Definition of SCR and SF Model

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

  1. vidhya36

    vidhya36 Very 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.

    Duc Thinh Vu likes this.
  2. mugono

    mugono Ton up Member

    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:,&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. vidhya36

    vidhya36 Very 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. mugono

    mugono Ton up Member


    The paper is titled: Solvency 2 calibration paper and was published on 15 April 2010
    vidhya36 likes this.
  5. vidhya36

    vidhya36 Very Active Member

    Thank you, mugono.

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