Life Settlements: Trading Life Insurance Policies

And now for something completely morbid. That is literally how Wilmott opens Chapter 74. We are talking about life settlements and viaticals. Contracts that are, to put it bluntly, about death.

If you ever thought finance was cold, this chapter will confirm it. But it is also fascinating. Because the math here is real, the money is real, and the ethical questions are real too.

What Are Life Settlements?

A life settlement is when someone sells their life insurance policy to a third party. The seller is usually an older person who no longer needs or wants the policy. Maybe they cannot afford the premiums anymore. Maybe they need cash for medical treatment. Maybe the policy was part of an estate plan that no longer makes sense.

The word “viatical” is used when the person selling has a terminal illness. The two terms are often used interchangeably, but viaticals carry that extra weight.

Here is how it works. You have a life insurance policy worth $1,000,000 on your death. The insurance company would give you some surrender value if you cancel it, but that number is usually way below what the policy is actually worth. So instead, you sell it to an investor for something between the surrender value and the face value. Say $375,000.

The investor now owns the policy. They pay your monthly premiums. When you die, they collect the $1,000,000.

Yes, you read that right. The investor profits when you die. The sooner you die, the more they profit, because they pay fewer premiums.

Life Expectancy: Sex, Health, and Actuarial Tables

To price these things, you need to estimate when someone is going to die. This is where actuarial science comes in.

The first factor is sex. Not how often, Wilmott jokes, but your gender. American males born today have a life expectancy around 74 years. American females around 79.5. Japanese women top the charts at 83. Men smoke more, drink more, are three times more likely to die from accidents, and four times more likely to be murdered.

The second factor is health. The World Health Organization measures “healthy lifespan” which accounts for disability. Japan leads at 75 years of healthy life. Sierra Leone sits at the bottom with 26. The US ranks 24th despite spending more on healthcare than anyone. The reasons include ethnic health disparities, higher HIV rates among young people, tobacco-related cancers, heart disease, and high violence levels.

When someone sells their policy, a medical examiner evaluates them and produces a life expectancy (LE) certificate. Interesting detail: what they call “life expectancy” is actually the median, not the mean. These are different numbers. The median is the age by which you have a 50% chance of dying. The mean is the average age at death across the whole distribution.

Death as Default

Wilmott takes all this actuarial data and reframes it in terms quants already understand: default probability. Death is modeled as default. No recovery.

You define p(a) as the probability of dying at age a. From actuarial tables, you get this function for different populations. Then P(a; a0) is the probability of still being alive at age a given you were alive at a0. The math looks like:

$$P(a; a_0) = e^{-\int_{a_0}^{a} p(s) , ds}$$

This is the same exponential decay formula used in credit default modeling. The probability density for age at death is just -dP/da. From there you can calculate expected age at death, median life expectancy, and all the statistics you need for pricing.

Pricing a Single Policy

Wilmott walks through a concrete example. A 70-year-old sells their policy:

• Face value: $1,000,000
• Monthly premium: $2,083
• Purchase price: $375,000
• Life expectancy: 5.2 years

The investor runs Monte Carlo simulations. For each simulation, you pick an age at death from the probability distribution, calculate all the cashflows (purchase price out, premiums out, principal in at death), and present value everything.

Using 10,000 simulations and a 3% interest rate, the mean present value of all cashflows is $310,120 with a standard deviation of $157,401. So on average, you nearly double your $375,000 investment.

But here is the catch. If the person lives past 84, you start losing money. Those monthly premiums add up. The distribution of outcomes has a long left tail of losses.

Internal Rate of Return

Most investors in this space think in terms of IRR rather than present value. For the example policy, the average IRR across simulations is 25.7%. Sounds great, right?

But the standard deviation is 36.5%. And the IRR calculation has a fundamental problem: if someone dies immediately after purchase, the IRR is essentially infinite. The metric is extremely sensitive to early deaths, making it not very informative as a standalone measure.

Portfolio Effects

Nobody sensible buys just one policy. You buy dozens or hundreds, and you rely on the law of large numbers to smooth things out. Since we can reasonably assume individual deaths are not correlated (one person dying does not cause another to die), diversification works.

Wilmott simulates portfolios of 5, 20, and 100 identical policies. As portfolio size grows, the distribution of present values gets tighter and the IRR distribution narrows. With 100 policies, you get a much more predictable outcome than with a single policy.

Extension Risk: The Big Danger

The scariest risk in life settlements is not that one person lives too long. It is that everyone lives longer than expected. This is called extension risk.

Medical advances, better nutrition, genetic research, improved healthcare access: all of these systematically push lifespans up. The probability of dying at any given age is currently decreasing by about 2% per year. So the hazard rate is not just a function of age, it is a function of calendar time too: p(a, t).

On the flip side, there are factors that could systematically decrease lifespans: catastrophes, pandemics, pollution, drug-resistant germs, war, increasing wealth inequality. Wilmott lists both sides.

The key insight is that individual death risk can be diversified away, but systematic extension risk cannot. If a breakthrough cure for cancer arrives next year, every policy in your portfolio becomes less profitable simultaneously. This is the equivalent of correlation risk in credit portfolios.

The Age of Quants: A Fun Aside

The chapter ends with a delightful mathematical appendix about the age distribution of quants. Wilmott models it as a population dynamics problem. New people enter the quant profession at different ages, and people leave (retire, change careers, or die) at a rate that depends on age.

The steady-state probability distribution for the age of quants depends on the entry rate n(a) and the exit rate alpha(a). If the exit rate is constant, the distribution decays exponentially from the peak entry age. It is a cute application of the same survival analysis math used for life settlements.

The Takeaway

Life settlements are a strange corner of finance where your profit literally depends on someone dying. The math is straightforward: it is just survival analysis combined with present value calculations. The pricing uses Monte Carlo simulation because the probability distributions do not lend themselves to nice closed-form solutions.

The real challenge is not the math but the assumptions. Life expectancy estimates from medical examiners are uncertain. Extension risk from medical progress is real and cannot be diversified. And the ethical questions about profiting from death are not ones that any equation can answer.

As Wilmott notes, this area is becoming increasingly popular with quants. More securitization, more packaging of policies into tradeable products, more sophistication in the modeling. Whether that is a good thing depends on your perspective.

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