Insurance Contracts and Pricing Basics: What Makes Insurance Actually Insurance
Book: Structured Finance and Insurance: The ART of Managing Capital and Risk Author: Christopher L. Culp Publisher: Wiley Finance, 2006 ISBN: 978-0-471-70631-1
We are now in Part 2 of the book, which covers Traditional Risk Transfer. Chapter 8 is about insurance, and it starts with a question that sounds simple but really is not: what exactly makes something insurance?
Insurance Is a Contract. That Matters.
Insurance started as a legal contracting device under English common law. So it carries baggage. A lot of its defining features come from centuries of legal tradition and industry custom, not from some clean economic definition.
Here is the thing. A put option and an insurance contract can look very similar. Both involve paying a fixed price now for compensation if something bad happens later. Both are forms of contingent risk capital. But they are not the same thing, legally or practically.
Culp walks through the features that distinguish insurance from other risk transfer products. Only one of these features is truly unique to insurance: insurable interest. And even that has been weakening in recent case law. So think of these as guidelines, not rigid rules.
Insurable Interest
To have an insurable interest, the buyer of insurance must actually be at risk of losing something. You cannot buy fire insurance on someone else’s house if you have nothing to lose from the fire. This is the big difference between insurance and derivatives. With a derivative, you can bet on interest rates going up even if rising rates do not hurt you at all. With insurance, you need skin in the game.
Aleatory Contracts, Triggers, and Benefit Amounts
Insurance contracts are aleatory. Fancy word, straightforward concept. It means the value to each party depends on some uncertain future event, and the obligations of the two sides can end up very unequal after the fact.
Two features make insurance aleatory: the trigger and the benefit amount. The trigger is the event that activates the payout. The benefit amount is what you get when the trigger fires.
Valued contracts pay a fixed amount when the trigger fires. Life insurance is the classic example. You die, your beneficiaries get $500,000. The amount does not change based on how much economic damage your death caused.
Indemnity contracts pay an amount proportional to the actual damage. Small fire, small payment. Total loss, full payment. But you cannot collect more than what you actually lost. This is the more common type for property and casualty insurance.
Culp gives a nice example with a $1 million house and fire insurance. A valued contract might pay $400,000 for any fire. An indemnity contract pays the exact difference between the house’s value before and after the fire. For fires causing less than $400,000 in damage, the valued contract is actually better. For bigger fires, indemnity wins. The tricky part is that you do not know the fire’s severity when you buy the policy.
I find the options comparison useful here. A valued contract is basically a binary put option. An indemnity contract is a traditional put option struck at the property value. But both require an insurable interest and a specific triggering event, which options do not.
Prospective, Retrospective, and Retroactive Coverage
This distinction tripped me up at first, but it is important.
Prospective insurance is the normal kind. You buy it before anything bad happens. The trigger has not fired and the damage is unknown.
Retrospective insurance is bought after the trigger event but before the damage amount is known. A chemical company’s truck has already spilled chemicals, but nobody has found out yet. The company can still buy insurance on the resulting liability because the final damage is still uncertain.
Retroactive coverage is not allowed. If the truck spilled chemicals and the company has already been found liable for $1 million, it is too late. The loss is known. It is no longer a risk. The contract would not be aleatory.
The line between retrospective and retroactive can get blurry. Culp uses the example of a company that has been sued but the verdict has not been reached. Technically, insurance is still possible because the outcome is uncertain. But if the company has already been found liable and only the damages amount is in question, it gets much harder to argue the contract is truly aleatory.
Other Key Features
A few more features round out what makes insurance, insurance:
Due consideration for risk transfer. The premium has to be reasonable relative to the risk transferred. Paying $10 million for a policy with a $10 million max payout is not insurance. There is no risk transfer there. The tricky question is how much risk transfer is enough. The industry has used an informal “10/10 rule” (10% chance of losing 10% of premium) as a heuristic, though some have moved to a stricter 20/20 standard.
Utmost good faith (uberimae fidei). The honesty standard for insurance is higher than for normal commercial deals. Both sides have to disclose relevant information. Breach of warranty, misrepresentation, or concealment by the buyer can void the policy. Culp tells a great anecdote about John Smith and his car insurance. If John says no driver under 18 uses the car but his 16-year-old daughter drives it regularly, the insurer can deny claims even if John himself was driving when the accident happened.
Adhesion. Insurance companies write their own contracts. If the language is ambiguous, courts will rule in favor of the policyholder. So if your policy is unclear, the insurer eats it.
Subrogation. When a third party causes the insured loss, the insurer gets the right to go after that third party. This prevents the insured from collecting twice, once from insurance and once from a lawsuit. It also discourages homeowners from, say, paying someone to commit arson and then collecting on both the insurance and a legal claim.
Annual term. Almost all traditional insurance lasts one year. This is mostly because brokers get commissions on renewals. Not the most elegant reason, but that is how the industry works.
Insurance Pricing: Rate Making
Insurance pricing has three components: pure premium, loading, and markup.
Pure premium (or actuarially fair premium) equals the expected loss. If there is a 5% chance of a $100,000 claim, the pure premium is $5,000. When all the Modigliani-Miller assumptions hold, this is all you would need to charge.
More formally, Culp shows that for a group of identical policyholders, the actuarially fair rate equals the probability of loss. This makes intuitive sense. If 5 out of 100 planes crash each year, the fair insurance rate is 5% of the coverage amount.
Loading covers administrative costs: loss adjustment expenses, underwriting costs, investment management, and so on. Loading is typically expressed as a percentage of the total premium. Culp gives the example of a Swiss auto insurer where loading is 40% of total premium. So if the pure premium is 100 CHF, the total price is about 166 CHF.
Insurance companies often target a stable loss ratio, the ratio of claims to premium. If the target is 65% and actual losses produce a 70% ratio, rates go up by about 7.7%. This is a simple and practical approach, but it ignores a lot of the incentive effects embedded in contract design.
Markup is the profit margin. The more competitive the market, the lower this goes. Culp does not spend much time on it.
My Take
What strikes me most about this chapter is how much insurance is really about legal tradition and contract law rather than pure financial theory. The options analogy works beautifully for understanding payoffs, but it misses the institutional reality. Insurable interest, utmost good faith, subrogation, adhesion. These are legal concepts that have shaped the product over centuries.
The rate-making section also feels surprisingly straightforward compared to derivatives pricing. Insurance pricing is fundamentally about estimating expected losses from historical data. The complications come from information problems, which Culp covers in the next section of this chapter.