Good news!
Our article, “Arbitrage Problems with Reflected Geometric Brownian Motion” by Dean Buckner, Kevin Dowd and Hardy Hulley, has just been accepted for publication by the prestigious journal Finance and Stochastics.
The abstract of the article states:
Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numeraire portfolios or equivalent risk-neutral probability measures, which makes them totally unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.
What this means in plain English is that our friend Guy Thomas’s article “Valuation of no-negative-equity guarantees with a lower reflecting barrier” in the Annals of Actuarial Science in 2020 is wrong, dead wrong.
We are told that AAS is a reputable actuarial journal. Be that as it may, their refereeing process seems to have failed on this occasion.
Not that we didn’t try to tell them, but they wouldn’t have it.
Instead, they then published a second Guy article on the same issue that appears to contradict the first – we might be wrong on that but debunking his first article took a lot out of us and life is too short. So we appear to have shot down not just one Guy article, but two.
To be fair to Guy, however, his (first) article is wrong in a very subtle but totally destructive way. More on that later.
Also wrong are all the other articles that purport to use RGBM models to price financial options, so that entire cottage industry goes off to join Guy’s article in Davey Jones’ locker. This is a big deal for equity release because it confirms, as we have always said, that there is only one correct model to price equity release mortgages and that is one based on Black ’76.
Our article also shows that a highly theoretical paper can have major practical implications for those of us who want to get ERM valuation right, as opposed, e.g. to practicing ERM actuaries who merely want to get high valuations so ERM firms can look (much) more profitable than they actually are.
This is a BIG new tank on the IFOA’s lawn.
It’s high time those guys woke up and had a look out of the window. Not to put too fine a point on it, but the IFOA’s stance on equity release – in essence, to ignore everything we have ever written on the subject to warn them about one incorrect valuation approach after another, and now this – is a total disgrace, and not least because it goes against their own professional standards.