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Measuring market and credit risk under Solvency II: evaluation of the standard technique versus internal models for stock and bond markets

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Abstract

The 2008–2009 Global Financial Crisis (GFC) has swayed regulators to set forth the Solvency II agreement for determining Solvency Capital Requirement (SCR) for insurance companies. In this paper, we apply novel internal models to investigate whether the latest version of the Solvency II standard model demands sufficient capital charges, both in normal and stressed times, for the different risk categories included in bond and stock portfolios. Because the GFC has shown that extreme events on the tail of probability distributions can occur quite often, our empirical findings indicate that the magnitude of the equity risk using the GJR–EVT–Copula method requires insurers to keep more SCR for stock portfolios than the Solvency II standard model. In the case of a bond portfolio, we conclude that the Solvency II standard model requires approximately the same SCR as our internal model for the higher quality and longer maturity bonds, whereas the standard model overestimates SCR for the lower quality and shorter maturity bonds. At the same time, the standard model underestimates interest-rate risk and overestimates spread risk. Overall, the discrepancies in the estimated SCRs between the Solvency II standard technique and our internal models increase as the level of the risks rise for both stock and bond markets. Our empirical results are in line with other competing internal modeling techniques regarding stock market investment and bond portfolios with the higher quality and longer maturity bonds, while for the lower quality and shorter maturity bonds, the results contradict other modeling procedures. The obtained empirical results are interesting in terms of theory and practical applications and have important implication for compliance with the Solvency II capital requirements. Likewise, it can be of interest to insurance regulators, policymakers, actuaries, and researchers within the field of insurance and risk management.

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(Source: QIS5 (Fifth Quantitative Impact Studies document [19]))

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Notes

  1. GJR stands for the Glosten–Jagannathan–Runkle model (for further details, see [24], and EVT denotes Extreme Value Theory.

  2. Financial time series have typical non-normal properties, such as leptokurtosis, fat tails, volatility clustering and leverage effect. In addition, calculating regulatory capital for a portfolio requires modeling the tail of the joint distribution. To that end, it is possible to describe the time series effectively using the GJR–GARCH–EVT–Copula technique, and for this reason, this paper applies the GEC approach to fit the portfolio return series. On the other hand, a bond portfolio has different types of risks, and as indicated in the empirical literature the technique of Lando and Mortensen [32] addresses those risks.

  3. It is important to emphasize that counterparty default risk is implicitly addressed in both the Solvency II standard model and our robust internal models.

  4. The percentage of interest and principal that a firm is paid back, according to seniority, is called the recovery rate. Thus, bonds’ recovery rate is considered to assess counterparty default risk.

  5. BRICS is the acronym for the association of five major emerging countries: Brazil, Russia, India, China, and South Africa.

  6. The coupon payment frequency for all corporate bonds is annual.

  7. Credit ratings are on the scale of Standard and Poor’s (S&P).

  8. The semi-deviation \(\sqrt {\frac{{\mathop \sum \nolimits_{r < mean}^{n} \left( {mean - r_{t} } \right)^{2} }}{n}}\) provides an effective measure of the downside risk, which evaluates the dispersion for the values of a dataset below the mean.

  9. The parametric VaR is also known as the linear VaR. This VaR approach is parametric in the sense that it assumes that the probability distribution is normal; and thus it requires the calculation of the variance and covariance parameters. For example, assume there is a portfolio that consists of two stocks. The VaR for that portfolio is calculated as follows: \(R = V_{p} \times Z_{\alpha } \times \sigma_{p}\), where, Vp, Zα, σp are the amount of invested capital, the inverse of the standard normal cumulative distribution and the standard deviation of portfolio respectively. Next, the standard deviation of the portfolio is calculated as \(\sigma_{p} = \sqrt {w_{1}^{2} \sigma_{1}^{2} + w_{2}^{2} \sigma_{2}^{2} + 2w_{1} w_{2} \sigma_{1} \sigma_{2} \rho }\), where, ρ, σ2 and w are the Pearson correlation coefficient, the variance and the corresponding weights of investment in each individual stock.

  10. \(SCR_{b,int}^{IM}\), \(SCR_{b, sp}^{IM}\) and \(SCR_{b}^{IM}\) stand for the Solvency Capital Requirement derived from the internal model for interest-rate risk, spread risk and the bond total risk respectively.

  11. \(SCR_{b,int}^{II}\), \(SCR_{b, sp}^{II}\) and \(SCR_{b}^{II}\) stand for the Solvency Capital Requirement derived from the standard model for interest-rate risk, spread risk and the bond total risk respectively.

  12. It is important to note that counterparty default risk is implicitly addressed in both the Solvency II standard model and our proposed internal models.

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Authors and Affiliations

  1. AAICCo (Arzeshpardaz, Aryan Investment Consultancy Co.), Tehran, Iran

    Saeed Asadi

  2. Tarbiat Modares University, Tehran, Iran

    Saeed Asadi

  3. Tecnologico de Monterrey, EGADE Business School, Santa Fe Campus, Av. Carlos Lazo 100, Col. Santa Fe, Del. Alvaro Obregón, C.P. 01389, Mexico City, Mexico

    Mazin A. M. Al Janabi

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Asadi, S., Al Janabi, M.A.M. Measuring market and credit risk under Solvency II: evaluation of the standard technique versus internal models for stock and bond markets. Eur. Actuar. J. 10, 425–456 (2020). https://doi.org/10.1007/s13385-020-00235-0

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