# Macroprudential Insurance Regulation: A Swiss Case Study

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## Abstract

**:**

## 1. Introduction

**Literature review.**The macroprudential perspective is closely related to the concept of systemic risk; for an overview of the existing literature on systemic risk in insurance we refer to [6]. The latter reference analyzes the ability of the insurance industry to disrupt the financial market. It is indeed observed that insurers may contribute to the instability of the financial sector, especially through their noncore activities, see [7,8,9,10,11]. These observations are based on systemic risk measures that allow for the study of the interconnectedness between insurers and other financial institutions, see [12,13,14]. Such measures were also applied to parts of the European insurance industry, see [15]. Network analysis of the EU insurance sector is considered in [16], and its interconnectedness with the European banking sector analyzed in [17]. For further mathematical analysis of systemic risk in financial networks we refer to [18]. For a discussion on macroprudential regulatory frameworks we refer to [19,20,21].

**Outline of this paper.**In the next section we formally introduce the market, in which we describe insurance companies and their balance sheets. Section 3 and Section 4 discuss the changes in the balance sheet positions when different risk factors are stressed. In Section 5 we provide a case study based on data from the Swiss private insurance market. We introduce an insurance market that has features similar to those of the Swiss market, see Section 5 for details. Then, we stress this market with different scenarios and analyze their impacts on the balance sheet positions of the insurance companies.

## 2. Insurance Market and Balance Sheet Structure

#### 2.1. Insurance and Financial Market

- ${\mathcal{V}}_{i}\left({a}_{j}\right)$ denotes the (market-consistent) value of company i’s investment into asset class ${a}_{j}$, $j=\phantom{\rule{3.33333pt}{0ex}}1,\dots ,J$.
- ${\mathcal{V}}_{i}\left({l}_{k}\right)$ denotes the total liabilities of company i in liability class ${l}_{k}$, $k=1,\dots ,K$. This value is before (gross of) reinsurance.
- ${\mathcal{V}}_{i}\left(r\right)$ denotes the total reinsured part of the gross liabilities of company i. Hence, the net liabilities faced by company i is given by ${\sum}_{k=1}^{K}{\mathcal{V}}_{i}\left({l}_{k}\right)-{\mathcal{V}}_{i}\left(r\right)$.
- ${\mathcal{V}}_{i}\left(e\right)={\sum}_{j=1}^{J}{\mathcal{V}}_{i}\left({a}_{j}\right)-{\sum}_{k=1}^{K}{\mathcal{V}}_{i}\left({l}_{k}\right)+{\mathcal{V}}_{i}\left(r\right)$ is the resulting own equity of company i that reflects its risk bearing capital.

#### 2.2. Balance Sheet Structure

## 3. Risk Factors and Their Impact on the Market

#### 3.1. Market Risk Factors

**Fixed-income securities, loans and mortgages**. The relative change in the total market capitalization of fixed-income securities with underlying currency $w\in \mathcal{C}$, maturity date $t\in \mathcal{T}$ and rating $r\in \mathcal{R}$ is given by

**Equity and equity investment funds**. The relative changes in total market capitalizations of equity for currency $w\in \mathcal{C}$ and of equity investment funds are given by

**Participations**. The relative change in market capitalization of participations in real estate related firms is modeled by

**Remark**

**1.**

**Other asset classes**. The market capitalizations of the asset classes in {hedge funds, private equity, real estate funds, residential real estate, commercial real estate, cash} are influenced by the market risk factors in Table 2 in the intuitive way. For simplicity, we assume that the asset classes ${a}_{\mathrm{ci},\mathrm{o}}$, ${a}_{\mathrm{ai},\mathrm{o}}$ and ${a}_{\mathrm{o}}$ are not influenced by changes in market risk factors. Due to the strong linkage of a company’s investments from unit-linked life insurance to its corresponding insurance provisions we assume that changes in these two positions are equal. Hence, a change in value of these investments does not affect the insurer’s risk bearing capital. As such, we forgo modeling impacts on asset class ${a}_{\mathrm{ul}}$ due to changes in the market risk factors.

**Remark**

**2.**

**Lemma**

**1.**

#### 3.2. Further Risk Factors and Cascade Effects

**Longevity risk**. We only consider longevity risk for life and accident insurance. Let ${q}_{x,0}\in [0,1]$ be the probability of a policyholder with age $x\in \mathbb{N}$ to die within the current accounting year $(t=0)$. Denote by ${q}_{x,t}$ the probability of a policyholder who is aged $x\in \mathbb{N}$ in accounting year $t\ge 1$ to die within that accounting year t. We assume that ${q}_{x,t}$, $x,t\in \mathbb{N}$, is of the form

**Decline in new business**. We consider a financial loss that arises due to planned but unearned future premium in new business. This assumes that administrative expenses of a company are non-linear in the earned premium on a short time scale. The unexpected relative change in new business is denoted by $\mathrm{\Delta}{Z}^{\mathrm{nb}}<0$. We model the resulting absolute loss in cash of firm $i=1,\dots ,I$ by

**Lapse risk**. We consider lapse risk only for individual life insurance. Lapse risk could also be considered in occupational benefit insurance (and in other lines of business). However, in contrast to individual life insurance, surrendered portfolios need to be transferred to other insurance companies or pension funds, including the investments. Therefore, the impact on the market as a whole presumably stays small. For this reason we only consider surrenders in individual life insurance, namely in unit-linked and endowment insurance. We denote the absolute change in the expected lapse rate by $\mathrm{\Delta}{Z}^{\mathrm{lapse}}>0$.

**Other risks**. Further risks such as underreserving, catastrophic events or a failure of reinsurers are discussed in the case study, see Section 5.

**Remark**

**3.**

## 4. Network Effects Followed from Changes in Risk Factors

**Market impact due to the sale of assets**. We assume that the sale of an asset in large amounts changes its price. This, in turn, impacts each insurer investing in this asset class. Let ${S}_{j}$ be the total value of asset ${a}_{j}$ sold by all the insurers, for instance, due to unexpected lapses or a liquidity shortage. We model the relative change in the total market capitalization of asset ${a}_{j}$ triggered by the sales of this asset by

**Remark**

**4.**

**Reinsurance**. We do not consider any explicit links between primary insurers and reinsurers within the insurance network (except potential participations, see below). In particular, we do not specify which reinsurers take over the reinsured liabilities ${\mathcal{V}}_{i}\left(r\right)$ of firm $i=1,\dots ,I$; note that reinsurance business is typically on a global scale, whereas we consider a local insurance market. Instead, we introduce a global reinsurer that undertakes all the reinsured liabilities ${\mathcal{V}}_{1}\left(r\right),\dots ,{\mathcal{V}}_{I}\left(r\right)$ of the network considered. In case this global reinsurer is not able to meet all or parts of its obligations, each company $i=1,\dots ,I$ pays reinsurance premiums again and increases its net values of liabilities accordingly. That is, we neglect diversification between reinsurers; for a more detailed model of a network consisting of insurers and reinsurers we refer to [34]. More details are given in Section 5.3, where we discuss a stress scenario based on the failure of reinsurers.

**Participations**. Consider a firm $i=1,\dots ,I$ that holds participation in another insurer ${i}^{\prime}\ne i$ of the network. If the own equity of firm ${i}^{\prime}$ changes by a factor $1+\mathrm{\Delta}{\mathcal{V}}_{{i}^{\prime}}\left(e\right)/{\mathcal{V}}_{{i}^{\prime}}\left(e\right)$, we assume that the corresponding holding of company i changes by

## 5. Case Study Based on Data from the Swiss Private Insurance Market

#### 5.1. Financial Market Scenarios

**Decline in risk-free rates**. We consider a decrease in each zero-coupon rate by 100 basis points, see green color in Figure 5 (rhs). The market dependencies imply, in particular, an expected increase in credit spreads and an expected decrease in the total values of equity, hedge funds and private equity, see orange color in Figure 5 (rhs). Figure 5 (lhs) illustrates the resulting impact on the CHF insurance market.

**Fall of the equity market**. We analyze the impact on the CHF insurance market when the total value in equity drops by $30\%$ for all currencies, see green color in Figure 6 (rhs). The market dependencies imply an expected drop of $45\%$ in total value of private equity, an expected drop of $16\%$ in total value of hedge funds and remarkable changes in risk-free rates and credit spreads, see orange color in Figure 6 (rhs). The impact on the CHF insurance market is illustrated in Figure 6 (lhs).

**Real estate market crash**. Next, we analyze the consequences of a real estate market crash for the CHF insurance market. For this, we set the changes in all real estate related market risk factors to $-40\%$. This decrease can be compared to the real estate crisis in Switzerland in the 1990’s, in which real estate price indexes declined by more than $35\%$, see [36]. The conditionally expected changes in the remaining risk factors and the resulting impact ratios ${\varrho}_{i}$ are illustrated in Figure 7.

**Financial crisis as of 2007/2008**. We consider a scenario where the market risk factors are stressed according to the financial crisis of 2007/2008. The changes in the risk factors corresponding to this crisis are provided by FINMA [37] and illustrated in Figure 8 (rhs). Credit spreads increase, all other risk factors are negatively shocked. The resulting impact ratios are summarized in Figure 8 (lhs).

**Stock market crash as of 2000/2001**. We consider a scenario where the market risk factors are stressed according to the stock market crash of 2000/2001. The changes in the risk factors corresponding to this crash are provided by FINMA [37] and illustrated in Figure 9 (rhs). Note that these changes are similar to the ones corresponding to the financial crisis 2007/2008, see Figure 8 (rhs), but less extreme. Therefore, the losses on the asset side are smaller compared to the previous scenario. The impact ratios in turn look more comforting, see Figure 9 (lhs).

#### 5.2. Real Estate Market Crash Together with Cascade Effects

#### 5.3. Failure of Reinsurers in a Stressed Market Situation

#### 5.4. Longevity and Underreserving

#### 5.5. Terrorist Attack

#### 5.6. Pandemic Event and a Big Earthquake

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

lhs | left-hand side |

rhs | right-hand side |

bn | billion |

SST | Swiss Solvency Test |

CHF | Swiss franc |

EUR | Euro |

USD | U.S. dollar |

FINMA | Swiss Financial Market Supervisory Authority |

FX | foreign exchange |

bp | basis points |

## Appendix A. Balance sheets considered for the case study

**Figure A1.**Aggregated balance sheets for each branch of insurance as used for the case study. Assets (

**top**) and liabilities (

**bottom**). Values on (lhs) are relative and in percentage, values on (rhs) are absolute and in billion CHF.

**Figure A2.**Life insurers’ assets (

**top**), liabilities (

**middle**) and insurance provisions (

**bottom**) as used for the case study. Values on (lhs) are relative and in percentage, values on (rhs) are absolute and in billion CHF. For each line of business we indicate by ▴, ⧫, ▾ the market shares based on earned premiums of the first, second and third largest insurer, respectively.

**Figure A3.**General insurers’ assets (

**top**), liabilities (

**middle**) and insurance provisions (

**bottom**) as used for the case study. Values on (lhs) are relative and in percentage, values on (rhs) are absolute and in billion CHF. For each line of business we indicate by ▴, ⧫, ▾ the market shares based on earned premiums of the first, second and third largest insurer, respectively.

**Figure A4.**Health insurers’ assets (

**top**), liabilities (

**middle**) and insurance provisions (

**bottom**) as used for the case study. Values on (lhs) are relative and in percentage, values on (rhs) are absolute and in billion CHF. For each line of business we indicate by ▴, ⧫, ▾ the market shares based on earned premiums of the first, second and third largest insurer, respectively.

**Figure A5.**Reinsurers’ assets (

**top**) and liabilities (

**bottom**) as used for the case study. Values on (lhs) are relative and in percentage, values on (rhs) are absolute and in billion CHF.

## References

- FINMA. Technisches Dokument zum Swiss Solvency Test. Version 02. Oktober 2006. Bern, Switzerland: Eidgenössische Finanzmarktaufsicht FINMA, 2006. [Google Scholar]
- A. French, M. Vital, and D. Minot. “Insurance and Financial Stability.” In Quarterly Bulletin 2015 Q3. London, UK: Bank of England, 2015. [Google Scholar]
- FINMA. “Elektronische Tabellen über den Versicherungsmarkt, 2015.” Eidgenössische Finanzmarktaufsicht FINMA. Available online: http://www.versichererreport.finma.ch (accessed on 12 December 2016).
- Bank of England. Procyclicality and Structural Trends in Investment Allocation by Insurance Companies and Pension Funds: A Discussion Paper by the Bank of England and the Procyclicality Working Group. London, UK: Bank of England, 2014. [Google Scholar]
- Swisscanto. Schweizer Pensionskassenstudie 2016. Zurich, Switzerland: Swisscanto Vorsorge AG, 2016. [Google Scholar]
- M. Eling, and D. Pankoke. Systemic Risk in the Insurance Sector: Review and Directions for Future Research. Working Papers on Finance; St. Gallen, Switzerland: Institute of Insurance Economics, University of St. Gallen, 2014, Volume 21. [Google Scholar]
- IAIS. Insurance and Financial Stability, 2011. Basel, Switzerland: International Association of Insurance Supervision, 2011. [Google Scholar]
- R.W. Klein. “Insurance Market Regulation: Catastrophe Risk, Competition, and Systemic Risk.” In Handbook of Insurance. New York, NY, USA: Springer, 2013, pp. 909–939. [Google Scholar]
- J.D. Cummins, and M.A. Weiss. “Systemic risk and the U.S. insurance sector.” J. Risk Insur. 81 (2014): 489–528. [Google Scholar] [CrossRef]
- G.N. Weiss, and J. Mühlnickel. “Why do some insurers become systemically relevant? ” J. Financ. Stab. 13 (2014): 95–117. [Google Scholar] [CrossRef]
- D. Kessler. “Why (re)insurance is not systemic.” J. Risk Insur. 81 (2014): 477–488. [Google Scholar] [CrossRef]
- T. Adrian, and M.K. Brunnermeier. CoVaR. Working Paper 17454; Cambridge, MA, USA: National Bureau of Economic Research, 2011. [Google Scholar]
- M. Billio, M. Getmansky, A.W. Lo, and L. Pelizzon. “Econometric measures of connectedness and systemic risk in the finance and insurance sectors.” J. Financ.Econ. 104 (2012): 535–559. [Google Scholar] [CrossRef]
- C. Brownlees, and R.F. Engle. “SRISK: A conditional capital shortfall measure of systemic risk.” Rev. Financ. Stud., 2016. [Google Scholar] [CrossRef]
- E. Berdin, and M. Sottocornola. “Insurance Activities and Systemic Risk, 2015.” Available online: https://ssrn.com/abstract=2701821 (accessed on 12 December 2016).
- I. Alves, J. Brinkhoff, S. Georgiev, J.C. Héam, I. Moldovan, and M. Scotto di Carlo. Network Analysis of the EU Insurance Sector. Frankfurt am Main, Germany: ESRB Occasional Paper, 2015, Number 7. [Google Scholar]
- K. Nyholm. “Insurance and banking interconnectedness in Europe: The opinion of equity markets.” Econ. Res. Int. 2012 (2012): 525089. [Google Scholar] [CrossRef]
- T.R. Hurd. Contagion! The Spread of Systemic Risk in Financial Networks. Cham, Switzerland: SpringerBriefs in Quantitative Finance, Springer International Publishing, 2016. [Google Scholar]
- J. Monkiewicz, and M. Małecki. Macroprudential Supervision in Insurance: Theoretical and Practical Aspects. London, UK: Palgrave Macmillan, 2014. [Google Scholar]
- A. Jobst, N. Sugimoto, and T. Broszeit. Macroprudential Solvency Stress Testing of the Insurance Sector. IMF Working Papers; Washington, DC, USA: International Monetary Fund, 2014, Volume 24. [Google Scholar]
- C. Christophersen, and J. Zschiesche. Macroprudential Objectives and Instruments for Insurance—An Initial Discussion. EIOPA Financial Stability Report—May 2015; Frankfurt am Main, Germany: European Insurance and Occupational Pensions Authority, 2015, pp. 72–90. [Google Scholar]
- S.E. Harrington. “The financial crisis, systemic risk, and the future of insurance regulation.” J. Risk Insur. 76 (2009): 785–819. [Google Scholar] [CrossRef]
- The Geneva Association. Systemic Risk in Insurance—An Analysis of Insurance and Financial Stability, 2010. Zurich, Switzerland: The Geneva Association, 2010. [Google Scholar]
- The Geneva Association. Key Financial Stability Issues in Insurance—An Account of The Geneva Association’s Ongoing Dialogue on Systemic Risk with Regulators and Policy-Makers, 2010. Zurich, Switzerland: The Geneva Association, 2010. [Google Scholar]
- H. Chen, J.D. Cummins, K.S. Viswanathan, and M.A. Weiss. “Systemic risk and the interconnectedness between banks and insurers: An econometric analysis.” J. Risk Insur. 81 (2014): 623–652. [Google Scholar] [CrossRef]
- M.P. Radice. Assessing the Potential for Systemic Risks in the Insurance Sector: Considerations on Insurance in Switzerland. FINMA Working Paper; Bern, Switzerland: Eidgenössische Finanzmarktaufsicht FINMA, 2010. [Google Scholar]
- IMF. Germany: Financial Sector Assessment Program: Stress Testing the Banking and Insurance Sectors—Technical Notes. IMF Country Report; Washington, DC, USA: International Monetary Fund, 2016, Volume 16. [Google Scholar]
- EIOPA. EIOPA Insurance Stress Test 2014. EIOPA–BOS; Frankfurt am Main, Germany: European Insurance and Occupational Pensions Authority, 2014, Volume 203. [Google Scholar]
- ESRB. Report on Systemic Risks in the EU Insurance Sector, 2015. Frankfurt am Main, Germany: European Systemic Risk Board, 2015. [Google Scholar]
- FINMA. “Standardmodell Schadenversicherung, 2015.” Eidgenössische Finanzmarktaufsicht FINMA. Latest Version. Available online: https://www.finma.ch/de/ueberwachung/versicherungen/spartenuebergreifende-instrumente/schweizer-solvenztest-sst (accessed on 12 December 2016).
- FINMA. “Wegleitung zum SST-Marktrisiko-Standardmodell, 2014. Ausgabe vom 23. Dezember 2014.” Eidgenössische Finanzmarktaufsicht FINMA. Latest Version. Available online: https://www.finma.ch/de/ueberwachung/versicherungen/spartenuebergreifende-instrumente/schweizer-solvenztest-sst (accessed on 12 December 2016).
- A.J. McNeil, R. Frey, and P. Embrechts. Quantitative Risk Management: Concepts, Techniques and Tools. Princeton Series in Finance; Princeton, NJ, USA: Princeton University Press, 2015. [Google Scholar]
- F. Caccioli, M. Shrestha, C. Moore, and J.D. Farmer. “Stability analysis of financial contagion due to overlapping portfolios.” J. Bank. Financ. 46 (2014): 233–245. [Google Scholar] [CrossRef]
- J. Blanchet, and Y. Shi. “Stochastic Risk Networks: Modeling, Analysis and Efficient Monte Carlo, 2012.” Available online: https://ssrn.com/abstract=2012987 (accessed on 12 December 2016).
- FINMA. “SST 2014 survey: FINMA report on the Swiss insurance market, 2014.” Bern, Switzerland: Eidgenössische Finanzmarktaufsicht FINMA, 2014. [Google Scholar]
- SNB. “Real Estate Price Indices – Total for Switzerland, 2016.” Swiss National Bank Data Portal. Available online: https://data.snb.ch/de/topics/uvo#!/cube/plimoincha (accessed on 12 December 2016).
- FINMA. “Financial Market Scenarios Template for SST, 2015.” Bern, Switzerland: Eidgenössische Finanzmarktaufsicht FINMA, 2014. [Google Scholar]
- P. Nolfi. “Die Berücksichtigung der Sterblichkeitsverbesserung in der Rentenversicherung nach der Optimalmethode der Spieltheorie.” Mitt. Ver. Schweiz. Versicher. 59 (1959): 29–48. [Google Scholar]
- FINMA. “Wegleitung Betreffend Szenarien und Stresstests im SST, 2014. Ausgabe vom 31. Oktober 2014.” Eidgenössische Finanzmarktaufsicht FINMA. Latest Version. Available online: https://www.finma.ch/de/ueberwachung/versicherungen/spartenuebergreifende-instrumente/schweizer-solvenztest-sst (accessed on 12 December 2016).
- SBB. Die SBB in Zahlen und Fakten, 2015. Bern, Switzerland: Schweizerische Bundesbahnen AG, 2015. [Google Scholar]
- BABS. “Nationale Gefährdungsanalyse—Gefährdungsdossier Konventioneller Anschlag, 2015.” Schweizer Eidgenossenschaft. Bundesamt für Bevölkerungsschutz. Available online: www.babs.admin.ch/de/aufgabenbabs/gefaehrdrisiken/natgefaehrdanalyse/gefaehrddossier.html (accessed on 12 December 2016).
- J. Piercy, and A. Miles. The Economics of Pandemic Influenza in Switzerland, 2003. Liebefeld, Switzerland: Swiss Federal Office of Public Health, 2003. [Google Scholar]
- Schweizerische Rückversicherungs-Gesellschaft Zürich. “Versicherungsdeckungen sind heute unzureichend. Was, wenn in der Schweiz die Erde bebt? ” Zurich, Switzerland: Swiss Re Publishing, 2000. [Google Scholar]
- SVV. Die Flächendeckende Erdbebenversicherung, 2008. Zurich, Switzerland: Schweizerischer Versicherungsverband, 2008. [Google Scholar]

^{1.}Only supplementary health insurance companies are considered, because basic health insurance is run like social insurance in Switzerland.

**Figure 1.**Market shares based on earned premiums of the three largest Swiss insurers in selected lines of business in year 2014, see [3]. The values shown are additive and different colors reflect different insurers/groups.

**Figure 2.**Asset allocations of 11 large Swiss life insurers by the end of year 2014, see [3]. The values shown are in percentage (lhs) and in billion Swiss franc (rhs), respectively.

**Figure 3.**Zero-coupon rates ${r}_{w,t}$ (lhs) and credit spreads ${s}_{w,r}$ (rhs) considered for the case study.

**Figure 4.**Market risk analysis of the CHF insurance market based on the Swiss Solvency Test (SST) guidelines. On the level of a single company, this analysis provides the contributions of selected market risk factors to the total market risk. Each box plot considers all companies in a given branch of insurance individually. The superimposed waterfall diagram illustrates weighted averages over all companies in a given branch of insurance. These diagrams also show the weighted average diversification effect for each branch of insurance. (

**a**) life insurance; (

**b**) general insurance; (

**c**) health insurance; (

**d**) reinsurance.

**Figure 5.**(rhs) illustrates the changes in market risk factors due to a decline in all zero-coupon rates. The changes colored green are predefined, the changes colored orange result from market dependencies. (lhs) illustrates the resulting impact ratios ${\varrho}_{i}$ of the insurance companies, where ▴, ⧫ and ▾ correspond to the impact ratios of the first, second and third largest company, respectively, in each branch of insurance.

**Figure 6.**(rhs) illustrates the changes in market risk factors due to a fall of the equity market. The changes colored green are predefined, the changes colored orange result from market dependencies. (lhs) illustrates the resulting impact ratios ${\varrho}_{i}$ of the insurance companies, where ▴, ⧫ and ▾ correspond to the impact ratios of the first, second and third largest company, respectively, in each branch of insurance.

**Figure 7.**(rhs) illustrates the changes in market risk factors due to a real estate market crash. The changes colored green are predefined, the changes colored orange result from market dependencies. (lhs) illustrates the resulting impact ratios ${\varrho}_{i}$ of the insurance companies, where ▴, ⧫ and ▾ correspond to the impact ratios of the first, second and third largest company, respectively, in each branch of insurance.

**Figure 8.**(rhs) illustrates the changes in market risk factors corresponding to the financial crisis of 2007/2008, see FINMA [37]. (lhs) illustrates the resulting impact ratios ${\varrho}_{i}$ of the insurance companies, where ▴, ⧫ and ▾ correspond to the impact ratios of the first, second and third largest company, respectively, in each branch of insurance.

**Figure 9.**(rhs) illustrates the changes in market risk factors corresponding to the stock market crash of 2000/2001, see FINMA [37]. (lhs) illustrates the resulting impact ratios ${\varrho}_{i}$ of the insurance companies, where ▴, ⧫ and ▾ correspond to the impact ratios of the first, second and third largest company, respectively, in each branch of insurance.

**Figure 10.**(lhs) illustrates the impact ratios ${\varrho}_{i}$ for the real estate market crash scenario (left plots), see Figure 7, together with declined new business and increased lapse rates (first cascade effect) (middle plots) and together with the market impacted triggered by the sale of assets (second cascade effect) (right plots). (rhs) illustrates the changes in market risk factors corresponding to the market impact. The changes colored green are caused by the price impact, the changes colored orange result from market dependencies.

**Figure 11.**Impact ratios ${\varrho}_{i}$ caused by a fall of the equity market (left plots), see Figure 6, and combined with the cascading failure of reinsurers (right plots).

**Figure 12.**(lhs) illustrates the impact ratios ${\varrho}_{i}$ for longevity risk and a reserve strengthening (left plots) as well as together with a cascading decline new business (right plots); (rhs) illustrates the impact ratios ${\varrho}_{i}$ resulting from a terrorist attack.

**Table 1.**Asset and liability classes under consideration, including their notation. The upper indexes run over maturity buckets $t\in \mathcal{T}$, currencies $w\in \mathcal{C}$ and ratings $r\in \mathcal{R}$, respectively.

Asset Classes ${\mathit{a}}_{\mathit{j}}$ | Liability Classes ${\mathit{l}}_{\mathit{k}}$ | ||
---|---|---|---|

real estate: | insurance provisions for | ||

− residential real estate | ${a}_{\mathrm{re},\mathrm{r}}$ | − collective life insurance: | |

− commercial real estate | ${a}_{\mathrm{re},\mathrm{c}}$ | occupational benefits insurance | ${l}_{\mathrm{ob}}^{t}$ |

participations in | − individual life insurance: | ||

− other network participants | ${a}_{\mathrm{part},\mathrm{ins}}^{w}$ | endowment insurance | ${l}_{\mathrm{ei}}^{t}$ |

− real estate related firms | ${a}_{\mathrm{part},\mathrm{re}}^{w}$ | pension annuities | ${l}_{\mathrm{pa}}^{t}$ |

− others | ${a}_{\mathrm{part},\mathrm{o}}^{w}$ | unit-linked life insurance | ${l}_{\mathrm{ul}}$ |

fixed-income securities | ${a}_{\mathrm{bonds}}^{w,t,r}$ | other individual life insurance | ${l}_{\mathrm{oli}}^{t}$ |

loans | ${a}_{\mathrm{loans}}^{w,t,r}$ | − non-life insurance: | |

mortgages | ${a}_{\mathrm{mortgages}}^{w,t,r}$ | accident insurance | ${l}_{\mathrm{ai}}^{t}$ |

equity | ${a}_{\mathrm{equity}}^{w}$ | health insurance | ${l}_{\mathrm{hi}}^{t}$ |

collective investments in | motor insurance | ${l}_{\mathrm{mi}}^{t}$ | |

− real estate funds | ${a}_{\mathrm{ci},\mathrm{ref}}$ | property insurance | ${l}_{\mathrm{pi}}^{t}$ |

− equity investment funds | ${a}_{\mathrm{ci},\mathrm{ef}}$ | casualty insurance | ${l}_{\mathrm{ci}}^{t}$ |

− others | ${a}_{\mathrm{ci},\mathrm{o}}$ | other non-life insurance | ${l}_{\mathrm{onli}}^{t}$ |

alternative investments in | − business abroad | ${l}_{\mathrm{ba}}^{w,t}$ | |

− hedge funds | ${a}_{\mathrm{ai},\mathrm{hf}}$ | − backing cover | ${l}_{\mathrm{bc}}^{t}$ |

− private equity | ${a}_{\mathrm{ai},\mathrm{pe}}$ | liabilities from insurance and | |

− others | ${a}_{\mathrm{ai},\mathrm{o}}$ | investment activities | ${l}_{\mathrm{la}}$ |

investments from unit-linked life insurance | ${a}_{\mathrm{ul}}$ | other liabilities | ${l}_{\mathrm{o}}$ |

cash and other assets | ${a}_{\mathrm{cash}}^{w}$, ${a}_{\mathrm{o}}$ |

**Table 2.**Market risk factors considered, including the notation for their changes. The lower indexes run over maturity buckets $t\in \mathcal{T}$, currencies $w\in \mathcal{C}$ and ratings $r\in \mathcal{R}$, respectively.

Market Risk Factors | |
---|---|

zero-coupon rates | $\mathrm{\Delta}{Z}_{w,t}^{\mathrm{zeros}}$ |

credit spreads | $\mathrm{\Delta}{Z}_{w,r}^{\mathrm{spreads}}$ |

exchange rates | $\mathrm{\Delta}{Z}_{w}^{\mathrm{FX}}$ |

equity | $\mathrm{\Delta}{Z}_{w}^{\mathrm{equity}}$ |

hedge funds, private equity and real estate funds | $\mathrm{\Delta}{Z}^{\mathrm{hf}}$, $\mathrm{\Delta}{Z}^{\mathrm{pe}}$, $\mathrm{\Delta}{Z}^{\mathrm{ref}}$ |

residential real estate and commercial real estate | $\mathrm{\Delta}{Z}^{\mathrm{re},\mathrm{r}}$, $\mathrm{\Delta}{Z}^{\mathrm{re},\mathrm{c}}$ |

participations | $\mathrm{\Delta}{Z}^{\mathrm{part}}$ |

**Table 3.**Market risk factors considered for modeling the market impact caused by the sale of assets in large amounts.

Market Risk Factors | |
---|---|

CHF zero-coupon rates for maturities $t\in \mathcal{T}$ | $\mathrm{\Delta}{Z}_{\mathrm{CHF},t}^{\mathrm{zeros}}$ |

CHF credit spreads for ratings $r\in \mathcal{R}\backslash \left\{\mathrm{RF}\right\}$ | $\mathrm{\Delta}{Z}_{\mathrm{CHF},r}^{\mathrm{spreads}}$ |

equity for currency CHF | $\mathrm{\Delta}{Z}_{\mathrm{CHF}}^{\mathrm{equity}}$ |

hedge funds, private equity and real estate funds | $\mathrm{\Delta}{Z}^{\mathrm{hf}}$, $\mathrm{\Delta}{Z}^{\mathrm{pe}}$, $\mathrm{\Delta}{Z}^{\mathrm{ref}}$ |

residential real estate and commercial real estate | $\mathrm{\Delta}{Z}^{\mathrm{re},\mathrm{r}}$, $\mathrm{\Delta}{Z}^{\mathrm{re},\mathrm{c}}$ |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Deprez, P.; Wüthrich, M.V.
Macroprudential Insurance Regulation: A Swiss Case Study. *Risks* **2016**, *4*, 47.
https://doi.org/10.3390/risks4040047

**AMA Style**

Deprez P, Wüthrich MV.
Macroprudential Insurance Regulation: A Swiss Case Study. *Risks*. 2016; 4(4):47.
https://doi.org/10.3390/risks4040047

**Chicago/Turabian Style**

Deprez, Philippe, and Mario V. Wüthrich.
2016. "Macroprudential Insurance Regulation: A Swiss Case Study" *Risks* 4, no. 4: 47.
https://doi.org/10.3390/risks4040047