The final PRA policy statement on equity release mortgages has too much to review in one post, so I will start with the tricky subject of Brownian motion.
Brown is of course Robert Brown, who practically invented the subject, after noting how pollen moved in mysterious ways. As the PRA notes (para 2.26), ‘the most common argument’ put forward by their detractors, ‘ was that the Black-Scholes formula rests on conceptual assumptions such as availability of liquid hedging instruments. Another limitation noted was that property price returns do not exhibit geometric Brownian motion, under which asset prices can get arbitrarily close to zero, which in the respondent’s view is unrealistic for residential UK properties’. My emphasis.
The PRA replies (2.28) that while it agrees that the attributes of the residential property market do not permit the derivation of the Black-Scholes formula via dynamic replication arguments, and that a closed form solution cannot directly capture conditional early repayment rates, ‘the conceptual assumptions mentioned by respondents are sufficient to allow derivation of the Black-Scholes formula, they are not necessary.
If you thought you heard that before, you are right. As we have noted a number of times (e.g. here), the textbook assumptions for the derivation of B-S are sufficient, but not necessary, and the pricing technique works perfectly well for autocorrelated, mean-reverting etc. price series. Also, as Kevin showed here, questions about Brownian motion are almost irrelevant to ERM valuation, given that most ERM maturities are either well in the money, or well out of the money.
And no one paid us for this.
Actually, the PRA may be quite wrong to state that the attributes of the property market do not permit the derivation of B-S via dynamic replication arguments, but never mind, Kevin and I will be discussing that in a later post, and possibly in an academic paper.
As for ‘liquid hedging instruments’, para 2.32 states
The PRA recognises that the lack of a deep and liquid market in deferred property possession makes it difficult to value the NNEG, but that does not change the economic characteristics of the NNEG.
That looks like a clear reference to the ABI-IFoA project to consider
whether there are any “halfway house” solutions between real world and risk-neutral approaches given, in relation to the latter, the absence of a deep and liquid market.
Looks like there aren’t, and if there are any doubts, the paper mentions the project (2.69), whose participants seem to have wanted the PRA to ‘defer finalising its policy until such time as the results of that research are available’.
Sadly no deal.
2.70 The PRA will consider the results of the IFoA research when they are available, which the PRA understands to be in 2019, along with any other future research and developments in this area. But it does not consider that further delay in finalising its proposals is desirable. The PRA has already consulted extensively on this subject, including a discussion paper and two consultations on supervisory statements.
IFoA should ask for its money back.
That’s all for now folks, more tomorrow.