# Author Archives: Oliver Withers

Analyst, Capital Market Solutions, RMS
As a member of the advisory team within capital market solutions, Oliver works on producing capital markets’ deal commentary and expert risk analysis. Based in London, he provides transaction characterization to clients, for bonds across the market and supports the deal team in modeling transactions. He worked on notable deals for clients such as MetroCat Re and VenTerra Re. He also helped create the analytical framework for Miu Pricing, a product that provides price metrics to ILS funds. Oliver holds a BA in mathematics from the University of Cambridge and is a Level II candidate for CFA.

# Cat Bond Pricing: Calculating the True Rewards

Commentary in the specialist insurance press has generally deemed pricing of catastrophe bonds in 2015 to have bottomed out. While true in average terms, baseline pricing figures mask risk-return values. True risk pricing can be calculated only by considering all dimensions of loss, including seasonal variations and the time value of money. New analysis by RMS does just that, and shows that cat bond pricing has actually been higher in 2015 than it was last year.

Pricing of individual cat bonds is based largely on the expected loss—the average amount of principal an investor can expect to lose in the year ahead. Risk modelers calculate the expected loss for each deal as part of the transaction structuring, but to obtain a market-wide view based on consistent assumptions, we first applied the same model across all transactions to calculate the average expected loss.

Care must be taken as all loss is not equal, a fact reflected in the secondary-market pricing of catastrophe bonds. Because of the time value of money, a loss six months from now is preferable to a loss today: you can invest the money you are yet to lose, and collect coupons in the meantime. We have calculated the time-valued expected loss across more than 130 issuances in the secondary markets, which we have called Cat Cost. It is dramatically different than unadjusted values, as shown in Figure 1.

The next step to reveal the true level of cat bond pricing involves accounting for secondary market pricing quotes. Figure 2 plots the same Cat Cost data as Figure 1, but now includes pricing quotes of the bonds, which we gleaned from Swiss Re’s weekly pricing sheets. Also plotted is the “Z-spread”—this is the spread earned if all future cash flows are paid in full and the metric is calculated using a proprietary cash flow model which determines future cash flows (floating and fixed), and discounts back to the current market price. The difference between the two—the space between the top and bottom lines—is the Cat-Adjusted Spread, which measures the expected catastrophe risk-adjusted return.

We can see clearly that on 30 September, 2014 the Cat Cost was 1.53%, identical to the Cat Cost on the same day in 2015. However, this year’s cat-adjusted spread for that day is 2.52%, compared to 2.22% for 2014. In other words, the pricing of cat bonds at the end of the third quarter of 2015 was thirty basis points higher than it was on the same date in in 2014, relative to the risk and adjusted for the time value of money.

The astute will have noticed that the bond spread rises each year as the hurricane season approaches, and falls as it wanes. To account for this seasonal pricing effect, and to reveal the underlying changes in market pricing, we have split the analysis between bonds covering U.S. hurricanes and those covering U.S. earthquakes.

The findings are plotted in Figure 3, and the picture is again dramatic. It is clear that the price of non-seasonal earthquake bonds is relatively static, while hurricane bond prices rise and fall based on the time of year.

This analysis further shows—for both hurricane and earthquake bonds—that spreads were higher this year than last, relative to adjusted risk. Steep drops in excess returns masked roughly static end-of-year returns in the cat bond market, rather than reflecting a risk-based price decline. Despite the prevailing commentary, the catastrophe bond market is returning markedly more to investors today than it did a year ago, when it bottomed out. But only accurate risk and return modeling reveals the true rewards.

This post is co-authored by Oliver Withers and Jinal Shah, CFA.

### Jinal Shah

Director, Capital Markets, RMS
With more than 10 years of experience in the Insurance Linked Securities (ILS) market, Jin is responsible for managing investor relationships and new ILS product development at RMS. During his time at RMS, Jin has led analytical projects for catastrophe bond placements , and has designed new parametric indices to facilitate trading of index-based deals in peak zones, as well as introduced new pricing initiatives to the ILS market.

Jin currently focuses on pricing deals and managing portfolios with RMS ILS investor clients, and leads the development of Miu, the RMS ILS portfolio management platform. Jin holds a bachelor’s in Mathematics from The University of Manchester Institute of Science and Technology, and a master’s in Operational Research from Aston Business School and is a CFA charter holder.

# Rising Storm Surge Losses in the U.S. Northeast

Co-authored by Anaïs Katz and Oliver Withers, analysts, Capital Market Solutions, RMS

A recent article in Nature Communications, picked up by the BBC, identified a record mean sea-level rise of 5” (127mm) along the coastline north of New York City during 2009-10. Sea levels fluctuate between years; a swing of this size, however, was unprecedented.

This extreme rise in 2009-2010 has been attributed to the downturn of a major current called the Atlantic meridional overturning circulation (AMOC). As changes to sea levels are sensitive to multiple factors, there is volatility around this increase. The AMOC is one of the ocean’s dynamics that is known to have greatly changed over time. It has been shown that weakening and variation of the AMOC is linked to increases of greenhouse gas emissions.

Sea level rise is one of the most tangible and certain consequences of a warmer climate. Climate models suggest that even if greenhouse gas emissions were reduced sea levels will continue to increase. Such a dramatic fluctuation, as seen in 2009-10, highlights the potential for significantly elevated storm surge risk in the region and raises the question what will the impact of future long-term sea-level rise have on storm risk.

A study by Kopp et al. has attempted to predict probability bands for sea rise. The figure below shows the distribution of expected sea-level rise at New York City’s Battery Park throughout the 21st century. The 50th percentile projection of sea level rise is represented as the red line in the figure. Also shown are the maximum rises in sea levels associated with previous hurricane storm surges.

Based on RMS’ estimate of the impacts from hurricanes on residential and commercial property in the Northeast US (from New Jersey north), the 2010 estimate of storm surge contribution to hurricane losses is about 10%. Even where the activity of hurricanes does not change, sea level rise will increase the damage associated with hurricane storm surges. Based on Kopp’s estimates of sea level rise, by 2100 surge losses would contribute about 25% of total hurricane losses.

The largest recent hurricane loss occurred on October 29th 2012, when Superstorm Sandy made landfall near Atlantic City, NJ. Based on the RMS best loss estimate, Sandy caused insured losses between \$20 and \$25 billion, with much of the damage due to storm surge, not wind.

In terms of a simple extreme value analysis, the storm surge caused by Superstorm Sandy combined with the tide at New York City’s Battery Park was approximately a 1-in-450 year return period for that location. Based on sea level rise alone, this surge and tide combination at this location would move closer to a 1-in-100 year event by the end of the century. The figure below shows the return periods for a storm surge as high as Sandy’s occurring at New York City’s Battery Park, under different sea-level assumptions.

A direct result of increasing amounts of greenhouse gases in the atmosphere will be an increase in sea surface temperatures. While increased sea surface temperatures are likely to cause changes to the activities and intensities of hurricanes, there is no consensus among climate modelers as to the magnitude and direction of these changes. For this reason, the figure below does not consider potential changes in hurricane activity, but focuses solely on sea-level rise, for which there is much more of a general agreement.

While the impacts of climate change remain much debated, changes in loss potential will have material effects on the risk to insurers. With the appreciation of the significance of climate change coming to the fore, the next decades will pose a research challenge for the insurance industry, as to how to incorporate evidence for changes in the level of risk.

This post was co-authored by Anaïs Katz and Oliver Withers.

### Anaïs Katz

Analyst, Capital Market Solutions, RMS
As a member of the advisory team within capital market solutions, Anaïs works on producing capital markets’ deal commentary and expert risk analysis. Based in Hoboken, she provides transaction characterizations to clients for bonds across the market and supports the deal team in modeling transactions. She has woked on notable deals for clients such as Tradewynd Re and Golden State Re. Anaïs has also helped to model and develop her group’s internal collateralized insurance pricing model that provides mark to market prices for private transactions. Anaïs holds a BA in physics from New York University and an MSc in Theoretical Systems Biology and Bioinformatics from Imperial College London.

# Modeling the Deal of the Year

The first storm surge catastrophe bond ever released in the insurance-linked securities markets was awarded “Deal of the Year” by Bond Buyer and the Insurance Risk Awards. What what is that made this bond, issued for New York’s Metropolitan Transit Authority (MTA) so special?

Sandy may not have been the strongest tropical storm to make landfall in the United States, but its insured losses of \$20-25 billion rank it as one of the most costly. And like Katrina, most of the losses were not driven by high winds, but by coastal flooding from extreme storm surge.

The MTA was badly hit, with roughly \$5 billion in flood damages. Alongside high industry losses, the traditional reinsurance market hardened, so to obtain funding the MTA turned to alternative sources through MetroCat Re Ltd., a parametric catastrophe bond modeled by RMS Capital Markets.

A parametric bond is different from a traditional reinsurance agreement in that it is triggered when a hazard value—in this case water level—reaches a specific threshold, as opposed to to a financial threshold trigger.

Although seldom seen in traditional reinsurance, parametric triggers are more frequently used in alternative capital. There’s no need to study detailed exposure and claims information before or after the event and payment can be made in weeks, not years.

How did RMS help?

Before Sandy, simple storm surge models based on storm parameters—such as angle of landfall, forward speed, and central pressure—were considered sufficient to model storm surge risk. Sandy, however, showed that it is important to understand the full lifecycle of a storm. Sandy wasn’t even a hurricane at landfall, therefore the parameters in simple storm surge models would have predicted a far smaller surge and missed a lot of the potential damage.

RMS provided a detailed understanding of the surge risk to MTA’s assets using the RMS version 13.0 North Atlantic hurricane model, which incorporates a state-of-the-art, hydrodynamic storm surge model to capture the impacts of local tide interactions, seafloor, and coastline on the size of the storm surge.

The modeling results were highly successful, with the surge across the region matching closely the observed surge:

Comparison of a) FEMA and b) RMS surge extents for Sandy around Battery Park, NY

Verification: RMS’ Sandy footprint against observed water heights

New York’s complicated coastline needed to be modeled in detail to accurately understand how the surge would develop—for example, around the Robert F Kennedy Bridge, the water shallows, leading to relatively uncorrelated areas that separate New York harbor from the Long Island sound. This correlation needed to be considered when we were constructing the parametric trigger for MetroCat – only triggering from one location wasn’t enough, therefore we based the index on both New York harbor and Long Island water levels.

We estimate a 20% chance that for a hurricane in the U.S. Gulf States, coastal flooding will dominate the losses. In the northeast U.S., the risk rises to 30%. MetroCat’s success showed that the ILS market can be a viable risk transfer mechanism for coastal storm surge flooding, if it is supported by detailed, holistic modeling of this complicated peril.