Just Share Discussion Threads

[spectoacc] 13/8/2018 16:22

@topvest - having admittedly not read the posts above - isn't the issue one of likely risk, ie the range of possibilities? Rather like the bank stress tests (& knock on effect on size of regulatory capital they need to hold) being based on some frightening but perfectly feasible scenarios. It may all be a bit finger-in-the-air but if there's one thing certain about worst-case, it's that it happens eventually.

[topvest] 13/8/2018 16:12

I'm struggling with the logic here. The particular asset on the balance sheet is the value of the original loan compounded with interest less any provisions where property prices end up being lower when the householder dies (say in 20 years time). If the house will be sold in 20 years time, then surely you have to make assumptions over how the price will change (using inflation or some other index) to determine whether the loan value is below the house price (t+20 years). I can understand that you might want to assume something more cautious for regulatory capital, but can anyone explain in plain english why the JUST methodology of assuming 4.25% inflation isn't appropriate if that is the judgement on long run property prices.

Why would you assume flat prices if that was not considered the most likely assumption? Surely this should be a sensitivity.

Longevity risk is also partially hedging their annuity liabilities, so you can see why its very attrace tive from that perspective.

Finally, what is wrong with the 3 main sensitivities on page 110 of the annual report:
Base mortality -5% +£30m
Immediate 10% property fall -£72m
Future property price growth -0.5% -£62m
I appreciate that it doesn't factor in a 30% property price drop, but they did disclose a 20% drop a few years back. Hardly armageddon.

I agree it could go pear shaped but the same is true of ANY real estate company with LTV above 40%.

[eumaeus] 13/8/2018 09:06

Lol I can confirm I have not worked for a fund since 1993. I worked at Bank of England (on the NNEG pricing project, as you can surely guess) now I am retired and sitting at home eating breakfast.

[18bt] 13/8/2018 08:43

Dean, can you confirm you are not still working for a headge fund shorting JUST?

[eumaeus] 12/8/2018 23:19

Quoting from SS 3/17 "(II) The economic value of ERM cash flows cannot be greater than either the value of an equivalent loan without an NNEG or the present value of deferred possession of the property providing collateral

3.15 This concept was introduced as the first proposition of paragraph 4.9 of Discussion Paper (DP) 1/16.1 It is derived from the following considerations:

(i) Given the choice between an ERM and an equivalent loan without an NNEG, a market participant would choose the latter, since either the guarantee is not exercised, in which case the ERM and the loan have the same payoff, or it is, in which case the ERM pays less.

(ii) Similarly, a market participant would prefer future possession of the property on exit to an ERM, given that the property will be of greater value than the ERM if the guarantee is not exercised, or the same value if it is."

[eumaeus] 12/8/2018 23:13

Sorry not to answer questions in the order you ask them, but I would prefer to deal in the logical order. Since you agree about the valuation of the deferment, it follows you must agree with the ‘upper bound’ logic of the PRA in CP 16/48 (and SS 3/17). They argue that the value of the ERM must be lower than both the pv of the loan at exit, and the pv of deferred possession. The logic is simple. If you are offered a choice between the non-defaultable loan and an ERM, you will choose the loan, which is not encumbered with the NNEG. Likewise, if you are to choose between deferred possession and an ERM, you will choose deferred possession, given that the NNEG may not bite, and if it does, the ERM is worth no more than deferred possession. QED. As for whether Black is valid, it doesn’t matter. Most firms, including Just, are using a closed form option solution such as Black. It follows that if they are pricing the ERM in a way that breaks the logic given above, then they are wrongly valuing it. Whatever pricing method they use, it must yield a result such that ERM(t) is less than min(pv loan, pv deferment). Does that answer your question?

[charlie] 12/8/2018 22:53

eumaeus, I answer your questions, but you don't answer mine!

I agree that the deferment price may be less than the spot price (although there are arguments I made earlier about different types of buyer).

What I'm unsure about is is taking that deferment price and plugging it into an option valuation formula which depends on continuous hedging. This step seems dodgy.

[eumaeus] 12/8/2018 22:13

So Charlie, I have the freehold a property with 20 years of the lease to run. PRA/Dowd pricing techniques tell me that the freehold, i.e. deferred possession is worth about 50% of the value of immediate possession. Indeed that’s about the current market value of the freehold, if you ask Savills or any other reputable valuer. I propose to sell you this for 100%, since you are so keen to benefit from future house price growth, and since you argue that the deferment cannot be hedged.

Would you accept my proposal? If not, why would you buy shares on a firm which valued its assets in exactly the same way?

[charlie] 12/8/2018 22:03

No. A static hedge and the possibility of arbitrage is what theoretically enforces the forward priced at the(r-d) rate, rather than just a balance of supply and demand. (But since this market doesn’t exist, I wouldn’t want to be dogmatic about it.)

A forward price doesn't, I agree, depend on continuous hedging. But the Black-Scholes equation does, as far as I can see.

[eumaeus] 12/8/2018 20:05

@Jane Deer, moving to a deferment rate of 50bp has already cost the firm about £880m by my reckoning. If you look at p.83 of their SFCR, under 'other valuation differences', you can see where it seems to be parked, offset by transitionals.

[eumaeus] 12/8/2018 20:03

@Charlie, do you accept that neither the value of the deferment nor of the forward contract, which are nothing to do with option pricing, depend on hedging? Yes or no.

[jane deer] 12/8/2018 19:59

Is JUST currently using a positive deferment rate of 50bps in its current internal models? So movingto 1% positive deferment rate (seemingly the minimum acceptable to the PRA) could lead to £160 million+. Increasing the volatility from 12% to 13% would add to these numbers. But if there were a 3year phase in then these numbers look just about manageable. The PRA does not appear to have an interest in reducing the matching ajustment - any attack on this (as Dowd would seem to want) would appear to have a much more significant impact on JUST’s capital position.

[charlie] 12/8/2018 19:54

Well please write about why the Black-Scholes model works if the underlying is unhedgeable. You haven't really answered this point (nor have the PRA).

As I understand it, the surprising idea that the drift in the price of the underlying "drops out" of option valuation depends on hedging. Without this, the Black-Scholes argument doesn't work, and you have to do something else.

[eumaeus] 12/8/2018 18:32

Ford writes: "Perform the calculation this [Dowd/PRA] way and the difference is startling. Prof Dowd has computed an illustrative case for a 40 per cent loan to value mortgage compounding at 5 per cent. Bolt in future house price inflation of 4.25 per cent, as he believes at least one firm is doing, then the cost of the NNEG is just 3 per cent of the loan amount. Do it more prudently and the cost rises to a thumping 52 per cent. Apply that to the £10bn odd of mortgages that have been written in the past few years at rising loan-to-value ratios and you get a potential capital shortfall of billions.

[eumaeus] 12/8/2018 18:30

The link got mangled. In any case, google Eumaeus project and you can follow the story as it happens. Jonathan Ford (FT) has just released a new story on it today, explaining the logic behind the correct pricing.

[eumaeus] 12/8/2018 18:17

The chart linked to below shows, for each maturity t up to t=40, the present value of the loan value at maturity, which is upward sloping because loan rate is typically higher than risk free (!), and the present value of deferred possession, which is downward sloping because deferment means loss of income or use hxxp://eumaeus.org/wordp/wp-content/uploads/2018/08/upper-bound.jpg

[eumaeus] 12/8/2018 18:14

Correct, and the spot price is the forward rate, calculated as S.exp((r-q)t), where S is current house price. From first principles, the ERM price can never exceed either the present value of the strike, or the present value of deferred possession, as argued in SS 3/17.

Kevin and I are going to write something about this next week. Despite the careful explanation in his paper (and in SS 3/17 and CP 13/18) there is evident misunderstanding of the ideas behind the pricing.

[charlie] 12/8/2018 18:01

OK, the strike price is the loan increased at the interest rate,is that it? So the options at say age 95 and above are slightly in-the-money (but not deep in-the-money), relative to the house price now.

But that doesn't seem to help with the absence of hedging, and without that, I still don't see how the Black-Scholes argument works. I'm still preferring a quantile from a stochastic model.

[eumaeus] 12/8/2018 16:27

I mis-typed (1), but let's focus on (2). A NNEG, as modelled using Black 76, is a whole portfolio of options. Why would all of those options be out of the money? Think about how you would calculate the strike price.

[charlie] 12/8/2018 16:16

Both legs (1) and (2) refer to in-the-money options, but all extant NNEGs are surely out-of-the-money, so I'm just confused now! Have you mis-typed something??

[eumaeus] 12/8/2018 14:16

‘Without continuous hedging, the whole Black-Scholes edifice crumbles.’ Two problems with this. (1) it’s not even true even for in in the money option, so long as we can estimate the volatility, but the reason for that is subtle. (2) For deep in the money options, hedging is unnecessary. As CP 16/48 points out, we cannot violate the upper bound of the ERM value. Its present value cannot exceed either the present value of the loan, or present value of deferment. The proof of that does not rely on any hedging assumption whatsoever.

[charlie] 12/8/2018 13:19

I agree with Wilkie et al 2004:

"However, we consider that the enthusiasm of some for the mathematics of option pricing has caused many to miss the essential point, which we repeat: dynamic hedging is simply one investment strategy (out of many possible ones), and it can be shown to be good at replicating option payoffs. If dynamic hedging is not possible, for whatever reason, then the mathematically modelled option prices have no practical application, and cannot be used for calculating ‘fair values’.

It is a mistake to use option pricing mathematics for the assessment of values of options for which no hedging strategy could exist; one example is an option to purchase one particular piece of property if some planning consent is obtained; it is just not hedgeable."

The NNEG doesn't really seem to be hedgeable. Without continuous hedging, the whole Black-Scholes edifice crumbles.

[charlie] 12/8/2018 12:55

Having thought about it a bit more, I think the "adding up lots of probability-weighted options" approach may be OK, if mortality at the portfolio level is treated as deterministic. But this still seems a bit dodgy. Many scenarios I can think of with extremely bad outcomes for house prices (making the guarantee more likely to bite) are plausibly associated with extremely bad outcomes for mortality (making the guarantee less likely to bite).

I don't see that a stochastic model necessarily gives a higher value for the guarantee. Any sensible stochastic model for house prices must have positive HPI on average; so I do 10,000 simulations and take the cost of the guarantee in the 50th lowest simulation as my 1-in-200 reserve. It's not obvious that's more expensive than the Black formula.

[eumaeus] 11/8/2018 17:55

As pointed out below there is a very large market for deferments in the shape of the freehold/leasehold market. Are you going to pay someone to live in your house for 10, 20 years? That would involve a negative deferment rate.

[eumaeus] 11/8/2018 17:52

The standard approach is to weight each option by probability of exit and treat as standard European. This approach was recommended by the original 2005 ERM paper by the Institute.



Yes stochastic modelling (including for prepayment) gives a more accurate value but makes the guarantee more expensive.



As for autocorrelation, that doesn’t matter, and to include HPI drift would be to make the same mistake as using forecasting. The value of the ERM for long maturities has to converge upon the deferment curve. Don’t imagine the PRA didn’t think carefully about this.