Our friend Guy Thomas has recently published an important article on the valuation of equity release mortgages: “Valuation of no-negative-equity guarantees with a lower reflecting barrier.” It is in a strong journal by UK actuarial standards: Annals of Actuarial Science. Our congratulations to him.
Guy’s article offers the first serious challenge to the Market Consistent (MC) approach that we have seen, and avoids the priceless errors we have seen in other anti-MC articles, such as conflating forward and future prices, dividing the net rental rate by 5 for no good reason or sticking an illiquidity premium in the wrong end of a valuation equation as one might do if one thinks of actuarial valuation as a game of ‘pin Donkey’s tail’. His point is that if policymakers set a floor or reflecting barrier to future house prices, then that policy implies that the valuations of No-Negative Equity Guarantees (NNEGs) can be a lot lower than those generated by the MC approach.
Guy’s argument had not occurred to me till he suggested it. But I immediately grasped its significance. We had to answer it or by default leave the field to him.
The (to me) obvious response that policymakers did not in fact set such a floor, seemed correct but hardly adequate. Guy’s article presumed such a floor, but his analysis really needed to be addressed at a deeper level: if his empirical premiss (that policymakers set such a floor) were correct, then is his valuation analysis correct? His argument seemed plausible and I lost a lot of sleep over it. Perhaps Guy was right.
After a lot of work Dean and I (by which I essentially, mean, Dean, with considerable help from Guy, for which many thanks, Guy) got to the bottom of it and it turns out that the reflecting barrier analysis doesn’t work. Phew!
Our response to Guy’s paper is the new Eumaeus Discussion Paper, EDP 2105: “Option Pricing in the Presence of a Reflecting Barrier.” The gist of our argument is the following:
A number of recent papers examine option pricing in the presence of a bound on the price of the underlying. One of these is Thomas (2020) which examines the valuation of the no-negative equity guarantees in equity release mortgages based on the premise that policymakers set a floor or reflecting barrier to future house prices. This approach is flawed, however. [1] It can give valuations that are indefensible because they violate the rational valuation principles for equity release set out by the United Kingdom Prudential Regulation Authority. [2] The introduction or removal of the reflecting barrier policy is likely to change both the current value of the underlying price and the value of the volatility, and Thomas does not allow for such impacts. [3] It is also possible to show that Thomas’ key valuation equation does not hold in the case of a deep in the money put option, which implies that the option pricing equation itself is incorrect. Finally, [4] the Thomas approach violates the no-arbitrage principle. Our results thus call into question the validity of the reflecting barrier approach not just in the equity release context, but in other contexts too.
Do read Guy’s article and our response to it and make your own mind up. Either he is right and we are wrong, or the other way round. As I said, Guy’s critique of the MC approach deserves to be taken seriously and cannot just be laughed out of court like certain previous efforts that come to mind.