Discounting by risk free

“As a way to commit crimes without interference from Batman, the Penguin once recruited an unnamed actuary. This actuary observed that the best way to commit a crime without being foiled by Batman was to do so in broad daylight”.
http://batmanytb.com/Actuary%20(Comics)

As I commented the other day, life insurers have for a long time used arbitrary methods of discounting insurance obligations. The idea permeates actuarial culture and most actuaries, including even the younger actuaries who qualified under the new actuarial syllabus designed to drag actuarial valuation into the 1950s, show surprise when you suggest that this is completely wrong.
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Insurance fundamentally different?

In a piece last week, Oliver Ralph of the FT says

Many insurers privately argue that the rules will fail to make accounts more comparable because insurance markets worldwide are fundamentally different. They say that the new standard simply imposes a huge burden on the industry in time, effort and expense, for little benefit.

I am sure they would privately argue that, but this is completely false.

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Trend or mean reversion?

Many readers, not all, will be familiar with the Herengracht chart shown above. As Wikipedia explains, the index – of house prices along the Herengracht canal in Amsterdam – was created by real estate finance professor Piet Eichholz of Maastricht University. Eichholz was frustrated by the tendency of papers to take a ‘long run’ view of house prices that only went back 20 years or so. He suspected there was a myth which says that real-estate values go up significantly over time, and that this is especially true for central city locations, so he began studying transaction records for the Herengracht area going back to the mid 16th century. More than 300 years of data should be sufficiently ‘long run’, right? His data ended up challenging that myth. Note that the chart here is adjusted for the Dutch retail price index.

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Minsky moment?

According to the Equity-release-graph, the product continues to grow apace. £1bn lent in the third quarter of 2018. But if the trend continues, it will lead to the first of the two problems I highlighted in this previous post. Lending will follow house price growth, house price growth will fuel the capitalisation model used by ERM firms, which will capitalise future predicted growth.  This will then result in the second problem, namely that if the growth is not realised, it will go horribly wrong. Note ‘not realised’. It will go horribly wrong even if the growth is flat, and because of the large amounts lent, it will be horribly wrong in a horrible way.

You have to ask what the BoE, the guardian of financial stability, was thinking of when it approved these models in 2016. Actually I know what it was thinking of, but cannot say.

Time decay

Most people with even the slightest familiarity with option pricing will know of time decay, or the tendency of the option value to decrease through time independent of any interest rate effect. The chart above shows the price of call option through 40 years, struck at 100 with the underlying price also constantly at 100, and with interest rate set to zero to remove the effect of interest carry. I.e. the only change to the model is the time to expiry. The effect of time decay or theta is apparent.

Now I have discussed in several posts, such as here, how a real option can be replicated by means of a synthetic option – a series of linear positions in the underlying market adjusted frequently to match the delta or sensitivity of the real option.

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