You are the CEO of a Florida based property insurer. Your company sells homeowners insurance in the

state of Florida only. Because of the narrow business focus, your company is highly exposed to

catastrophic losses. For simplicity we are going to ignore all non

$-$

hurricane related losses

$($

We are

assuming that they have already been paid, just as we are assuming all of the premiums for the policies

you sold have already been collected

$)$

$.$

$$The total surplus that your company has is $

$7$

$0$

$0$

$$million$.$ You

control

$1$

$0$

$$percent of the Florida homeowners insurance market. In other words, you can expect your

share of all hurricane related losses to be

$1$

$0$

$\%$

$$of the total insured hurricane losses. However,

historically your share of hurricane losses has been anywhere from

$5$

$$percent to

$1$

$5$

$$percent of total

insured losses. Your company is currently rated A by A

$.$

$$M

$.$

$$Best and you have been told by A

$.$

$$M

$.$

$$Best

that if your surplus falls below $

$4$

$0$

$0$

M you will be downgraded. You have consulted with your

reinsurance brokers and you have been able to narrow down your capital structure decisions to one of

four choices.

$1$

$.$

$$Do nothing. Do not purchase any reinsurance, nor do anything with Cat Bonds. In other words,

go bare.

$2$

$.$

$$Purchase a reinsurance contract that has a $

$1$

$2$

$5$

M policy limit

$($

per occurrence

$)$

$$and a $

$2$

$5$

M

retention. This reinsurance contract will cost $

$4$

$0$

M

$($

out of your $

$7$

$0$

$0$

M surplus

$)$

$.$

$3$

$.$

$$Purchase a reinsurance contract that has a $

$3$

$0$

$0$

M policy limit

$($

aggregate

$)$

$$and a $

$1$

$0$

$0$

M

aggregate retention. This reinsurance contract will cost $

$1$

$0$

$5$

M

$($

out of your $

$7$

$0$

$0$

M surplus

$)$

$.$

$4$

$.$

$$Issue a Catastrophe bond that pays you $

$2$

$0$

$0$

M if aggregate industry losses exceed $

$2$

B in a

storm season. The cost of issuing the cat bond is $

$2$

$5$

M

$($

out of your $

$7$

$0$

$0$

M surplus

$)$

$.$

Based on these choices, you must answer the following questions

$($

Justify each answer

$)$

$$using simulation

analysis:

$1$

$.$

$$Which capital structure yields the highest insurer capital?

$2$

$.$

$$Which capital structure yields the lowest likelihood of bankruptcy? What is that likelihood?

$3$

$.$

$$Which capital structure yields the lowest likelihood of a ratings downgrade? What is that

likelihood?

$4$

$.$

$$Which capital structure would you recommend, why?

$5$

$.$

$$Do your answers change if the prices changed? Suppose the price of the cat bond goes up to

$

$4$

$0$

M and the cost of reinsurance policy #

$2$

$$fell to $

$8$

$5$

M

$.$

$$Re

$-$

answer questions

$1$

$$through

$4$

$$with

the new prices.

$6$

$.$

$$What if

$2$

$0$

$1$

$6$

$+$

$$data were not included in the analysis, do your answers change?

a

$.$

$$Did the distributions change?

b

$.$

$$Re

$-$

answer questions

$1$

$$through

$4$

$$with the new data.

While doing the project, there are a few other questions you will need to answer:

$1$

$.$

$$Which frequency distribution did you pick? Why?

$2$

$.$

$$Which severity distribution did you pick? Why?

$3$

$.$

$$Some data is recorded for the years

$2$

$0$

$1$

$6$

$+$

$,$

$$but you question its accuracy. Is the data recorded

for

$2$

$0$

$1$

$6$

$-$

$2$

$0$

$2$

$3$

$$accurate$?$ Did you adjust the data recorded for

$2$

$0$

$1$

$6$

$-$

$2$

$0$

$2$

$3$

$($

at a minimum you

need to add

$2$

$0$

$1$

$9$

$-$

$2$

$0$

$2$

$3$

$$data

$)$

$?$

$$How did you make adjustments to it

$?$

$$If so

$,$

$$did it change your

answers? This is addition frequency "Year Frequency

$19161$

$19170$

$19181$

$19190$

$19201$

$19210$

$19221$

$19231$

$19241$

$19253$

$19261$

$19273$

$19281$

$19291$

$19300$

$19311$

$19321$

$19330$

$19340$

$19350$

$19360$

$19370$

$19381$

$19391$

$19400$

$19410$

$19420$

$19431$

$19441$

$19451$

$19461$

$19470$

$19482$

$19490$

$19501$

$19511$

$19520$

$19531$

$19540$

$19550$

$19561$

$19570$

$19580$

$19591$

$19600$

$19610$

$19620$

$19631$

$19640$

$19650$

$19660$

$19671$

$19680$

$19691$

$19700$

$19711$

$19722$

$19730$

$19741$

$19751$

$19760$

$19771$

$19781$

$19790$

$19800$

$19810$

$19820$

$19830$

$19841$

$19850$

$19861$

$19870$

$19881$

$19890$

$19900$

$19910$

$19922$

$19930$

$19940$

$19953$

$19960$

$19970$

$19980$

$19991$

$20001$

$20012$

$20020$

$20030$

$20044$

$20054$

$20060$

$20070$

$20080$

$20090$

$20100$

$20110$

$20120$

$20130$

$20140$

$20150$

$20171$

$20181$

$20191$

$20201$

$20211$

$20222$

$20231"$ This is the addition severity "Florida Losses $($$ Millions$)$

$$1,393\mathrm{.}48$

$