two or more securities to work out the portfolio standard deviation. Variance is a 'squared' unit of measurement. Taking the square root gives the standard deviation: and is in the same unit of measurement that the capital requirement is measured in.

Hope that helps.

vidhya36 likes this.
3. ### vidhya36Very Active Member

Thanks a lot for the direction, mugono, can you share the CEIOPS DOC number for the paper, please. The link is breaking. They migrated the website, I believe.

4. CEIOPS-SEC-40-10.

The paper is titled: Solvency 2 calibration paper and was published on 15 April 2010

vidhya36 likes this.
5. ### vidhya36Very Active Member

Thank you, mugono.