non-life windstorm risk
A practical study in the Netherlands under the
Solvency II framework
Willeke de Tree
Master’s Thesis to obtain the degree in Actuarial Science and Mathematical Finance University of Amsterdam
Faculty of Economics and Business Amsterdam School of Economics
Author: mw. C.W. de Tree BSc Student nr: 10215832
Email: willekedetree@gmail.com
Date: July 24, 2016
University supervisor: mw. Y. Yue MSc
Second reader: dhr. prof. dr. R.J.A. Laeven
Company supervisors: mw. dr. A.E. van Heerwaarden AAG & mw. E.T.C. van Nes MSc
its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
Based on the increase of windstorm events and the new regulatory framework Solvency II that came into effect on January 1, 2016 in the Netherlands, a research field has arisen which has as main objective to explore how catastrophic events can be (re)insured under the new regulatory framework. In this thesis, the case of a hypothetical medium-sized Dutch non-life fire insurer with insured property only in the Netherlands is considered, where the focus is on non-life natural catastrophe risk caused by windstorm events. To manage the windstorm risk two main risk mitigation techniques are available: tra-ditional reinsurance and insurance-linked securities. The existing literature about the comparison of both risk mitigation techniques does not take into account all various costs associated with these techniques and/or a practical research approach. Therefore, this thesis investigates the effect of the use of different risk mitigation techniques on the Solvency Capital Requirement (SCR) by optimising the choice of the risk mitiga-tion techniques with respect to the SCR and the associated costs under the Solvency II standard formula. Comparing the different techniques, the results in this thesis show that it is never optimal for the hypothetical non-life insurer to reinsure with CAT bonds assuming that CAT bonds are priced with a linear model and are issued by the insurer itself, due to the higher costs for CAT bonds. This conclusion is robust given the as-sumptions in this thesis. The position of the layer of reinsurance with a CAT bond also has an influence on the total costs for the insurer. The total costs are the lowest when CAT bonds are used for medium-sized losses, and eventually for large losses. This partly contradicts the results of earlier research, which state that the optimal mix of risk mitigation techniques includes traditional reinsurance contracts for the coverage of small losses and CAT bonds only for the coverage of large losses.
Keywords catastrophe risk, CAT bonds, insurance-linked securities, risk mitigation, Solvency II, Solvency Capital Requirement, traditional reinsurance, windstorm risk
Preface vii
1 Introduction 1
2 Solvency II 4
2.1 Solvency II . . . 4
2.2 Solvency Capital Requirement . . . 5
2.3 Relevant main risks of a non-life insurer . . . 5
2.3.1 Non-life premium and reserve risk . . . 6
2.3.2 Non-life lapse risk . . . 6
2.3.3 Non-life catastrophe risk . . . 6
2.3.4 Counterparty default risk . . . 7
2.3.5 Market risk . . . 7
2.4 SCR calculation . . . 8
2.4.1 SCR of non-life underwriting risk . . . 8
2.4.2 Implementing risk mitigation techniques in SCR . . . 11
2.4.3 SCR of counterparty default risk . . . 11
2.4.4 Total SCR . . . 13
3 Risk mitigation techniques 14 3.1 Traditional reinsurance . . . 14
3.1.1 Types of traditional reinsurance . . . 14
3.1.2 Excess of loss reinsurance per event . . . 15
3.1.3 Pricing methods for excess of loss reinsurance . . . 16
3.2 Insurance-linked securities . . . 17
3.2.1 CAT bonds . . . 17
3.2.2 Characteristics of CAT bonds . . . 19
3.2.3 Pricing methods for CAT bond spreads . . . 19
3.3 Earlier research on using risk mitigation techniques . . . 20
4 Methodology 22 4.1 Portfolio of the non-life insurer . . . 23
4.2 SCR excluding risk mitigation techniques . . . 26
4.3 Catastrophe modelling . . . 27
4.4 Gross losses in one year . . . 30
4.4.1 Frequency modelling . . . 31
4.4.2 Severity modelling . . . 32
4.4.3 Gross losses in one year . . . 35
4.4.4 Gross annual losses . . . 36
4.5 Determination of layers . . . 37 v
5.5 Optimisation of different risk mitigation techniques . . . 47
5.6 Sensitivity analyses . . . 50
5.6.1 CAT bond pricing according to theoretical pricing principles . . 50
5.6.2 CAT bond pricing like traditional reinsurance . . . 52
5.6.3 Adjusting the loading of traditional reinsurance . . . 53
5.6.4 The use of a transformer vehicle . . . 54
5.6.5 Changing the layers of reinsurance . . . 55
6 Conclusion 57 Bibliography 60 Appendix A: Correlation coefficients for windstorm risk 63 Appendix B: Risk weights for windstorm risk 72 Appendix C: Complete overview of premiums and costs 73 C.1 Premiums of CAT bonds according to theoretical pricing principles . . . 73
C.2 Premiums of CAT bonds like traditional reinsurance . . . 75
C.3 Premiums of CAT bonds with different loadings for transformer vehicle . 76 C.4 Changing the layers of reinsurance . . . 77
Preface
In front of you lies the Master’s Thesis ‘Risk mitigation techniques for non-life windstorm risk – A practical study in the Netherlands under Solvency II’. It has been written to fulfil the graduation requirements of the Master Actuarial Science and Mathematical Finance. From March to July 2016 I have been engaged in the research for and the writing of this thesis. In this thesis the optimisation of the use of different risk mitigation techniques for non-life windstorm risk in the Netherlands is discussed under the new Solvency II framework. I have chosen the subject of windstorm risk, because in the recent years a lot of natural catastrophes have occurred whereby the damage of each catastrophic event seems to grow. Since the topic insurance is of great importance in the Master Actuarial Science and Mathematical Finance, I wanted to explore how an insurer deals with windstorm risk. At request of my supervisors at EY, I have chosen to optimise the use of different risk mitigation techniques for non-life windstorm risk for a Dutch non-life insurer. The topic of using different risk mitigation techniques is already discussed in the literature and therefore I have added the restriction of a Dutch insurer and used a practical approach using the new Solvency II framework.
During my literature study I fortunately did not encounter major difficulties. I was able to find sufficient literature about the Solvency II framework and the risk mitigation techniques in order to write a detailed literature review about these subjects. However, during the practical research I did encounter some difficulties. During the implementa-tion of the progressive scheme in my research, I encountered problems caused by the fact that I did understand the theory but at the same time I missed the practical experience to solve the problems. However, with the help of my supervisors at EY, my supervisor at the University of Amsterdam, and Gijs Kloek from Achmea Reinsurance Company N.V. I have been able to solve all problems and finish my research.
I would like to thank the people without whom I could not have realised this thesis. First, I would like to thank my supervisors at EY, Angela van Heerwaarden and Lisanne van Nes, for helping me to find a suitable subject, for guiding me through the process and for the critical questions during this process. Second, I would like to thank my su-pervisor at the University of Amsterdam, Yuan Yue, for all her advices and critical notes during my research and for the corrections during the writing of this thesis. A special thanks goes to Gijs Kloek from Achmea Reinsurance Company N.V. for the interviews we have had, for the help with setting up a concrete progressive scheme and for the answers to my questions about my research. I also would like to thank Harold Hendriks from EY/De Nederlandsche Bank for the answers to my questions about traditional reinsurance. Furthermore, I would like to thank Frie Roijers from Achmea Reinsurance Company N.V., who explained the legal side of issuing CAT bonds. Next, I would like to thank Paul Wonderman for explaining the rules about counterparty default risk under the new Solvency II framework. Last, I would like to thank my parents, my sister, my partner and my friends for their support during the past months.
I hope you enjoy reading this thesis. Willeke de Tree BSc,
Chapter 1
Introduction
Between late May and the beginning of June this year, the news in multiple countries in northern Europe was all about flooded rivers and torrential rains. In Paris, the Louvre Museum closed its doors for a couple of days because of the probability of a flooding of the Seine. Also several Paris train stations and roads were closed because of the rising water levels. In Hamburg, a tornado was seen passing by and some severe storms ripped off roofs and uprooted big trees. In Genappe, a town south of Brussels, a deluge of muddy water went through the streets and damaged property. In the rest of France, Belgium, Germany, and also in Italy, Austria and Poland, there were thousands of reports about thunderstorms. In those countries lightning struck homes and trees, which caused electricity blackouts and damaged cars. In total, seventeen persons lost their lives as a result of these storms.
All these damages were caused by storms and flooding from a windstorm named Elvira passing parts of northern Europe (AON Benfield, 2016d). The provisional eco-nomic damage of this windstorm is estimated aroundAC4 billion. However, this has not been the only windstorm which has passed Europe in the past year. At the end of March this year a windstorm named Jeanne, also called Katie, passed the United Kingdom, France, the Netherlands, Germany and Scandinavia, causing a total economic loss es-timated in excess of $100 million and one death (AON Benfield, 2016c). In February 2016 two windstorms passed over Europe. Windstorm Norkys (Henry) caused provi-sional total economic losses aroundAC70 million and windstorm Ruzica (Imogen) caused seriously injuries to several people and total economic losses estimated aroundAC90 mil-lion (AON Benfield,2016a). In January, windstorm Marita (Gertrude) caused estimated total economic losses exceeding $100 million (AON Benfield, 2016b). In 2015, among others windstorms Ted (Desmond), Eckard (Frank), Heini (Barney), Nils (Clodagh) and Zeljko passed Europe causing billions of euros damage and several people losing their lives (AON Benfield,2015b,c,a).
According to the latest Sigma study ofSwiss Re(2016) based on the Sigma standards there were 353 catastrophic events in 2015 across the world and, of those events, 198 events can be categorised as natural catastrophe events. Natural catastrophe events are caused by natural processes of the earth and include floods, hurricanes, tornadoes, vol-canic eruptions, earthquakes and tsunamis.Swiss Re(2016) also states that the number of natural catastrophe events in 2015 is the highest ever recorded in one year. However, the Sigma selection criteria are very strict. To be counted as a catastrophic event, the insured claims, total losses or the number of casualties need to exceed certain thresholds, which can be found inSwiss Re(2016). Therefore, not all windstorms mentioned above are counted as catastrophic events according to the Sigma study. But also these less severe catastrophic events can cause substantial damage. Even without including the less severe catastrophic events it remains true that the number of catastrophic events keeps rising. This conclusion raises the question whether and how all economic losses related to catastrophic events are insured and whether the insurance sector is able to
requirements were not tailored to the actual risks the insurers were facing and therefore there were insufficient incentives for proper risk management (De Nederlandsche Bank, 2015). Also, Solvency I did not provide sufficient insight in the actual financial posi-tion of the insurers and in the risk sensitivity of this financial posiposi-tion, which had as consequence that it was uncertain whether the insurers could meet their future commit-ments. Lastly, seen from a European point of view, an unequal and indistinct measure of protection of the policy holder existed in Solvency I and there was also only space for supervision on group level to a limited extent (De Nederlandsche Bank,2015).
The main objective of the new regulatory framework Solvency II is to improve the solvency of the (re)insurance sector and underpin the stability of the broader financial system (Directorate General for Economic and Financial Affairs, 2007)1. On January 1, 2016 the Solvency II regime came into effect in the Netherlands and changed among other things the reporting standards of (re)insurers. This new regulatory framework regulates how much capital a (re)insurer must hold to meet the Solvency Capital Re-quirement (SCR), the most important capital reRe-quirement of Solvency II. Interesting questions arising under this new regulatory framework are how this capital could be managed optimally and whether it is possible to reduce the amount of capital required. Based on the above stated questions, an interesting research field concerning catastrophe risk and the new regulatory framework has arisen. The main objective of this research field is to explore how catastrophic events can be (re)insured under the new regulatory framework Solvency II. This thesis considers the case of a hypothetical medium-sized Dutch non-life fire insurer with insured property only in the Netherlands, since one of the risks affecting the SCR for a non-life insurer is catastrophe risk. In particular, this thesis focuses on non-life natural catastrophe risk caused by windstorm events. For the Netherlands, windstorm risk and hail risk are the only risks that can affect the SCR under Solvency II. However, the probability of severe damage due to hail risk is con-sidered to be only 0.02% (Annex VIII of the European Parliament and the Council (2015)) in comparison with a probability of 0.18% for windstorm risk (Annex V of the European Parliament and the Council (2015)) and therefore hail risk is not considered when looking at reinsurance for the non-life insurer in this thesis.
To mitigate the windstorm risk of a non-life insurer, two main risk mitigation tech-niques are available: traditional reinsurance and insurance-linked securities. Traditional reinsurance is basically insurance for an insurer and is commonly known and used by insurers in the Netherlands. With a traditional reinsurance contract the non-life catas-trophe risk will reduce, but at the same time counterparty default risk of the reinsurer is introduced under the Solvency II framework. To prevent the introduction of counter-party default risk, it is rational to consider other risk mitigation techniques for which this type of risk does not exist. A known group of these other risk mitigation tech-niques are insurance-linked securities, which are financial instruments sold to investors and whose value is affected by the insured loss event. The most famous example is a catastrophe (CAT) bond, which transfers catastrophe risk from an insurer to investors in the financial market.
In the literature the theoretical pricing of CAT bond spreads is intensively discussed, for example in Galeotti, G¨urtler & Winkelvos (2013), G¨urtler, Hibbeln & Winkelvos (2014) and Braun (2015). Also comparisons on the use of both risk mitigation
tech-1
The Directorate General for Economic and Financial Affairs is a Directorate-General (branch of an administration dedicated to a specific field of expertise) of the European Commission.
niques can be found, for example in Nell & Richter (2000), Doherty & Richter (2002), B¨auerle (2004) and Finken & Laux (2009). However, according to the author of this thesis the literature about the comparison of both risk mitigation techniques does not take into account all various costs associated with these techniques and/or a practical research approach. Therefore, this thesis will consider the costs of the risk mitigation techniques and it will also consider the new regulatory framework Solvency II to be consistent with the current legislation for the Dutch insurer. In conclusion, this thesis investigates the effect of the use of different risk mitigation techniques on the SCR by optimising the choice of the risk mitigation techniques with respect to the SCR and the associated costs under the Solvency II standard formula.
The sequel of this thesis is constructed as follows. Chapter 2 reviews the new regu-latory framework Solvency II and the relevant components of the SCR and explains how the SCR can be calculated for the hypothetical non-life insurer considered in this thesis. Next, in chapter3 the risk mitigation techniques are discussed, together with a description of earlier research on the comparison of different risk mitigation techniques. An important result of this earlier research is that the optimal portfolio for an insurer should consist of traditional reinsurance for low losses and CAT bonds only for high losses. Chapter 4 contains the methodology of the empirical research of this thesis. It describes the data of the hypothetical Dutch non-life insurer and the progressive scheme which is needed to calculate the effect of the use of different risk mitigation techniques by optimising the risk mitigation techniques based on the SCR and the associated costs for the Dutch non-life insurer. The next chapter, chapter 5, describes the final results of the optimisation and the sensitivity analyses for the non-life insurer. Finally, chapter
Chapter 2
Solvency II
Before introducing the risk mitigation techniques, it is described how the risk mitigation techniques can be implemented in the calculations of the Solvency Capital Requirement. This chapter serves as a theoretical support of the calculation of the Solvency Capital Requirement for non-life insurers under the Solvency II framework. Some simplifications will be applied where this does not disturb the topics studied in this thesis. A short review of the Solvency II framework is presented in section 2.1 and in section 2.2 the Solvency Capital Requirement is described. Next, section 2.3 gives an overview of the main risks for a non-life insurer with fire insurance and a main focus on non-life natural catastrophes. Section2.4deals with the calculation of the Solvency Capital Requirement for this non-life insurer.
2.1
Solvency II
On January 1, 2016 the Solvency II framework was put into operation in the Nether-lands. Before the financial crisis of 2006-2008, Solvency II was a project of the European Commission, where the objective was to build a reference regulatory framework that would apply well in normal and in crisis circumstances (EIOPA, 2011)1. Around the same time the European Commission started their project, financial institutions (in-cluding insurance companies) tend to create and hold more and more complex financial instruments, such as asset backed securities with collateralized debt obligations (ABS CDOs). During the crisis of 2006-2008 financial institutions ran into liquidity prob-lems due to these instruments and on that account the robustness of the risk system of financial institutions was questioned. As a consequence, there was an increase in the awareness of risks the insurance companies were exposed to and the importance of proper risk management and measurement was highlighted. The problems caused by the financial crisis helped the European Commission finish their project and this led to the final Solvency II framework in which the supervision and the regulation of insurance companies is the main objective.
Solvency II is a regulatory directive that provides a risk-, economic- and principle-based framework for the supervision of (re)insurance companies. The main objective of Solvency II is to improve the solvency of the (re)insurance sector and underpin the stability of the broader financial system (Directorate General for Economic and Finan-cial Affairs,2007)2. This main objective is divided in four general objectives (European Commission,2007):
- deepen the integration of the European insurance market; - enhance the protection of policyholders and beneficiaries;
1
EIOPA is the abbreviation of European Insurance and Occupational Pensions Authority.
2
The Directorate General for Economic and Financial Affairs is a Directorate-General (branch of an administration dedicated to a specific field of expertise) of the European Commission.
- improve the international competitiveness of European (re)insurers; - promote better regulation.
To implement the objectives of the Solvency II framework, a three-pillar structure was set up, where each pillar covers a different aspect of the Solvency II requirements. These pillars are set by the European Commission(2004) and are among others described by De Nederlandsche Bank (2016). The first pillar focuses on quantifiable risks, related provisions and capital requirements. The second pillar contains risk management and operational management of insurance companies. The last pillar deals with the require-ments applying to public disclosure of information and supervisory reporting. For the purpose of this thesis the focus will be only on the quantitative requirements prescribed in the first pillar.
2.2
Solvency Capital Requirement
Under the Solvency II framework, insurance companies need to hold sufficient economic capital and therefore they have to meet new quantitative requirements. The most impor-tant capital requirement is the Solvency Capital Requirement (SCR) and is formulated in the first pillar. In the directive of Solvency II, made by theEuropean Parliament and the Council(2009), two definitions of the SCR can be found:
- the SCR “shall correspond to the Value-at-Risk of the basic own funds of an in-surance or reinin-surance undertaking subject to a confidence level of 99.5% over a one-year period” (article 101.3).
- the SCR “should be determined as the economic capital to be held by insurance and reinsurance undertakings in order to ensure that ruin occurs no more often than once in every 200 cases or, alternatively, that those undertakings will still be in a position, with a probability of at least 99.5%, to meet their obligations to policy holders and beneficiaries over the following 12 months” (remark 64). Basically, the SCR covers all the risks that an insurer faces in a period of the next twelve subsequent months. There are three ways to estimate the SCR in the Netherlands: by using an internal model, by using the standard formula or by using a combination of those two models. An internal model is complicated and costly to build and the use of the model has to be approved by De Nederlandsche Bank, so most insurance companies use the standard formula. The use of the standard formula is less complicated and prescribed in the Solvency II framework. First, a set of shocks is applied to certain risk drivers and the impact on the value of the assets and liabilities is calculated for various risks. Next, these shocks are calibrated to the 99.5% Value-at-Risk level and then predefined correlation matrices are used to aggregate to the total SCR. In Figure
2.1the different modules of the standard formula for the SCR are shown.
2.3
Relevant main risks of a non-life insurer
For a non-life insurance company the non-life underwriting risk module is the most important risk module. According toEIOPA (2014b) non-life underwriting risk is “the risk arising from non-life insurance obligations, in relation to the perils covered and the processes used in the conduct of business” (SCR.9.1.) and it also includes “the risk resulting from uncertainty included in assumptions about exercise of policyholder op-tions” (SCR.9.2.). The module consists of three sub-modules: the non-life premium and reserve risk sub-module, the non-life lapse risk sub-module and the non-life catastrophe risk sub-module (SCR.9.4.). In addition, when risk mitigation techniques are involved, then counterparty default risk becomes also of interest. Of course, the non-life insurer also has to deal with other risks, such as market risk, but for the scope of this thesis only
Figure 2.1: Different modules of the standard formula for the SCR (see alsoEIOPA(2014b)).
the above mentioned risks are taken into account as variable values in the calculations. Market risk, however, is included in the calculations of the SCR to make an illustrative example of the hypothetical insurer considered in this thesis.
In this thesis, the main focus will be on the natural catastrophe risk sub-module which is located in the life catastrophe risk sub-module. For this reason, the non-life premium and reserve risk and non-non-life lapse risk are shortly described in paragraph
2.3.1and paragraph2.3.2, but in the sequel of this thesis the value of the SCR of these sub-modules is taken as given. Subsequently, the non-life catastrophe risk sub-module is discussed in paragraph2.3.3and the counterparty default risk module is discussed in paragraph2.3.4. Finally, the market risk module is shortly described in paragraph2.3.5
and also the value of the SCR of this module is taken as given. 2.3.1 Non-life premium and reserve risk
According to EIOPA(2014b) the non-life premium and reserve risk sub-module “com-bines a treatment for the two main sources of underwriting risk, premium risk and reserve risk” (SCR.9.8.). The non-life premium risk deals with future risks. These risks can already be liabilities to the insurer and are then covered by the premium reserve, which is the provision for unearned premium and unexpired risks. These risks can also relate to policies expected to be written during the risk period and are then covered by the expected premium income. The non-life reserve risk deals with the liabilities for insurance policies covering historical years and is the risk in the claims reserve, which is the provision for outstanding claims.
2.3.2 Non-life lapse risk
The non-life lapse risk includes the risks of a change in value which is caused by devia-tions of the actual rate of policy lapses from the expected rate. The capital requirement for non-life lapse risk “should be equal to the loss in basic own funds of undertakings that would result from the combination of two shocks” (SCR.9.33.) according toEIOPA (2014b).
2.3.3 Non-life catastrophe risk
EIOPA(2014b) defines non-life catastrophe risk as “the risk of loss, or of adverse change in the value of insurance liabilities, resulting from significant uncertainty of pricing and
provisioning assumptions related to extreme or exceptional events” (SCR.9.36.). The extreme or exceptional event where EIOPA is referring to is defined as the 1-in-200-year catastrophic event, which is the catastrophic event corresponding to a Value-at-Risk measure with a 99.5% confidence level (EIOPA,2014a).
The non-life catastrophe risk sub-module is divided in four sub-modules: the natural catastrophe risk sub-module, the sub-module for catastrophe risk of non-proportional property reinsurance, the man-made catastrophe risk sub-module and the sub-module for other non-life catastrophe risk (EIOPA,2014b, SCR.9.39.).
The natural catastrophe risk module and the man-made catastrophe risk sub-module are again divided into different sub-sub-modules (EIOPA,2014b). The natural catas-trophe risk sub-module accounts for all possible natural perils, whereby it has different sub-modules, depending on the nature of the non-life catastrophe risk. The different risks are windstorm risk, earthquake risk, flood risk, hail risk and subsidence risk (SCR.9.41.). The man-made catastrophe risk accounts for all possible man-made perils and also has different sub-modules. The sub-modules are based on extreme or exceptional events arising from motor risk, fire risk, marine risk, aviation risk, liability risk and credit & surety ship risk (SCR.9.106.).
As already stated, the main focus in this thesis is on the natural catastrophe risk sub-module. Therefore, the value of the SCR of the other sub-modules in the non-life catastrophe risk sub-module is taken as given in the sequel of this thesis. Furthermore, in Annex V-VII of the ‘Delegated Acts’ from theEuropean Parliament and the Council (2015) is stated for which countries which natural perils must be included in the cal-culation of the SCR. For the Netherlands, the natural catastrophe risks to be included in the calculation of the SCR are windstorm risk and hail risk. Since the probability of severe damage due to hail risk is considered to be only 0.02% (Annex VIII of the European Parliament and the Council (2015)) compared to a probability of 0.18% for windstorm risk (Annex V of the European Parliament and the Council (2015)), more precise results can be obtained by looking only to windstorm risk. Therefore, this thesis focuses on windstorm risk and takes the value of the SCR for hail risk as given. 2.3.4 Counterparty default risk
According to EIOPA(2014b) the counterparty default risk module “should reflect pos-sible losses due to unexpected default of the counterparties and debtors of undertakings over the forthcoming twelve months” (SCR.6.1.). Two kinds of exposure exist in the counterparty risk module. Type 1 exposures cover the exposures “which may not be diversified and where the counterparty is likely to be rated” (SCR.6.6.) and consists of exposures in relation to risk mitigation contracts, cash at bank, deposits with ceding undertakings and some specific types of commitments. Type 2 exposures cover the expo-sures “which are usually diversified and where the counterparty is likely to be unrated” (SCR.6.9.), such as receivables from intermediaries, policy holder debtors, residential mortgage loans, deposits with ceding companies and some specific types of commit-ments. Both reinsurance contracts and insurance-linked securities are covered by the first type of exposure and therefore this thesis only considers type 1 exposures of coun-terparty default risk as variable. The value of the SCR of type 2 exposures of counter-party default risk is left out of account in the sequel of this thesis.
2.3.5 Market risk
The market risk in the market risk module “arises from the level or volatility of market prices of financial instruments” according to EIOPA(2014b, SCR.5.1.), where the “ex-posure to market risk is measured by the impact of movements in the level of financial variables such as stock prices, interest rates, real estate prices and exchange rates”. It
In this section the formulas for calculating the SCR for the relevant (sub-)modules are desribed. First, the calculation of the SCR of non-life underwriting risk is discussed in paragraph 2.4.1and thereafter the way in which risk mitigation techniques are im-plemented in the calculation of the SCR is presented in paragraph 2.4.2. Third, the calculation of the SCR of counterparty default risk is given in paragraph 2.4.3 and, finally, in paragraph 2.4.4the calculation of the total SCR is described. All definitions, formulas and correlation matrices used for the calculations of the SCR can be found in the ‘Technical Specifications for the Preparatory Phase’ from EIOPA (2014b) and/or in the ‘Delegated Acts’ from theEuropean Parliament and the Council (2015).
2.4.1 SCR of non-life underwriting risk
The calculation of the SCR for the non-life underwriting risk (SCRnon−lif e) is a
com-bination of the risks in the different sub-modules, namely non-life premium and reserve risk (nl prem res), non-life lapse risk (nl lapse) and non-life catastrophe risk (nlCAT ). This is done by using the following formula:
SCRnon−lif e= s X i,j CorrN L(i,j)· SCRi· SCRj , where
CorrN L(i,j)= Entries of correlation matrix for non-life underwriting risk for
sub-modules i and j,
SCRi, SCRj = Capital requirements for non-life underwriting risk sub-modules i and j,
and where the correlation matrix CorrN L(i,j) (NL stands for non-life) is defined as:
N Lprem res N LCAT N Llapse
N Lprem res 1.00 0.25 0.00
N LCAT 0.25 1.00 0.00
N Llapse 0.00 0.00 1.00
The calculation of the SCR for non-life catastrophe risk is a combination of the risk in the different sub-modules, namely natural catastrophe risk, catastrophe risk of non-proportional property reinsurance, man-made catastrophe risk and other non-life catas-trophe risk. The SCR for non-life catascatas-trophe risk is calculated as follows:
SCRnlCAT =
q
(SCRnatCAT + SCRnpproperty)2+ SCR2mmCAT + SCR2CAT other ,
where
SCRnatCAT = Capital requirement for natural catastrophe risk,
SCRnpproperty = Capital requirement for the catastrophe risk of non-proportional
property reinsurance,
SCRmmCAT = Capital requirement for man-made catastrophe risk,
Since the focus of this thesis is on non-life natural catastrophe risk, only the calculation of this sub-module is described here. The SCR for natural catastrophe risk is calculated with the following formula:
SCRnatCAT = s X i SCR2 i ,
where SCRi denotes the capital requirement for risk sub-module i, where the different
sub-modules are windstorm risk, earthquake risk, flood risk, hail risk and subsidence risk. For the Dutch situation, the formula for natural catastrophe risk becomes:
SCRnatCAT =
q SCR2
windstorm+ SCR2hail .
Since the SCR of hail risk is given, only the SCR of windstorm risk has to be calculated. The SCR for windstorm risk is calculated by
SCRwindstorm= v u u u t X (r,s)
CorrW S(r,s)· SCR(windstorm,r)· SCR(windstorm,s)
+ SCR2(windstorm,other) ,
where the sum includes all possible combinations (r, s) of the regions (countries) and CorrW S(r,s)= Correlation coefficient for windstorm risk for region r and s,
SCR(windstorm,r) = Capital requirement for windstorm risk in region r,
SCR(windstorm,s) = Capital requirement for windstorm risk in region s,
SCR(windstorm,others) = Capital requirement for windstorm risk in regions other than
member states of the European Union, Principality of Andorra, Republic of Iceland, Principality of Lichtenstein, Principality of Monaco, Kingdom of Norway, Republic of San Marino, Swiss Confederation and Vatican City State.
This thesis focuses on Dutch insurers with insured property solely in the Netherlands. This means there is only one region involved, so region r and s stand for the Netherlands. Therefore, the SCR of windstorm risk can be simplified to
SCRwindstorm=
q
SCR2(windstorm,r) = SCR(windstorm,r) .
For a particular region r the capital requirement for windstorm risk is the larger of the capital requirement for windstorm risk in region r according to scenario A and the capital requirement for windstorm risk in region r according to scenario B:
SCR(windstorm,r) = max SCR(windstorm,r,A); SCR(windstorm,r,B) .
According to the European Parliament and the Council(2015) the capital requirement for windstorm risk in region r according to scenario A is equal to “the loss in basic own funds of insurance and reinsurance undertakings that would result from the following sequence of events: (a) an instantaneous loss of an amount that, without deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles, is equal to 80% of the specified windstorm loss in region r; (b) a loss of an amount that, without deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles, is equal to 40% of the specified windstorm loss in region r”. The two consecutive
the following sequence of events: (a) an instantaneous loss of an amount that, without deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles, is equal to 100% of the specified windstorm loss in region r; (b) a loss of an amount that, without deduction of the amounts recoverable from reinsurance contracts and special purpose vehicles, is equal to 20% of the specified windstorm loss in region r”. Again, the two consecutive events must be independent and the (re)insurance compa-nies are also not allowed to enter into new risk mitigation contracts between the events. The instantaneous windstorm loss in region r needed in both scenarios is calculated as:
L(windstorm,r) = Q(windstorm,r)·
s X
(i,j)
Corr(windstorm,r,i,j)· W SI(windstorm,r,i)· W SI(windstorm,r,j) ,
where the sum includes all possible combinations of windstorm zones (i, j) and Q(windstorm,r)= Windstorm risk factor for region r,
Corr(windstorm,r,i,j)= Correlation coefficient for windstorm risk in windstorm zones i
and j of region r,
W SI(windstorm,r,i)= Weighted sum insured for windstorm risk in windstorm zone i of
region r,
W SI(windstorm,r,j)= Weighted sum insured for windstorm risk in windstorm zone j of region r.
For the Netherlands, the windstorm risk factor is equal to Q(windstorm,r)= 0.18% (Annex V of theEuropean Parliament and the Council(2015)) and the ninety windstorm zones in the Netherlands are based on postal codes3. The correlation coefficients between the different windstorm zones in the Netherlands can be found in Appendix A. The weighted sum insured for windstorm risk in windstorm zone i of region r is calculated by
W SI(windstorm,r,i)= W(windstorm,r,i)· SI(windstorm,r,i)
= W(windstorm,r,i)· SI(property,r,i)+ SI(onshore−property,r,i) , where
W(windstorm,r,i)= Risk weight for windstorm risk in windstorm zone i of region r
(see Appendix B),
SI(windstorm,r,i)= Sum insured for windstorm risk in windstorm zone i of region r,
SI(property,r,i)= Sum insured by the (re)insurer for fire and other damage to
property insurance in relation to contracts that cover wind-storm risk and where the risk is situated in risk zone i of region r,
SI(onshore−property,r,i)= Sum insured by the (re)insurer for marine, aviation and
trans-port insurance in relation to contracts that cover onshore
property damage by windstorm and where the risk is situated in risk zone i of region r.
2.4.2 Implementing risk mitigation techniques in SCR
In the previous paragraph, the calculation of the SCR for the non-life underwriting risk module is described. The value of the SCR is calculated without taking into account the risk mitigation techniques and is therefore called the gross SCR. This SCR is needed to calculate the risk mitigation effect for the counterparty default risk module, which is described in the next paragraph. Implementing the risk mitigation techniques in the SCR means transforming the gross SCR into a net SCR, which is done by subtracting the risk mitigation value of the risk mitigation techniques per layer of reinsurance from the gross SCR in scenario A and in scenario B and choosing the maximum value of these scenarios. The risk mitigation value is the value by which the windstorm events considered in scenario A and B is decreased through the use of risk mitigation techniques. 2.4.3 SCR of counterparty default risk
When implementing risk mitigation techniques in the calculation of the SCR, counter-party default risk is introduced. This countercounter-party default risk has to be taken into account in the calculation of the total SCR. The capital requirement for counterparty default risk consists of the capital requirements for type 1 exposures and type 2 expo-sures, which should be calculated separately, in combination with a small diversification effect. The formula for counterparty default risk is:
SCRdef =
q
SCR2def,1+ 1.5 · SCRdef,1· SCRdef,2+ SCR2def,2 ,
where
SCRdef = Capital requirement for counterparty default risk,
SCRdef,1= Capital requirement for counterparty default risk of type 1 exposures,
SCRdef,2= Capital requirement for counterparty default risk of type 1 exposures.
As stated in paragraph2.3.4, type 2 exposures are not taken into account in this thesis, so only the type 1 exposures have to be calculated. The capital requirement for type 1 exposures depends on the estimated loss-given-default (LGD ) of an exposure and the probability of default (PD ) of the counterparty. This can be formulated as follows:
SCRdef,1= 3 · σ if σ ≤ 7% ·P iLGDi 5 · σ if 7% ·P iLGDi < σ ≤ 20% ·PiLGDi P iLGDi if 20%PiLGDi ≤ σ ,
where the sum contains all independent counterparties with type 1 exposures and LGDi = Loss-given-default for type 1 exposures of counterparty i,
V = Variance of the loss distribution of the type 1 exposures, σ =
√
V = Standard deviation of the loss distribution of the type 1 exposures. The variance of the loss distribution of type 1 exposures is the sum of Vinter and Vintra:
V = Vinter+ Vintra =X (j,k) P Dk· (1 − P Dk) · P Dj· (1 − P Dj) 1.25 · (P Dk+ P Dj) − P Dk· P Dj · T LGDj· T LGDk +X j 1.5 · P Dj· (1 − P Dj) 2.5 − P Dj ·X P Dj LGDi2 ,
bearing a probability of default P Dk,
P Di = Probability of default of counterparty i,
the sum in Vinter covers all possible combinations (j, k) of different probabilities of
de-fault on single name exposures, the first sum in Vintra covers all different probabilities
of default on single name exposures and the second sum in Vintra covers all single name
exposures that have a probability of default equal to P Dj.
An insurer prefers to collaborate with a reinsurer for which a credit assessment by a nominated ECAI4 is available, since the capital requirement for such reinsurers is lower as well as the costs associated with it. Therefore, this thesis only regards rein-surers with a given credit rating. The probability of default per credit quality step is given in Table2.1. Credit quality step 0 means that the counterparty has a AAA rating, credit quality step 1 stands for a AA rating, until credit quality step 6, which stands for a rating lower than B (Joint Committee of the European Supervisory Authorities, 2015). When there is more than one credit quality step available for a counterparty, the second-highest step is used.
Credit quality step 0 1 2 3 4 5 6
P Di 0.002% 0.010% 0.050% 0.240% 1.200% 4.200% 4.200%
Table 2.1: Probability of default per credit quality step.
The loss-given-default of an exposure is the loss of basic own funds which the insurer would suffer if the counterparty defaults. For a reinsurance arrangement or securitisation i, the loss-given-default is
LGDi = max (50% · (Recoverablesi+ 50%RMre,i) − F · Collaterali; 0) ,
where
Recoverablesi = Best estimate recoverables from the reinsurance contract (or SPV) i
plus any other debtors arising out of the reinsurance arrangement or SPV securitisation,
RMre,i= Risk mitigating effect on underwriting risk of the reinsurance
arrange-ment or SPV securitisation i,
Collaterali = Risk-adjusted value of collateral in relation to the reinsurance
arrange-ment or SPV securitisation i,
F = Factor to take into account the economic effect of the collateral ar-rangement in relation to the reinsurance arar-rangement or securitisation in case of any credit event related to the counterparty i.
The risk mitigating effect on underwriting risks of a type 1 exposures is according to theEuropean Parliament and the Council (2015) the “difference between the following capital requirements: (a) the hypothetical capital requirement for underwriting or market risk of the insurance or reinsurance undertaking that would apply if the reinsurance
arrangement, securitisation or derivative did not exist; (b) the capital requirement for underwriting or market risk of the insurance or reinsurance undertaking”. The risk mitigating effect thus depends on the degree of influence of the risk mitigation technique. These risk mitigation techniques will be worked out in more detail in the next chapter. 2.4.4 Total SCR
The different risk modules are combined to estimate the total SCR. The calculation of the total SCR consists of the calculation of the Basic Solvency Capital Requirement (BSCR) plus the capital requirement for operational risk plus the adjustment for the risk absorbing effect of technical provisions and deferred taxes. As a simplification, this thesis will not take into account the operational risk and the adjustment for the risk absorbing effect and therefore the SCR equals the BSCR. The total SCR is calculated by using the following formula:
SCR = BSCR = s X ij Corrij · SCRi· SCRj , where
Corrij = Entries of the correlation matrix Corr,
SCRi, SCRj = Capital requirements for the individual SCR risks according to the
rows and columns of the correlation matrix Corr,
and where the correlation matrix Corr for the hypothetical non-life insurer considered in this thesis is defined as:
Market Default Non-life Market 1.00 0.25 0.25 Default 0.25 1.00 0.50 Non-life 0.25 0.50 1.00
Chapter 3
Risk mitigation techniques
This chapter serves as a theoretical background of risk mitigation techniques which can be used by non-life insurers. Risk mitigation is the process in which a company uses specific measures to minimise or eliminate unacceptable risks associated with its oper-ations. There are different types of risk mitigation measures: some reduce the severity of risk consequences, some reduce the probability of the risk materialising and some re-duce the company’s exposure to the risk. In this chapter, two important risk mitigation techniques for reducing the non-life windstorm risk for non-life insurers are discussed. In section 3.1 traditional reinsurance is presented and in section 3.2 insurance-linked securities (ILS) are described. Furthermore, in section 3.3 earlier research on the use of different types of risk mitigation techniques is discussed. This last section shows in which way this thesis contributes added value to the scientific literature.
3.1
Traditional reinsurance
In a nutshell, traditional reinsurance is insurance for an insurer. Traditional reinsur-ance helps insurers to manage their risks by absorbing some of their losses. Traditional reinsurance is defined as an agreement between an insurer, called the cedent, and a reinsurer, where the reinsurer agrees to indemnify the cedent against (a part of) a loss which the cedent may incur under certain policies of insurance it has issued. In return, the cedent has to pay a premium and discloses information to assess, price and manage the risks covered by the reinsurance agreement (Swiss Re,2004).
Insurers choose for traditional reinsurance for multiple reasons. Traditional reinsur-ance reduces the volatility of the underwriting results and provides capital relief and flexible financing by stabilising the results of the insurance company (Munich Re,2010). Also traditional reinsurance gives insurers access to reinsurers’ expertise and services and therefore enables the growth and innovation of the insurance company to continue. Last, traditional reinsurance guards against extreme events, thereby reducing the sever-ity of claims (Swiss Re,2013).
In paragraph 3.1.1 an overview of the different types of traditional reinsurance is pre-sented. To mitigate non-life natural catastrophe risk, the most commonly used type of reinsurance is excess of loss reinsurance per event, so paragraph3.1.2pays more atten-tion to this particular type of reinsurance. Last, paragraph3.1.3describes the methods for pricing excess of loss reinsurance.
3.1.1 Types of traditional reinsurance
Traditional reinsurance can be split up in two different main types: facultative reinsur-ance and treaty reinsurreinsur-ance (Munich Re,2010). Facultative reinsurance is a transaction on an individual risk basis, where the cedent has the option to offer an individual risk
to the reinsurer and the reinsurer retains the right to accept or reject the risk. On the other hand, treaty reinsurance, also called obligatory reinsurance, is a transaction en-compassing a block of the cedent’s book of business and the reinsurer must accept all business included within the terms of the reinsurance contract.
Both facultative and treaty reinsurance can be split up in proportional and non-proportional reinsurance. Swiss Re (2013) states that with proportional reinsurance a reinsurer takes a predetermined percentage share of the premiums and liabilities of each policy a cedent writes, while with non-proportional reinsurance a reinsurer pays losses incurred by the cedent above a fixed threshold.
Proportional reinsurance, also called pro rata reinsurance, is the collective name of all forms of quota share and surplus share reinsurance (Munich Re,2010). Advantages of proportional reinsurance are that it is easy to administer, it provides a good protec-tion against frequency or severity potential, it provides protecprotec-tion of net retenprotec-tion on first-dollar basis and it permits recovery on smaller losses.
Quota share reinsurance is defined as the form of reinsurance where the cedent is compensated for a fixed percentage of loss on each risk covered by the contract, where the premiums and the liabilities are shared from the first dollar. Surplus share reinsur-ance is the type of reinsurreinsur-ance where the proportion ceded depends on the size and the type of the risk. The cedent has the right to decide how much of the risk it wants to hold itself, so the reinsurer is only obligated to pay losses above a certain retention level in a proportional way.
Non-proportional reinsurance consists of excess of loss reinsurance and stop loss reinsur-ance (Swiss Re,2013). With excess of loss reinsurance, the reinsurer gets only involved in a loss when the loss exceeds the retention level, which is the level up to which the cedent pays the losses itself. Excess of loss reinsurance is the most common form of non-proportional reinsurance and has two different types. The first type is excess of loss reinsurance per risk, where the reinsurer compensates the cedent for any loss that exceeds the predetermined retention level on each risk (Munich Re,2010). The second type is excess of loss reinsurance per event (or occurrence), where the cedent is protected against losses arising from a single major catastrophic event. This type of reinsurance contract is often used when non-life natural catastrophes are concerned.
The other type of non-proportional reinsurance is stop loss reinsurance. This type is similar to excess of loss reinsurance and provides reinsurance for losses during the term of the contract in excess of either a specified loss ratio or a predetermined amount. So whatever causes the loss for the cedent, the reinsurer covers the part of the total loss which exceeds the determined loss ratio or absolute amount.
The main advantage of non-proportional reinsurance over proportional reinsurance is that non-proportional reinsurance allows for tailor-made solutions which are fitted as close and as flexible as possible to the risk profile of the cedent (Eves, Fritsch & M¨uller, 2015). Also, with non-proportional reinsurance a cedent can limit its liability with a deductible which reflects the willingness and capacity of the cedent to bear risk (Swiss Re, 2013). It thus provides a good protection against frequency or severity potential. Furthermore, it allows a greater net premium retention and the premiums are lower than for proportional reinsurance (Munich Re,2010). From the perspective of the reinsurer, the main advantage is that the reinsurer is able to determine the price of the risk which it might take over from the cedent.
3.1.2 Excess of loss reinsurance per event
Excess of loss reinsurance per event (or occurrence) is a traditional reinsurance contract, where the cedent is protected against losses arising from a single major catastrophic event. The objective is to provide per occurrence protection for losses that exceed a
Figure 3.1: Typical structure of excess of loss reinsurance for catastrophes (seeEves et al.(2015)).
predetermined retention level. The retention level is based on the level of losses that the cedent can absorb itself.
For excess of loss reinsurance per event it is normal that the insured sum is placed in a series of layers (Eves et al.,2015). One reinsurer or a group of reinsurers is willing to cover the risk just above the retention level of the cedent up to a specified amount, at which point another reinsurer or group of reinsurers is willing to cover the excess risk up to a higher specified amount. Above a certain amount, the risk is reverted to the cedent itself. A loss that reaches only the lowest reinsured layer will only affect the reinsurer which covers that layer, but it will not affect the reinsurers on higher layers. By design, all the losses due to a single catastrophic event are aggregated and the reinsurer covers the part of the aggregated loss X that exceeds the trigger level l. In practice, the reinsurer usually limits the covered part by an upper bound l + m. The part Z covered by the reinsurer then becomes (Albrecher & Haas,2011):
Z = 0 if X ≤ l X − l if l < X ≤ l + m m if X > l + m ,
and the part C of the loss the cedent has to pay itself is (Albrecher & Haas,2011):
C = X if X ≤ l l if l < X ≤ l + m X − m if X > l + m .
A graphical reproduction can be found in Figure 3.1, where the net retention (white area of the most right bar) is the part of the loss the cedent has to pay and the grey area of the same bar is the loss covered by the reinsurer.
3.1.3 Pricing methods for excess of loss reinsurance
The prices of excess of loss reinsurance are agreed upon between cedents and reinsur-ers, through direct negotiation or through (reinsurance) brokers. There are two main methods to calculate the premium for an excess of loss contract: the experience-based method and the exposure-based method.
The experience-based method aims to forecast the losses covered by the reinsurer based on the available information of historical claims (Desmedt, Chenut, Snoussi & Walhin, 2012). This claim information might be corrected to the current economic environment. The most common method is the burning cost method, which calculates the proportion of observed ground-up losses that would have produced a loss for a given layer (Eves
et al.,2015). So it simply compares the historical reinsured losses on a given portfolio with the corresponding premium of the cedent. The burning cost ratio is the annualised amount of losses divided by the annual premium and, expressed as a percentage of the layer limit, it is called the net rate on line (ROL). Next, the risk margins, expense mar-gins and brokerage are added to the net ROL to obtain the gross ROL.
The exposure-based method is used for treaties with insufficient loss experience, for example rare natural catastrophes and high layers, or as second opinion for experience-based rated treaties (Eves et al., 2015). The method is based on the profile of the portfolio as a starting point and is widely used in the reinsurance industry to estimate the expected loss cost of a reinsurance contract. The method simulates ground-up loss several thousand times and then calculates the necessary ROL for a given layer by using a probabilistic loss exceedance curve. The loss exceedance curve is a severity distribu-tion which is used to model the loss cost per claim.
For excess of loss reinsurance for natural catastrophes, a common feature in the con-tract is the reinstatement provision (Anderson & Dong,1998). The reinstatement puts a limit on the number of occurrences or the aggregate losses that will be paid under the contract. If this limit is exceeded, then the cedent has to pay a reinstatement premium to be able to continue the contract.
This reinstatement provision can be paid in two ways. If the reinstatements are free (prepaid), the reinstatement provision is paid up front. On the other hand, if the reinstatements are paid, then a portion of the reinstatement premium, also called re-imbursement, is paid after the occurrence of a catastrophic event. The reinstatement premium can be determined in multiple manners and therefore can differ when compar-ing the different manners. The premium may be based on the amount of reinstatement (pro rata to full limit or pro rata capita), on the time remaining in the contract (pro rata to full time or pro rata temporis) or on a combination of both.
3.2
Insurance-linked securities
Insurance-linked securities (ILS), also called risk-linked securities, are financial instru-ments which are sold to investors and whose value is affected by the insured loss event. They allow insurers to offload risk and raise capital and, on the other hand, investors to receive attractive rates of return on investment. The most famous example of insurance-linked securities are catastrophe bonds, often abbreviated to CAT bonds. CAT bonds transfer catastrophe risk, mostly natural catastrophe risk, from an issuer (sponsor) to investors where the investors receive a rate of return on investment for taking over the catastrophe risk.
In paragraph 3.2.1 the structure of CAT bonds is discussed together with the rea-sons why sponsors and investors choose for CAT bonds. Thereafter, paragraph 3.2.2
discusses the main characteristics of CAT bonds and paragraph 3.2.3 presents a short overview of the methods for the pricing of CAT bond spreads found in the literature.
3.2.1 CAT bonds
CAT bonds are securities designed by insurers and reinsurers to transfer natural catas-trophe risk to the capital markets (Braun,2015;Galeotti et al.,2013). They pay regular coupons to investors unless a predefined event occurs, which leads to a full or partial loss of capital for the investors. According to Galeotti et al. (2013) the main idea is that a sponsor, often an insurer or a reinsurer, enters into an alternative reinsurance contract with a special purpose vehicle (SPV). A SPV is a legal entity created by a
Figure 3.2: Typical structure of a CAT bond transaction (seeBraun(2015)).
sponsor by transferring assets to the SPV, to carry out some specific purpose or cir-cumscribed activity or a series of such transactions (Gorton & Souleles, 2005). This alternative reinsurance contract lasts for multiple years (most common is three years) and has a known and unalterable price. The sponsor is then insured against high losses (to a certain limit) which are caused by a specified catastrophic event. The SPV issues CAT bonds to investors to be able to guarantee the insurance coverage and the investors receive a rate of return on investment for their share.
The SPV sells protection against a catastrophe loss to the sponsor via a reinsurance contract (Braun,2015). As can be seen in Figure3.2, the SPV receives the CAT bond spread (SCAT), also called the insurance premium, from the sponsor, which consists of the expected loss of the tranche plus a risk premium. In the case that a catastrophic event occurs during the risk period the SPV has to make a payment to the sponsor, otherwise no payment is due. To fund the risks the SPV takes over, the SPV issues CAT bonds to investors and uses the proceeds to purchase collateral, which is held in a trust account. In the case that a catastrophic event occurs, the collateral is liquidated and the money (all of a part) is used by the SPV to pay the sponsor, causing the investors to loose (a part of) their principal invested. To bear this risk, investors are compen-sated with regular coupons, which consist of a payment based on a variable interest rate based on the market returns (MMF ) plus the CAT bond spread. The variable interest rate based on the market returns is often the London Interbank Offered Rate (LIBOR rate), whose maturity depends on the maturity of the CAT bond. When no catastrophic event occurs during the risk period, the investors receive their full principal back at the maturity of the CAT bond.
According to G¨urtler et al.(2014) the sponsor’s main motivation to issue a CAT bond is to obtain insurance against catastrophe risk. Other reasons to choose for CAT bonds arise from the concern about counterparty credit in case of the happening of an catas-trophic event, the will to diversify the sources of capital and shortage or pricing problems of available traditional reinsurance (Swiss Re,2012). Last, the CAT bonds have the ad-vantage over traditional reinsurance that they are set up for a multi-year period and provide known costs during the reinsurance cycles (Weber,2011, chapter 5). This leads to multi-year pricing stability, which is advantageous for the sponsor (Swiss Re,2012). For investors, the main motivation to choose for investing in CAT bonds is due to the diversification effect they provide (G¨urtler et al.,2014). Since CAT bonds have low correlations with other securities traded on capital markets, due to the fact that their value is linked to non-financial risks, it has a large diversification effect on the portfolio of the investor (Swiss Re,2012). Also, the low volatility compared to other asset classes and the relatively high yields attract investors to invest in CAT bonds.
3.2.2 Characteristics of CAT bonds
A CAT bond has multiple characteristics, which might influence the price of the CAT bond spread paid by the sponsor. For a CAT bond the sponsor, the SPV and the issue volume are always stated. Furthermore, the main characteristics of CAT bonds are the trigger mechanism, the type of peril, the peril region and the rating of the bond. According to Weber (2011, chapter 5) there are four main types of triggers: indem-nity triggers, industry loss triggers, parametric index triggers and modelled loss trig-gers. There is another category of triggers, the so-called hybrid triggers, which combine two or more main trigger types. The CAT bonds which use an indemnity trigger are structured to benefit from an excess-of-loss coverage, which is comparable to a standard reinsurance contract. If the loss of the sponsor exceeds a predetermined volume, the proceeds of the CAT bonds issued are used by the SPV to cover the claim payments to the sponsor. For the industry loss triggers, the CAT bond losses are determined with reference to an industry loss index. Thus, if the losses of the whole insurance sector are above the predetermined volume, the sponsor receives a claim payment. Parametric triggers are measured parameters, such as wind speeds or earthquake intensity, of the relevant catastrophic event which trigger the claim payments. So parametric triggers do not depend on claim sizes, but on the severity of the catastrophic event. Last, the modelled loss triggers are used for synthetic portfolios of assets exposed to different catastrophic events. They require physical parameters of the catastrophe events which are entered into an escrow model to estimate the relevant losses.
The last three main types of triggers together are also referred to as non-indemnity triggers. The indemnity trigger is directly related to the loss incurred by the sponsor, while the non-indemnity triggers are not (Braun, 2015). Therefore, the non-indemnity triggers expose the sponsor to basis risk, since the actual loss incurred by the sponsor is in general not perfectly correlated with the variable referenced by the trigger. The type of peril and the type of region together specify the natural hazard risk se-curitised in CAT bonds (Braun,2015). The type of peril relates to the underlying type of catastrophic event, where earthquakes, windstorms and hurricanes are best known. The type of region, or covered territory, relates to the geographic area in which a catas-trophic event has to occur and is mostly defined in terms of countries, regions or states. The most common regions are the United States, Europe and Japan.
According to Galeotti et al. (2013) the purpose of a CAT bond rating is to provide independent and professional information for the investors. Since buyers use ratings to compare yields on CAT bonds with the yields of other corporate securities, Cummins (2008) argues that obtaining a financial rating is a critical step in issuing a CAT bond. But because CAT bonds are fully collateralized, the CAT bond ratings have the ten-dency to be determined by the probability that the bond principal will be hit by a catastrophic event. This means that the bond ratings actually only indicate the layer of catastrophic risk coverage provided by the bond.
3.2.3 Pricing methods for CAT bond spreads
When calculating the price of the CAT bond spread, the main characteristics of the CAT bond will possibly have an influence on the price of the spread. In addition to these main characteristics there are also other factors which might influence the price of the spread. The most important factors are the expected loss, the number of peril types, the number of peril regions, the state of the traditional reinsurance market, the probability of the occurrence of a catastrophic event and the state of the financial mar-ket. The expected loss of a CAT bond is defined as the best estimate of the average
Wang2 transformation model. Using the notation of Galeotti et al. (2013), the linear model has the form:
SCAT = α + β · EL +
N
X
i=1
γi· yi+ ε,
where α is a constant, β is the “price” per unit expected loss, γi (i = 1, ..., N ) is the
“price” per unit factor risk yi, N is the number of factors yi and ε is the error term.
Next, the loglinear model has the form (Galeotti et al.,2013): ln(SCAT) = α + β · ln(EL) +
N
X
i=1
γi· yi+ ε,
with α a constant, β the “price” per unit of the logarithm of the expected loss ln(EL), γi (i = 1, ..., N ) the “price” per unit factor risk yi, N the number of factors yi and ε
the error term. Last, the Wang2 transformation model has according toGaleotti et al. (2013) the form:
SCAT = 1
2 · Qk(Φ
−1(P F L) + λ) + Q
k(Φ−1(P LL) + λ) + εk,λ,
where PFL is the probability of the first loss, PLL is the probability of the last loss and λ is the market price of risk, that is, the “price” per unit total risk. Qk stands
for the Student’s t-distribution with k degrees of freedom, Φ for the standard normal distribution and εk,λthe error term. Beside these common used models, other and more
advanced models can be used to calculate the price of the CAT bond spread.
Among others, Braun (2015), Galeotti et al. (2013) and G¨urtler et al. (2014) have explored the possible factors affecting the price of the CAT bond spread. Braun(2015) and G¨urtler et al. (2014) use a linear model, while Galeotti et al. (2013) use both the linear model, the loglinear model and the Wang2 transformation model and compare the models with each other. They all conclude that the expected loss has the greatest influence on the price of the CAT bond spread and therefore should always be included. Furthermore, Braun (2015) concludes that the peril region, the credibility of the sponsor, the state of the traditional reinsurance market and the BB corporate bond spread have major influence on the price of the CAT bond spread beside the expected loss, based on his data set. He also states that the issue volume, the trigger type and the type of peril have little influence on price of the CAT bond spread.
Galeotti et al. (2013) find that the rating, the type of peril and the peril region influence the price of the spread mostly. They also state that the time to maturity and the trigger type partly influence the price, depending on the considered period.
The main conclusion of G¨urtler et al.(2014) is that the financial crisis significantly affected the price of the CAT bond spreads and that the perceived risk of CAT bonds increased after natural catastrophic events. In addition, they state that the type of peril, the number of peril types, the peril region, the number of peril regions, the rating of the bond, the state of the traditional reinsurance market and the corporate spreads also influence the price of the CAT bond spread.
3.3
Earlier research on using risk mitigation techniques
As stated above, the theoretical pricing of CAT bond spreads is intensively discussed, among others byBraun(2015),Galeotti et al.(2013) andG¨urtler et al.(2014). However,
the comparison of the use of risk mitigation techniques is far less discussed in literature. According to the author of this thesis, most of the earlier research on the comparison of the use of traditional reinsurance and CAT bonds is written from a theoretical point of view and does not include all various costs associated with the risk mitigation tech-niques. In contrast, this thesis approaches the problem in a more practical manner and also takes into account the Solvency II capital requirements. The author of this thesis is aware of the fact that the Solvency II standard formula is not considered as the ‘best’ risk measure in the literature, but it has become a valid risk measure now that it is applied by the prudential insurance supervisor.
Nell & Richter (2000) address the trade-off between basis risk and transaction cost by introducing a simple model that analyses CAT bonds and traditional reinsurance as sub-stitutional risk management tools in a standard insurance demand theory environment. They find that, given a certain reinsurance budget, the existence of insurance-linked securities such as CAT bonds changes the structure of the demand for reinsurance. Namely, the optimal mix of risk allocation instruments includes traditional reinsurance contracts for the coverage of small losses and insurance-linked securities for the coverage of large losses.
Also,Richter(2003) investigates how the trade-off between default or credit risk and basis risk affects the optimal risk management solution, when traditional reinsurance and insurance-linked securities are used simultaneously. Consistent with the findings of Nell & Richter (2000), he finds that an insurance-linked security is primarily used to replace traditional reinsurance for high losses. Moreover, he concludes that in the presence of credit risk, insurance-linked coverage is used always if it has some quality as a hedging tool. Furthermore, Nell & Richter (2004) look at the problem from an expected utility approach and have a conclusion that is in line with bothNell & Richter (2000) and Richter(2003). Another study, conducted by Ling & Fei(2007), also states that CAT bonds increase the reinsurance compensation when the loss volume is low and decrease the reinsurance compensation when the loss volume is high. The optimal portfolio should therefore consist of traditional reinsurance for low losses and CAT bonds for high losses, which is in line with the findings of the other studies described here.
Doherty & Richter(2002) show that if the insurance-linked security is without trans-action costs, it is always optimal to purchase some insurance-linked coverage as long as there is a positive correlation between the index where the insurance-linked security is based on and the actual losses the insurer faces. They also describe the concept of gap in-surance, a policy that covers the difference between the recovery on the insurance-linked security hedge and the own loss of the insurer, and find that a hedge with insurance-linked securities is always supplemented by a positive amount of gap insurance.
Furthermore, B¨auerle (2004) considers a stochastic risk reserve process where the risk exposure is dynamically controlled by applying traditional proportional reinsurance and by issuing CAT bonds. She finds that CAT bonds can only be a substitute for traditional reinsurance on a limited scale, where the number of CAT bonds is always bounded. She states that CAT bonds can only be used when the correlation between the trigger event and the losses of the insurer is large enough and when the insurer faces a moderate premium rate difference.
Last, Finken & Laux (2009) show that CAT bonds can play an important role in the pricing of traditional reinsurance contracts when there is asymmetric information between inside and outside reinsurers about the risk of an insurer. They find that a CAT bond with a parametric trigger or an index trigger is insensitive to asymmetry in information and thus can change the equilibrium in the traditional reinsurance market. The introduction of CAT bonds gives low-risk insurers an alternative for traditional reinsurance, provided that the basis risk is not too high, and therefore leads to less cross-subsidisation in the traditional reinsurance market.
