Cat Bonds
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?
Part A:
To set the coupon of the re-insurance contract so that it is valued at par, we need to calculate the present value of the expected cash flows and set the coupon rate accordingly.
Step 1: Calculate the Present Value of the Expected Cash Flows
We have three possible loss scenarios and their probabilities:
- $300 million loss with a probability of 0.50
- $50 million loss with a probability of 0.25
- $20 million loss with a probability of 0.25
To calculate the expected loss, we multiply each loss amount by its corresponding probability and sum them up:
Expected Loss = ($300 million * 0.50) + ($50 million * 0.25) + ($20 million * 0.25)
= $150 million + $12.5 million + $5 million
= $167.5 million
Step 2: Calculate the Present Value of the Principal
The principal amount of the contract is $100 million. We need to discount this amount to its present value using the appropriate Libor zero price.
As per the given information, the intensity period is from 0 to 0.5 years, and the Libor zero price during this period is 0.982652. Therefore, the present value of the principal is:
Present Value of Principal = $100 million * 0.982652
= $98.2652 million
Step 3: Calculate the Required Coupon Rate
To set the contract value at par, the present value of the expected cash flows should be equal to the present value of the principal. We can set up the following equation to solve for the required coupon rate:
Present Value of Expected Cash Flows + Present Value of Principal = Principal
$167.5 million + $98.2652 million = $100 million + Coupon * Present Value of Principal
Solving for Coupon:
Coupon = ($167.5 million + $98.2652 million - $100 million) / Present Value of Principal
= ($265.7652 million - $100 million) / $98.2652 million
= $165.7652 million / $98.2652 million
= 1.68785
The required coupon rate is approximately 1.68785.
Part B:
If you are concerned that the re-insurance coverage described in Part A will be insufficient, there are additional hedging strategies you can implement:
1. Increase Re-Insurance Coverage: You can purchase additional re-insurance coverage to increase the amount that will be paid out in case of a hurricane. This can help protect your company from larger losses beyond the original coverage.
2. Catastrophe Bonds (Cat Bonds): Cat bonds are another form of insurance-linked securities. These are debt instruments that transfer the risk of a specific catastrophe event to investors. By issuing Cat bonds, you can raise additional capital to hedge against potential losses from severe hurricanes.
3. Derivative Contracts: You can enter into derivative contracts, such as options or futures, that are specifically designed to hedge against hurricane-related losses. These contracts allow you to offset potential losses by gaining from the movement in the underlying index or asset.
4. Risk Pooling: You can also consider participating in a risk pool or joining a consortium of insurance companies that collectively bear the risk of hurricanes. By pooling resources and risk exposure, you can mitigate the potential impact of severe hurricanes and share the losses among the participating companies.
It's important to analyze the costs, benefits, and feasibility of each additional hedging strategy based on your specific circumstances and risk tolerance. Consulting with risk management professionals or experts in the insurance industry can also provide valuable insights and guidance in selecting the most suitable hedging strategy.