Interview with David Blake, Review of “A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration”

The most cited American Risk and Insurance Association (ARIA) article from their Journal of Risk and Insurance (JRI) of all time is “A two-factor model for stochastic mortality with parameter uncertainty: Theory and calibration.” The article was co-authored by Andrew J. G. Cairns, David Blake, and Kevin Dowd. It was published in 2006, JRI Volume 73, Issue 4 and has 433 citations. To celebrate the article’s success, I recently reached out to author and ARIA member David Blake to tell us a little more about this important research.


Q: For those who didn’t read the article can you provide a brief and simple summary in plain language?

A: Prior to the publication of the Cairns-Blake-Dowd (or CBD) model, the main extant stochastic mortality model was the widely-used Lee-Carter (LC) model.  This was a single-factor model which assumed that the rate of mortality change was constant for all ages.  This was not consistent with the recent evidence which indicated that mortality rates were falling faster at higher ages than lower ages. Another problem was forecasting future mortality.  Forecast confidence intervals were much smaller than the volatility in historical mortality data suggested – in other words, the forecasts were too smooth.

We, therefore, decided to build a two-factor model, with one factor to explain the overall rate of mortality change and another to allow for different rates of change at different ages.  At the same time, we introduced a parametric structure to explain the shape of mortality rates in the form of simple linear and quadratic terms. This resulted in a more parsimonious model than LC, making it easier to fit data since identifiability was also much easier.

Q: Why did you choose this topic?

A: The main reason for choosing this topic was that a good stochastic mortality model is an essential prerequisite for developing the Life Market – the major new global capital market for transferring longevity risk from corporate pension schemes and annuity providers to reinsurers and capital-market investors. The risk is transferred using instruments like longevity bonds and derivatives, such as swaps, options, and forward contracts.  Pricing these bonds and contracts needs a good and robust stochastic mortality model, like CBD. To date, at least $600 billion of longevity risk globally has transferred using these instruments, along with the buy-outs and buy-ins used by insurance companies to take over the risk.


Q: Why do you think this topic has been the most widely cited?

A: While the CBD and LC models are now widely used as the basis for comparing newer mortality models, this is probably not the main reason why the CBD model is so widely cited. The main reason is more likely to be the use of the model in designing longevity hedges and in growing the Life Market. This market is potentially enormous with estimates ranging between $60-80 trillion for the total amount of longevity risk currently locked in the world’s corporate pension plans. Dealing with this risk is taking far too much corporate management time and is impeding company investment and dividend programs.

Q: What was the most interesting or difficult part of your research on this project?

A: The most interesting thing is how the CBD model led an explosion of global research on stochastic mortality modelling and on designing numerous different types of longevity hedge.  The most difficult challenge in terms of the model itself is working out when there has been a change in trend mortality rates. This is because the model uses historical data, so it takes some years before it becomes clear whether the recent mortality numbers are temporary outliers that will soon return to trend or whether they signal a genuine change in trend. LC has the same problem, of course.


Q: Have you learned anything further about this research since publication or is there anything in the article that wasn’t shared that people may be interested in?

A: The biggest remaining challenge in developing the Life Market as a global capital market with adequate liquidity is to attract sufficient numbers of investors.  The key attraction of assets linked to longevity risk is that their returns are uncorrelated with those on conventional asset classes such as equities, bonds, and real estate.  This makes them an important new risk-diversifying asset class.  The problem is that investors are still wary of longevity-linked assets because they are concerned that those offloading the longevity risk, mainly insurers and reinsurers, know much more about the risk than they do and they are worried that they will be sold a ‘lemon’.  This is an example of asymmetric information where one party to the contract knows much more than the other.  The classic solution to this problem is for the (re)insurer to ‘keep some skin in the game’ by co-sharing the risk with investors using vehicles such as ‘sidecars’.  Investors currently using sidecars to access the Life Market include sovereign wealth funds, family offices, high net worth individuals, and investors who have previously own insurance-linked securities. But we clearly still have a long way to go to reach even a trillion dollars of longevity risk transfers, let alone $60-80 trillion!