Tag Archives: cat-bonds

Some stylized facts about large risk covers

A couple of weeks ago, David Cummins (here) was giving a talk in Laval University. And we’ve seen a series of extremely interesting graphs and figures about catastrophe reinsurance market, as well as Cat Bonds prices. The first one was the rate one line index for catastrophe reinsurance (the rate on line is the excess of loss premium expressed as a percentage of the reinsurance cover), from Guy Carpenter (2010, page 10 here).

Following hurricane Andrew in 1992, prices went up quite high. But following hurricane Katrina (which is, so far, the most costly insured disaster following the second World War, with a cost exceeding 70 billions US$ – 2008 $ – while Andrew was only 24 billions – again 2008 $), the bump is much smaller. I though cycles where much larger in the reinsurance industry.

Then there was a discussion about cat bond pricing, with a graph from Lane Financial (2010, page 13, here) with the ratio premium over expected loss

This is extremely interesting, even if it is only about cat bond, and not about reinsurance covers. Usually, when we introduce premium principles in actuarial courses, we start with the pure premium, i.e.

http://freakonometrics.blog.free.fr/public/perso2/chargement-PP-02.gifThen we explain that with such a price, ruin probability is certain (with an infinite time horizon), so we need to add a safety margin, and a standard idea (but that can be criticized since the expected value has – usually – nothing to do with the variability) is to add a loading proportional to the pure premium. Then the premium is

http://freakonometrics.blog.free.fr/public/perso2/chargement-PP-01.gifFor small risks, like motor insurance, the loading is not huge. Actually, if risks have finite variance, it can be obtained simply using the central limit theorem (but I’ll get back on that point in a couple of weeks). Here, we see that loading http://freakonometrics.blog.free.fr/public/perso2/thetaloading.gif can be large (up to 400% in 2009).

An finally an updated graph with a comparison between BB corporate bondscoupon, and BB catastrophe bonds coupon,

(I guess the source is again Morton Lane). I found surprising the recent gap (following Katrina) between the two spreads. I guess financial market started to be scared and understood that catastrophes are not that rare…. I wonder what 2008 and 2009 prices looked like.

Measuring and Covering Catastrophic Risks

Short course on Measuring and Covering Catastrophic Risks at the Maresias Conference in Sao Paulo, April 2009. Slides are now online.

There has been recently a large interest in catastrophic risks, especially following hurricane seasons in 2004 and 2005. But measuring those risks and providing an appropriate cover might be difficult. In this course, we will first describe those risks, especially climate risks (or climate related), man based risks (large fires or business interuption), and mortality risks. For those risks, we will also discuss possible covers, from classical (re)insurance to securitization (cat or mortality bonds) or insurance-linked securities (cat options). As we will see, the pricing of those products can simply be related to the choice of a risk measure. We will then discuss risk measures for large risks, and conclude with the aggregation issue.

Cat bond securitization will be studied in this course, explaining why they can be an additional tool (instead of an alternative technique) to insure against natural catastrophes.
while a Cat Bond mechanism is the following
For a more fancy description, it can be described as follows,

Two examples of natural catastrophes securitization will be studied carefully

  • WinCat : Winterthur securitization in 1997
  • The Mexican Earthquake 2007 Cat Cond.

The dataset used in this example was kindly provided by Dr. Miguel A. Santoyo (here)

  • Longevity and Mortality Risk