On the Basis Risk of Industry Loss Warranties

Seminar Paper, 2012

29 Pages, Grade: 2,0


Table of contents


Table of figures

Index of tables

Table of symbols

1 Introduction

2 Characteristics of Industry Loss Warranties
2.1 Examples of an Industry Loss Warranty contract
2.2 Basis Risk
2.3 Comparison with other risk-transfer instruments

3 Simulation Study
3.1 Approach
3.1.1 Measuring basis risk
3.1.2 Premium calculation
3.1.3 Risk measurement
3.2 Numerical analysis
3.2.1 Value at risk and tail value at risk
3.2.2 Varying coefficient of correlation
3.2.3 Varying industry loss trigger
3.2.4 Varying retention
3.2.5 Varying limit of protection

4 Summary


Eidesstaatliche Erklärung


illustration not visible in this excerpt

Table of figures

Figure 1: The transparency and basis risk for various types of triggers

Figure 2: Comparison of value at risk and tail value at risk

Figure 3: Basis risk depending on coefficient of correlation

Figure 4: ILW price depending on coefficient of correlation

Figure 5: Basis risk depending on industry trigger Y

Figure 6: Premiums depending on retention

Figure 7: Premiums depending on limit of protection

Index of tables

Table 1: Comparison of risk-transfer instruments

Table 2: Input parameters of the reference contracts

Table of symbols

illustration not visible in this excerpt

1 Introduction

The following paper discusses industry loss warranties (ILWs). The aim of this essay is to analyze basis risk with the help of Excel simulation study and to perform a risk and pricing sensitivity analysis. Furthermore, on the basis of obtained results the hedging effectiveness of ILW contracts in comparison to traditional reinsurance shall be assessed.

In company with traditional reinsurance and catastrophic bonds (cat bonds) ILWs protect buyers against natural catastrophes. The increased number of natural disasters in last years (Hurricane Katrina and Ivan in 2005, Hurricane Irene in 2011) led to lack of supply capacity in the traditional reinsurance and retrocession market. Insurers required additional capital. Therefore new and innovative catastrophic instruments – such as industry loss warranties or cat bonds – were developed (see Gatzert and Schmeiser, 2009, p.2).

These new index-linked instruments have several advantages in comparison to tradi­tional reinsurance, e.g. reduction of moral hazard or lower underwriting costs, but a potential buyer has also to consider the drawbacks: The most important one is basis risk (see Gatzert and Kellner, 2011a, p. 132).

In the beginning this paper describes the characteristics of ILWs and discusses their pros and cons in comparison to other insurance instruments. In addition, the most com­mon definitions of basis risk are introduced. An introduction of simulation study follows, beginning with a theoretical presentation of the approach used in the study. Subsequently, every single step as well as the formulas and the methods used are described. A following numerical analysis discusses the obtained results from the simulation study and sensitivity analysis. Lastly a conclusion is drawn, where ILWs and their hedging effectiveness on the basis of gained information are compared to the traditional reinsurance.

2 Characteristics of Industry Loss Warranties

ILWs cover industry-wide losses caused by natural catastrophes. The payoff is linked to two triggers or, depending on the type of ILW, to one. A trigger is a certain preset threshold. There are an indemnity-based trigger[1] and an industry trigger in case of indemnity-based ILW or only industry trigger in case of binary ILW. Industry trigger is “linked to the value of an independent index, such as an industry loss index, or a parametric index, which is linked to a certain outcome (e.g. the intensity of earthquake activity or wind speed in a specified region).” (SwissRe sigma 4/2009, 2009, p. 4). The most popular indices that provide a basis for ILW’s industry trigger are ISO’s Property Claims Services (PCS) in the US, SwissRe’s sigma and Munich Re’s NatCat SERVICE in Europe. Indemnity trigger is the insured loss of policyholder. Both triggers are individually defined in the contract.

In the beginning the primary buyers and sellers of ILWs were insurers and reinsurers, nowadays they are being mostly traded by hedge funds. The hedge funds eliminate the indemnity trigger, what transforms the ILW to a derivative (see SwissRe, 2009, p. 16). Consequently this form of ILW – the binary – depends only on index trigger. In case of an indemnity-based contract both triggers – indemnity and index trigger – have to be hit before the buyer is entitled to receive a payoff. The presence of indemnity triggers makes ILWs similar to traditional reinsurance, what is in many countries relevant for ILWs to be accepted as risk transfer instruments for reducing solvency capital require­ments. But this threshold is usually set very low in order to reduce company specific underwriting costs (see Gatzert and Schmeiser, 2009, p. 5). Since the indemnity trigger in case of an indemnity-based contract is very likely to be exceeded, the compensation depends only on second trigger: The industry losses. The data for industry losses is provided by independent agencies, thus the complexity of contract design is low, the transaction costs are minimal and hence ILWs are easy to underwrite.

2.1 Examples of an Industry Loss Warranty contract

The contracts for ILWs may look like one of the following examples (see Ishaq, 2005, p. 76):

- A hurricane with industry-wide loss in Texas and Florida in excess of USD 5bn
- A tsunami with industry-wide loss anywhere in the world in excess of USD 10bn but less than USD 25bn
- An earthquake with industry-wide loss in California in excess of USD 10bn and with company loss in excess of USD 100,000

In the first example the payout will only occur if the hurricane causes more than USD 5bn damage to the industry in Texas and Florida. In the second example the trigger is in between USD 10bn and USD 25bn, i.e. the insured company will not get the premium if the losses exceed USD 25bn or go below USD 10bn.

The above two cases indicate a binary contract, i.e. the compensation depends only on the industry-wide loss index, whereas the third example illustrates a so-called indem­nity-based contract. In these contracts not only the industry-wide threshold (USD 10bn in California) has to be exceeded, but also the loss of the policyholder has to amount more than USD 100,000 in order to receive the claims pay off.

Swiss Re’s sigma 4/2009 provides another good example of typical ILW with following parameters:

Term: 12 months from January 1st, 2010

Industry loss attachment (warranty): USD 20bn

Limit of protection: USD 10m

Retention: USD 10,000 (usually small)

Rate-on-line: 10 %

Reporting period: 36 months from the date of loss

According to the data, if a natural catastrophe occurs within the next 12 months starting from January 1th, 2010 and the industry-wide damage exceeds USD 20bn, the policy­holder will receive a payoff in the amount of USD 10m. If ILW contract is double triggered (indemnity-based contract), the indemnity trigger also has to be hit to fulfill the requirements for a payoff. In this case it means, that the sustained loss of sponsor must exceed USD 10,010,000 (limit of protection and retention). The price for the protection amounts to USD 1m. If industry-wide losses are less than USD 20bn, the buyer has 36 months to claim the premium, if the damage hits the preset threshold.

The payment modalities may differ. For instance, there is an option of a linear payoff. Applied to above example, the linear payoff between industry losses of USD 20bn and USD 30bn means that in the event of a USD 20bn or less the policyholder would receive 0 % of premium, in the event of a USD 25bn loss 50 % of protection limit (i.e. USD 5m) and if the damage reaches USD 30bn limit or higher the payoff is 100 %, i.e. USD 10m.

2.2 Basis Risk

As the preceding paragraphs indicate the industry loss warranties always contain a cer­tain basis risk. Zeng (2000) defines basis risk as a “conditional probability that the ILW policy does not pay off given the actual loss sustained by the policyholder exceeds a critical level.” (Zeng, 2000, p. 27). It means that sustained losses of the insured company are severe while the industry-wide losses are not triggered, so the damage is not covered. It can occur if the policyholder’s losses and industry-wide losses are not fully correlated. (see Zeng, 2000, p. 27; World Economic Forum (WEF), 2008, p. 18-19). Basis risk means a difference between index based payoff and the company’s actual losses (see Gatzert, Schmeiser and Toplek, 2007, p. 3; WEF, p. 8). On the opposite side, the discrepancy can also lead to a basis gain (see Zeng, 2000, p. 27), i.e. the actual loss is quite small whereas the industry-wide loss is substantial and exceeds the threshold leading to pay out.

Basis risk varies on the trigger used, on the portfolio of sponsor, on the index data quality and on the specific peril (see WEF, 2008, p. 18). There are various types of triggers; some of them imply greater basis risk than others:

- An industry loss index is based on the industry-wide index of losses provided by an independent reporting agency like PCS in the US.
- An indemnity trigger depends on the actual loss of the policyholder.
- A modeled loss trigger determines the losses by entering the actual physical data into an agreed-upon model, which then calculates the losses.
- In a Modeled Industry Trigger Transaction (“MITT”) the industry index is calculated post-event using modeled loss techniques.
- A pure parametric trigger is based on the actual reported peril, e.g. earthquake magnitude or wind speed of hurricane.
- A parametric index is a refined version of a pure parametric trigger using more complicated formulas and more detailed measurements (see WEF, 2008, p. 10; SwissRe, 2009, p. 6).

While investors seek for more transparency, the sponsors attach more importance to basis risk. Figure 1 illustrates the six types of trigger depending on basis risk exposed to sponsor and the transparency for investors.

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Figure 1 : The transparency and basis risk for various types of triggers, Source: SwissRe sigma No. 4/2009

As stated in the WEF Report, 2008, basis risk will also vary according to the diversity of sponsor’s portfolio, “the quality of the risk model used to estimate the impact of cer­tain catastrophic events on the specific portfolio for which protection is sought, the quality of the data available with respect to such portfolio, and on the specific peril.” (WEF, 2008, p. 18). The possible negative impacts of basis risk have to be identified and minimized via internal risk management.

2.3 Comparison with other risk-transfer instruments

Comparing industry loss warranties to other elected insurance-linked securities helps to understand the advantages and disadvantages of this instrument. It is common practice in the literature (see Gatzert and Schmeiser, 2009, p. 10; Ishaq, 2005, p. 77; SwissRe, 2009, p. 24) to compare ILWs to cat bonds and traditional reinsurance. The following table summarizes the attributes of mentioned risk transfer instruments on the basis of different criteria.

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Table 1: Comparison of risk-transfer instruments

Complexity and costs of the contract

As already mentioned in the preceding paragraphs (see the introduction to this chapter) an ILW contract can be designed in two ways: Binary contract that transforms ILWs into a derivative or indemnity-based, where payoff depends on two triggers (see Gatzert and Schmeiser, 2009, p. 5; SwissRe, 2009, p. 16). Regardless of the contract’s concept the industry loss triggers are always index based. The high transparency of index makes the underwriting of ILWs and claim processes simple and therefore less expensive. In fact, the integration of index leads to high standardization of ILW contracts. Cat bonds and traditional reinsurance require customized contracts. For instance, the level of an attachment point has to be set, so the seller has to estimate the buyer’s portfolio and his future losses. Particularly cat bonds are complex and demand an individual analysis of sponsor’s business (see Gatzert and Schmeiser, 2009, p. 5; Ishaq, 2005, p. 78).

The transaction costs relate to complexity of contract design. If the underwriting and claim processes are simple, transaction costs will be set at low level. Drawing up an ILW contract requires no legal costs or due diligence; the index is the only pricing component. Hence, the documentation is simplified and the costs are kept low. Due to the higher complexity of cat bonds and traditional reinsurance the transaction costs are higher. The cost advantage of ILW is passed to the buyer by offering lower nominal amounts. E.g. an ILW offering starts with USD 1m layer limit, while cat bonds need to cover at least USD 100m to be economical (see Gatzert and Schmeiser, 2009, p. 5; WEF, 2008, p. 14).

Basis risk

As mentioned above (see chapter 2.2) basis risk is inevitable for index-based instru­ments. Therefore, basis risk of ILW can be significant. Since the traditional reinsurance doesn’t use index at all, basis risk is negligible (see Ishaq, 2005, p. 77).


[1] In the following, the indemnity-based trigger is synonymously named the „indemnity trigger“, the „priority“, the „retention“ or the „attachment point“.

Excerpt out of 29 pages


On the Basis Risk of Industry Loss Warranties
Friedrich-Alexander University Erlangen-Nuremberg
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ISBN (eBook)
ISBN (Book)
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The following paper discusses industry loss warranties (ILWs). The aim of this essay is to analyze basis risk with the help of Excel simulation study and to perform a risk and pricing sensitivity analysis. Furthermore, on the basis of obtained results the hedging effectiveness of ILW contracts in comparison to traditional reinsurance shall be assessed.
basis risk, industry loss warranties, ILWs, traditional reinsurance, reinsurance, insurance, risk management, simulation study, index-linked instrument, catastrophic reinsurance instrument
Quote paper
Elena Rudnikevic (Author), 2012, On the Basis Risk of Industry Loss Warranties, Munich, GRIN Verlag, https://www.grin.com/document/190947


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