From the Just Group 2020 interim:
There has been significant academic and market debate concerning the valuation of no negative equity guarantees in recent years, including proposals to use risk-free based methods rather than best estimate assumptions to project future house price growth.
To be sure, there has been significant debate about the subject, but there still seems to be significant confusion about what the debate is.
It is not as though one side is predicting that house prices will grow by best estimate assumptions (say 3% per year) whereas the other side is predicting that house prices will grow by the risk free rate. Clearly the latter is absurd (why risk free?), and the former is just a speculation. The question is how to arrive at the current price of a forward contract, and the correct method is to determine the value of lost rental income, which is a cost to the buyer, and the value of lost interest, which is a cost to the seller.
Now the price of the forward contract, once determined, may go all over the place, and all we can safely say is that it will converge with the property price at maturity. And as for the property price at maturity, no one can safely say. The future price of a forward contract is utterly different from its current price.
The PRA pointed this out as early as December 2016 CP 48/16:
Many respondents mentioned a version of the Black-Scholes formula known as ‘Black 76’, where the underlying price is the ‘forward price’ of the property. This version uses the current price of a forward contract. Some respondents appeared to conflate this with the forecast future price of the property, but provided no justification for why house price inflation was relevant to the current price of a forward contract.
Very true, and we underscored the same point in our Eumaeus Guide to equity release valuation, (2nd edition June 2020).
The forward house price should not be confused with future house prices or expected future house prices:
- Forward prices for future period are known (or can be approximated) now and we need to be able to price options using information available now.
- Options cannot be priced using future house prices because future house prices are currently unknown.
- Expected future prices do not appear in the Black ‘76 option pricing formula.
We should also keep in mind that although the original Black ‘76 article discussed options on futures, futures prices are the prices of futures contracts, a form of forward contract, not actual or expected future prices of any sort.
No one seems to have told the actuaries!