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Water, wind, and wildfire. It’s been a devastating three months for the U.S.

Total insured losses from Hurricanes Florence and Michael, and the Camp and Woolsey wildfires are estimated by RMS in the range US$18.6 billion to US$28 billion (see table below):

September 1Hurricane Florence$2.8 – $5.0 billion

October 8Hurricane Michael$6.8 – $10.0 billion

November 8Camp Wildfire$7.5 – $10.0 billion

November 8Woolsey Wildfire$1.5 – $3.0 billion

TOTAL INSURED LOSSES $18.6 – $28 billion

While California wildfires may seem far removed from Atlantic storms, for capital markets investors the fires may make the difference to how 2018 is remembered. Insurance Linked Securities (ILS) eyes are now trained on multi-peril aggregate catastrophe bonds.


Diversifying to Grow

Bundling multiple perils under a single coverage makes good sense for the capital markets.

ILS sponsors benefit from simplicity and efficiency of risk transfer. Multi-peril transactions mimic what traditional (re)insurance can provide, and the relative frictional costs of issuance are reduced. On the other side of the trade, ILS investors have historically been happy with the diversification benefits and returns of broader coverage.

Indeed, multi-peril ILS transactions are nothing new. U.S. hurricane and earthquake risks have been partnered for decades. These were quickly packaged with international peak-perils, like European windstorm and Japanese earthquake risk.

The mid-2000s then saw severe convective storm, winter storm, and wildfire introduced to the multi-peril mix. Before long, investor appetite for diversifying risk drove down spreads, encouraging the inclusion of volcanic eruption and even meteorite impact in cat bonds.

As comfort around multi-peril and non-modeled risk grew, so too did issuance. USAA, Chubb, and Nationwide Mutual have all contributed significantly to the multi-peril market, sponsoring the Residential Re, East Lane, and Caelus series respectively.

Multi-peril Breakdown

These transactions typically trigger on an annual aggregate indemnity basis. In other words, payouts are a function of reported claims across multiple events in a given year.

Named storms usually drive the risk in such deals. Thereafter, depending on region and attachment level, severe convective storms and earthquakes typically contribute most to expected loss, followed by winter storms and wildfires.

Annual aggregate structures can be particularly sensitive to attritional losses from frequent perils such as tornados. As a result, transactions tend to include a minimum event severity to mitigate the impact of small events. Nonetheless, annual aggregate structures can be subject to hidden risk if the perils are not well quantified.

Most multi-peril aggregate bonds in the market include wildfire risk as a modeled peril. Its contribution to risk, however, tends not to dominate the headline metric.

That may now need to change. While wildfire has historically been considered a source of attritional loss, the magnitude of individual losses in 2017 (Tubbs, Atlas, and Mendocino Complex) and 2018 (Camp and Woolsey) is forcing investors and issuers to rethink the potential for wildfires to contribute significantly on an occurrence basis.

Contributions from the 2017 wildfires to the 2014 Residential Re aggregate erosion, for example, were on par with the combined losses from Harvey and Irma. And the 2018 wildfires have highlighted the impact of the losses caused by Florence and Michael.

Rethinking Wildfire

2017 revealed the potential for wildfire to cause extensive damage. Reconnaissance of the Wine Country wildfires supported an economic loss estimate of US$6 billion to US$8 billion.

As with all catastrophes, this and last years’ devastating wildfires have surfaced important insights. The events emphasized the effects of smoke in driving both damage and evacuation costs. The events also illustrated the significant role of embers and Diablo winds in fire propagation.

Leer Wildfire

Typical large ember found near a home burned in the Northern California Tubbs Fire, October 2017 (Image Credit: RMS)

Stimulated by liability concerns, the summer of 2018 saw the first wildfire-only catastrophe bonds.

Cal Phoenix Re Ltd. 2018-1 and SD Re Ltd. 2018-1 offer California wildfire liability coverage on an indemnity basis to Pacific Gas and Electric (PG&E) and Sempra Energy respectively.

California utility providers are responsible for insurable wildfire losses that are caused by their infrastructure. This not only includes insured and uninsured property and casualty exposure, but also business interruption and fire suppression costs.

If PG&E is found to be responsible for the ignition of the Camp fire in Butte County, then the Cal Phoenix bond will provide a full US$200m payout to PG&E to help cover its liability. This coverage, though well received, would be dwarfed by the overall size of the loss, which RMS estimates is of the order of US$7.5 billion to $10 billion.

If the potential impact to wildfire-only transactions isn’t enough to make investors question their current understanding of the peril, then the distressed prices of some multi-peril annual aggregate bonds and collateralized reinsurance positions certainly will.

Building Understanding

The scale of impact from the Camp and Woolsey wildfires has rightfully brought the peril into focus.

Wildfires have the potential to generate significant annual losses – not only in aggregate, but also as individual events.

The need for wildfire coverage is evident, as is the appetite for multi-peril aggregate risk. Now more than ever, high-resolution loss modeling, which comprehensively captures the frequency and severity of potential impacts, is required to deepen insight and rebuild confidence in our understanding of the peril.

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Unpacking Basis Risk

When catastrophe strikes, it is not unusual for the insurance payout to differ from the policyholder’s expectation. The possibility of such a discrepancy is referred to as “basis risk”. The term, however, can be ill-defined and easily misunderstood. Therein lies the problem, without definition it is easy for the basis risk associated with a structure to remain unidentified and unquantified. If left unspoken, basis risk can lead to problems down the line, when events do occur. So, as a starting point, we can most simply define basis risk as the “difference between expectation and outcome”. Parametric insurance is most commonly associated with basis risk, though when defined like this, it becomes clear that basis risk exists within all insurance structures. For indemnity insurance, basis risk could stem from the possibility that a contract fails to pay because of a legal miswording; for a modeled loss trigger, the difference between modeled loss and measured loss after an event; and for pure parametric insurance, the difference between the index loss calculated from a wind speed measurement and the total actual loss. The primary drivers of basis risk vary between structures. To quantify basis risk, it is first necessary to identify the primary sources of uncertainty with respect to each structure. Once identified, the basis risk can then be quantified and communicated. Once quantified and understood, the structure can then be tailored to modify the expectation as appropriate. Let’s examine some typical methods for quantification of basis risk in two types of parametric structure. Pure parametric, in which a measured parameter is used to proxy the loss, and a simple modeled loss structure, where a modeled footprint is used with exposure, vulnerability, and financial models to create a modeled loss for the event. Pure Parametric A range of methods have been developed to assess basis risk in pure parametric structures, these can also be applied in modeled loss and indemnity cover. To develop this idea, we will use a theoretical example of a parametric wind trigger in which there is a linear payout based on the wind speed measured at a single location. Following the previous definition of basis risk, the expectation with this structure is that wind speed during an event correlates with total loss. Conveniently, it is possible to use catastrophe models to uncover this correlation. Each point in Figure 1 represents a stochastic event, with its associated modeled loss and modeled wind speed at the measurement location. Figure 1: Hazard against modeled lossThe form follows that of the vulnerability of the underlying exposure. The function that describes this relationship is contained within the index formula, which is used in combination with an exposure weight to transform the wind speed to an index loss. The results of this transformation of hazard to index loss are displayed in a basis risk plot (Figure 2): Figure 2: Basis risk plotThe correlation between the two variables is one measure of the overall basis risk. However, basis risk is a two-sided coin, it has positive and negative components, termed as overpayment and shortfall. Overpayment describes the situation in which the payout from a structure is greater than the loss experienced during an event, whereas shortfall describes the more important situation for the risk holder, in which the payout is less than the loss. It is more insightful to measure basis risk with respect to a target layer. Overpayment and shortfall can then be measured as a percentage of the total layer width. Figure 3 displays regions of shortfall and overpayment with respect to a target indemnity layer of 200 XS 200, for the same events as displayed in Figures 1 and 2. Figure 3: Shortfall and overpayment with respect to a target indemnity layerThe degree of shortfall or overpayment can then be calculated. The following formulae are commonly used to calculate the basis risk for parametric structures with a linear payout. We can calculate these basis risk metrics for all stochastic events, and produce conditional probability plots which describe the expected degree of overpayment or shortfall. Shortfall is conditional on an event exceeding an indemnity attachment, and conversely overpayment is conditional on an event attaching on the index side. Shortfall and overpayment can be further quantified and visualized using conditional probability plots. Figure 4 displays the probability shortfall or overpayment of exceeding a range of thresholds. As can be implied from Figure 3, and quantified in Figure 4, the example structure shows a moderate bias towards shortfall. Figure 4: Conditional probability plotUsing these methods, it is possible to understand and communicate the basis risk associated with the structure. This helps to refine the trigger mechanisms to a point where all stakeholders are comfortable with the levels of associated basis risk. It is important to note that while hazard and loss uncertainty can and should also be factored in, we should remember that basis risk metrics calculated within a model cannot account for all the uncertainty that exists. Indeed, basis risk can be most well understood if measured using independent models and methods. Minimizing Parametric Basis Risk Once quantified, there are ways to close the gap between the expectation and outcome. The simplest of these is to change the attachment level. If the expectation from a risk holder is that a payout should be received after any event that makes the news, then the index attachment level can be lowered, and the trigger can be biased towards overpayment. This transfer of basis risk from shortfall to overpayment comes at the cost of a higher premium. A less costly option may be to introduce a phased attachment, where there is a small binary payout at a lower attachment threshold, with the remaining principal more closely tied to an indemnity layer. This stepped payout mechanism may help to manage the reputational risk associated with a binary parametric trigger structure. A more technical approach to reducing basis risk requires a more detailed understanding of the sources of uncertainty. Within the confines of the model, the overall basis risk in pure parametric structures primarily derives from: The displacement of the exposure from the measurement station(s) The ability of the index formula to capture the vulnerabilities of the exposure One way to reduce the basis risk is to increase the number of measurement stations, and assign exposure to the station which best proxies the hazard at the exposure. Another is to use more index formulae to better capture the range of vulnerabilities. Modeled Loss The obvious extension is that a simple modeled loss based trigger solves both of these problems, where we effectively know the hazard at all locations, and can use the true vulnerabilities of the exposure. Surely this reduces the basis risk to zero? Not necessarily. The primary sources of uncertainty in a modeled loss trigger are often distinct from those in pure parametric. The nature of the uncertainty is also more structure specific, making it difficult to generalize the drivers of basis risk in “modeled loss”. For example, in different forms of modeled loss triggers, the process used to generate the modeled hazard footprint, or the development of loss curves from limited historical data might drive basis risk in a modeled loss trigger. The example of modeled loss draws out an important feature of basis risk; some sources of uncertainty can be quantified easily using models, and some cannot. A model is well placed to quantify the correlation between hazard and loss in a pure parametric structure, but less well equipped to convey the uncertainty that exists within itself, which can be relatively more significant in a modeled loss structure. In light of this, when assessing basis risk in modeled loss triggers we need step outside the confines of the model at hand, and assess the structure independently using external models and the real world. A daunting task, with project resources and the historical record often restricting the insight that can be gained, though one which can greatly enhance the success of the structure. On What Basis Importantly, and somewhat contrary to common perception, both modeled and un-modeled sources of basis risk exist in all structures. The balance between the two shifts depending on the dominant driver of uncertainty, be it within pure parametric, modeled loss, or indemnity. In all cases, identification, quantification, and communication are the keys to understanding basis risk. The benefits of a clear understanding of the basis risk are well worth the effort in attaining it. Structural decisions can be made with greater confidence, potential options can be measured against one another, and the expectation that a structure always pays out when there is a loss can be set appropriately. Ultimately, the potential for surprises is reduced with greater understanding, and the risk transfer is more likely to function as expected. Basis risk can never be entirely eradicated, though with the right analytical approaches it becomes much more manageable.…

Conor Meenan
Conor Meenan
senior consultant

Conor is a senior consultant in the Capital and Resilience Solutions team in London. He works on a broad range of catastrophe bond transactions, and has particular experience in modeling parametric structures, leading on recent innovative transactions including MetroCat Re Ltd. 2017-1.

Additionally, Conor researches the application of catastrophe models to public sector resilience initiatives. This includes modeling critical urban infrastructure in Mexico for 100 Resilient Cities, modeling linear transport networks in coastal U.S. states, and working with the U.K. Department for International Development to assess the suitability of a catastrophe risk pool in Asia.

Conor holds a masters in Natural Sciences from the University of Cambridge.


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