Category: models

Posted on

Happy New Year and Some News

1 January 2024

Happy New Year to everyone!

We trust you all had a nice Christmas break and raring to go in 2024.

A couple of bits of news from us.

First, our article “Arbitrage Problems with Reflected Geometric Brownian Motion” has just been published. The full reference and the Open Access link is given here:

“Arbitrage Problems with Reflected Geometric Brownian Motion.” (D.E. Buckner, K. Dowd and H. Hulley) Finance and Stochastics (2023) 28: 1-26.

We will have more to say on reflected GBM processes soon, as Annals of Actuarial Statistics, the journal that published Guy Thomas’s devastatingly flawed articles on the subject, seems to think it is OK to published flawed models that could bankrupt a company that uses them, without allowing anyone (i.e. us) to make any comment to that effect in its hallowed pages. This is like a maths journal that publishes an article saying that 2 plus 2 equals 5, and that’s OK because 2 plus 2 equals 4 is merely an opinion and other actuaries might have a different opinion.

We will how well that opinion holds up in due course. We have a cunning plan to address this issue.

Second, my new book on free banking is out. The link is:

The Experience of Free Banking, second edition.

There is a blog on it here, which also explains what free banking actually is.

Posted on

Arbitrage Problems with Reflected Geometric Brownian Motion

Good news!

 

Our article, “Arbitrage Problems with Reflected Geometric Brownian Motion” by Dean Buckner, Kevin Dowd and Hardy Hulley, has just been accepted for publication by the prestigious journal Finance and Stochastics.

The abstract of the article states:

 

Contrary to the claims made by several authors, a financial market model in which the price of a risky security follows a reflected geometric Brownian motion is not arbitrage-free. In fact, such models violate even the weakest no-arbitrage condition considered in the literature. Consequently, they do not admit numeraire portfolios or equivalent risk-neutral probability measures, which makes them totally unsuitable for contingent claim valuation. Unsurprisingly, the published option pricing formulae for such models violate classical no-arbitrage bounds.

 

What this means in plain English is that our friend Guy Thomas’s article “Valuation of no-negative-equity guarantees with a lower reflecting barrier” in the Annals of Actuarial Science in 2020 is wrong, dead wrong.

Continue reading “Arbitrage Problems with Reflected Geometric Brownian Motion”

Posted on

New ERM publication

We are pleased to announce that our long-waited ‘definitive’ article on ERM valuation has just been published in the Journal of Demographic Economics. The full citation is:

Buckner, K. Dowd and H. Hulley (2023) “A Market Consistent Approach to the Valuation of No-Negative Equity Guarantees and Equity Release Mortgages.” Journal of Demographic Economics Vol 89, pp. 349–372. https://doi.org/10.1017/dem.2023.6.

We welcome Dr. Hardy Hulley from UTS Sydney to our ERM working party.

Another brick in the wall tank on the lawn for the Institute and Faculty of Actuaries.

Anyone who has any trouble downloading the article please just drop us a line and we will send it to you.

Posted on

Brownian Blancmange

Whilst we were, er, snoozing, our friends Andrew Smith and Oliver Bentley came out with a doozy of an article in The Actuary (of all places!): ‘Taking Shape,’ The Actuary, January/February 2022, pp. 31-33. As they explain:

Brownian motion has many uses in actuarial work, but stochastic models based upon it can be complex and difficult to replicate. By their nature, Monte Carlo scenarios start from a common point but end in random places. We show how to construct paths that are similar to Brownian motion, using a deterministic method that is simple and easily replicated, and which has end points that a user can choose. Applications include the assessment of Value at Risk for dynamically hedged portfolios.

The deterministic method they propose is their Brownian Blancmange fractal ‘random’ walk and we won’t try to explain that here. Read the paper: it is only 3 pages long.

Among other uses, it allows the user to simulate a fractal (i.e., non-random) series whose frequency and starting and ending points are set by the user. Moreover, if the position being simulated is, say, an option, the user can also set the implied or predicted volatility (think of the vol parameter fed into the option price or trading strategy at inception) and the realised volatility (the volatility of the synthetic option or delta hedge).

Obvious applications are to dynamic VaR, stress testing and hedging analyses. On the latter, one particular sentence jumps out at us: ‘When implied and realised volatilities coincide, the hedge should, in theory, work perfectly with sufficiently frequent trading.’

As it happens, we had found the same result in our recent work on option pricing, and it of central importance. A lot more later on that.

An Excel workbook illustrating all eight fractals and the VBA code necessary to generate them can be found at github.com/AndrewDSmith8/Fractals-and-Hedging.

Our congratulations to Andrew and Oliver on a fine piece of work.

Posted on

Pull to par – from the postbag

Source: Moody’s

Golden Retriever (golden.retriever@dogs.k9.gov) sent us a long email about the previous post. This reminds me I haven’t replied to his previous mail about whether actuaries should be regulated. I didn’t reply because I didn’t know the answer, but UKSA is currently preparing its submission to the BEIS consultation so I may have an answer soon.

In the previous post I wrote

It necessarily follows that there is some cast iron guaranteed way of making money by buying into dips in the credit market. As bond prices fall, buy more bonds in the certainty that they will rise again.

Retriever objects:

If a bond is currently trading below par, then would I not expect to make money by purchasing the bond and redeeming it at par? Not a cast iron guarantee perhaps, but pretty likely surely, since investment grade corporate bonds don’t seem to default very often.

Continue reading “Pull to par – from the postbag”

Posted on

The Cladding Scandal – a generation trapped?

On YouTube as I speak.

Why you should watch: There may be as many as 11 million people trapped in apartments that are unmortgageable (and hence unsaleable) as a result of building deficiencies revealed after the Grenfell disaster. Remediating those deficiencies could cost well over £10 billion – vastly more than the £1.6 billion that the government has budgeted for.

Who pays?

Legally, at present, it’s the leaseholders – who can face bills up to £100,000, on top of insurance premiums that shot up five-fold. ‘Morally’, it might be the developers – if you can find them. It doesn’t seem to be the freeholders. This is a major issue – economically, financially, socially, and politically. At present, there is point-scoring in Westminster, with Labour demanding that leaseholders shouldn’t pay anything, and Government ministers backtracking a bit from a firm pledge to a softer promise that leaseholders shouldn’t be faced with ‘unaffordable’ bills.

Maybe this is an area where a bit of financial innovation wouldn’t come amiss…

Moderator: Andrew Hilton (Director, CSFI) Panellists: Sir Bob Neill is the Conservative MP for Bromley and Chislehurst. A barrister, educated at LSE, he was formerly a member of the London Assembly and Shadow Local Government Minister. He is chair of the Justice Select Committee, and has recently become chair of an APPG on the cladding issue. Martina Lees is a senior property writer at The Times and the Sunday Times, where she previously spent ten years as a digital section editor. She began her journalistic career as a crime reporter in Johannesburg. Dean Buckner is policy director at the UK Shareholders’ Association, and a trustee of the Leasehold Knowledge Partnership. He is a former insurance data specialist at the PRA and BofE, and, before that, spent a number of years in the City.

 

Posted on

It was twenty years ago today

Source: Aviva

The chart above shows one of the stranger features of equity release mortgages: the wide variation between the projected indexed value of a property, and the actual sale value it achieved at auction. The data is based on Aviva’s Equity Release Funding No. 4.

The red line is the rebased value of the property index used by the fund, the Halifax, from October 2007 to July 2020.

Continue reading “It was twenty years ago today”

Posted on

Excess mortality – official

Source: New York Times

There has been endless debate in the, er, Trumpier bits of social media suggesting that the whole virus thing is a hoax, that dying with corona virus is different from dying from it or because of it. The chart above, showing deaths in New York, suggests that people are in fact dying from it. Of course you can’t prove anything, as one acquaintance suggested, but then outside of mathematics and logic you can’t prove anything anyway.

Our British actuarial colleagues found much the same as the New Yorkers, in a report published by the IFoA of all places.  That settles it then.

Posted on

Insurers can’t model pandemics

An article here in InsuranceERM quotes Nita Madhav, chief executive of epidemic risk analytics company Metabiota, as saying that insurers are not prepared to model the effect of crises such as the current coronavirus one.

From the insurance sector perspective, they are not well prepared to handle epidemics,” says Madhav. “A lot of times companies are applying very crude shock scenarios to the portfolio. For example, they are not taking into account the difference in countries preparedness. It is an area where insurers are not embracing the full power cat [catastrophe] modelling can bring.

I would not be surprised. The shape of the curves I have been posting in our cvirus coverage is not a biological property of the virus itself. With no concerted action, the curve will keep on rising and will only flatten out when pretty everyone is either infected and recovered, or die. The flattening effect is caused by the concerted action, and different administrations will have different reaction times to the crisis.

Can insurers model anything, we wonder?