An ingenious objection

Ingenious objections are always interesting, particularly when they are wrong. An actuary has objected to my post here, where I considered a put written at 90 on a price series which goes 95,96,95 etc. The point of the post was to show that the standard formula works perfectly well for such a distribution. The objector objects that if the series really does oscillate between 95 and 96, the price will clearly never reach 90, so the standard pricing formula must be wrong. The true price of the put must be zero.

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Just an update

Just Group’s business update for the 9m period ended 30 September 2018 is here. Shares were up 5% on the news this morning.

Headlines: £483m of ERM business written, which they say is CP 13/18 compliant, and they write:

CP13/18 is for us primarily a back book issue. The Group has no further clarity on the outcome of the consultation

In the same period, they took on about £1bn of defined benefit derisking business. ‘Derisking’ is actually an odd name for this kind of business, but Kevin and I shall be discussing that in Q1 next year.

The firm awaits the publication of the PRA’s final supervisory statement, as we all are. As I commented here, it is not certain whether it is just the implementation that has been delayed, or the publication. All we know is that it will be published in due course.

Get on with it then!

Weird distributions #2

The Institute says, in its reply to CP 13/18  (p.10), that

Using the Black-Scholes formula in pricing NNEG will affect the cost of the guarantee, since allowance is not made for the features of mean reversion, momentum and jumps described above. Under geometric Brownian motion the volatility increases with the square root of time while for other models it does not; the value for long term derivatives such as NNEG could materially differ from that assumed under the Black-Scholes model.

This second article on strange distributions discusses the mean reversion claim.

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Update from the Bank

Update 25 October 2018 from the Bank.

The consultation period for PRA CP13/18 ‘Solvency II Equity Release Mortgages’ closed on 30 September 2018. The proposed implementation date for the proposals in the CP was Monday 31 December 2018. Based on feedback to the consultation, the PRA has decided that the implementation date will not be before 31 December 2019. The PRA is making this announcement now in order to clarify the position for insurers planning their year-end 2018 processes. The PRA is currently giving careful consideration to the consultation responses and the impact, if any, of the updated implementation date to the proposed phase-in period. The PRA will publish final policy and supervisory statements in due course.

This is hardly surprising.

[edit] Our own letter to the consultation team is here. It said (point 1).

It is a worry that the consultation as a whole has taken such a long time. The Dowd report ‘Asleep at the Wheel’ identified a number of letters going back to October 2014 and resulting in a stream of consultation papers, discussion papers and supervisory statements (see, e.g., CP 48/16, CP 23/17, CP 24/17, DP 1/16 and SS 3/17) expressing concerns on ERM valuation. Yet the valuation issue is a simple one: once the decrements have been quantified using standard longevity modelling, the ERM valuation model embeds a simple European put option. Clearly the deferment rate concept has caused an intellectual challenge for some, but it is a natural consequence of modern derivative pricing theory, which dates back more than 40 years. The PRA has apparently confirmed this assessment in judging that the valuation changes are not a consequence of Solvency II, but should have been applied all along. Yet during this extended consultation period the ERM market has grown significantly and the PRA has approved the raising of sub-debt and tier 3 debt, not to mention dividend payments, all based on valuation models it has known to be flawed. Investors could rightly complain that they have been misled.

Our emphasis. How long does it take to price a simple European put option?

Top 3 posts

Here are the top 3 posts since we began on August 7 2018, in order.

1.  Hidden in plain view Could the unexplained change in ‘other valuation differences’ reported by Just Group between 2016 and 2017 be possibly explained by the fact they changed their deferment rate assumption to comply with new PRA requirements? They aren’t telling us.

2. Asleep at the Institute Roughly, “the Institute has just published a paper that (a) shows complete ignorance of developments in financial economics and (b) is almost certainly the product of entrenched commercial interests.”

3. Mulheirn vs Harding The much vaunted shortage of homes is a myth. “The theory and the data clearly indicate that a shortage of homes has not contributed to the 150 per cent rise in UK real prices over the past two decades. ”

On the last one, one common explanation of the house price rise, popular both with the general public and with actuaries, is ‘supply and demand’.

A moment’s reflection suggests this is silly. First, it’s not the supply or demand that changes the price, it is expectations about supply or demand. There might be no issue with current supply at all, but if the available information suggests a shortage of supply in a few years’ time, that will be reflected in the price now.

Second, expectations about supply and demand would not explain a prolonged change in price. Assuming nothing else changes, the expectations would be immediately reflected in the price.

Objectors will object that this assumes market efficiency, i.e. the tendency for market prices to reflect available information, and perhaps they have a point, but enough for now.

 

Fascinating but toxic

Geeks only. The chart above shows why Equity Release Mortgages are both fascinating and toxic. We have discussed ERM valuation in a number of earlier posts, but ERMs are used as assets to back conventional annuity books under what’s called ‘matching adjustment’, but we need to consider both sides of the balance sheet, because the insurance industry has weird ways of valuing liabilities too.

The PRA (and IFRS) allows firms to discount insurance liabilities at the estimated rate of return on the assets, which is absolutely bonkers but the industry lobbied hard in 2012 for it and here we are. Thus there is a ‘matching adjustment benefit’ arising from the higher discount rate, which effectively creates equity on the books of an MA firm.

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Past and present tense

Our postbag is bursting its seams with comments, largely critical, about how we have misunderstood the ‘two balance sheet’ approach used by Just group. We have claimed that Just were (past tense) using an implied deferment rate of minus 2.75% for both their IFRS and Solvency II balance sheet. Our critics say that, while the firm are using that rate for the IFRS balance sheet, they are (present tense) using a rate of 0.5% for Solvency II purposes. See their 2017 Solvency report, p.54.

We are wrong, and must apologise immediately!

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