Cat Bonds

Question

An insurance company has sold insurance to cover damage that arises from hurricanes in the South
Texas area. If a hurricane occurs, the insurance company is faced with losses as it pays out claims. The
magnitude of the losses will depend on many factors: the severity of the hurricane and the type of
damage (wind, rain).
In a major hurricane, the losses to the company could be substantial. To hedge this risk exposure, the
insurance company buys a one year re‐insurance contract. The principal of the contract is $100 million.
The company self‐insures for $25 million; that is, it takes the first $25 million of losses. The contract is
structured similar to a bond. Absence an event, the company will pay a fixed rate of interest every six
months. If an event occurs, the company pays the accrued interest up to the day of the event. The bond
terminates and the principal minus the losses due to the event are paid to the re‐insurance company.
If a hurricane occurs, the loss distribution is described as follows: the losses are equal to $300 million,
with probability of 0.50, $50 million with probability of 0.25 and $20 million with probability 0.25.
Part A
How you would set the coupon of the re‐insurance contract so that the contract is valued at par? Please
explain in detail each step in your analysis. You are given the following information. The intensity is used
to determine the probability of a hurricane.
Intensity Period (years) Libor Zero Prices
0.02 0 ‐ 0.50 0.982652
0.04 0.50 – 1.00 0.965605
Part B
A hurricane is approaching Texas and is expected to make landfall in three days’ time. It is being
described as “the hurricane of the century” and is predicted to cause severe damage. You are an
executive of the insurance company and concerned that the re‐insurance coverage, described in Part A,
will be insufficient. What additional hedging strategies could you implement?