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.

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”

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.

The Harry I Knew

Roger J. Brown

[This guest posting from Dr. Roger Brown from his latest MathEstate newsletter gives a uniquely personal obituary to the late, great Harry Markowitz, the inventor of modern portfolio theory. Harry died in San Diego on 22 June 2023 at the age of 95. May he rest in peace.]

Lost one of my heroes

In the final year of the last Century, my last year of Graduate School, the San Diego Union Tribune did an article on Harry Markowitz. Thus, I learned he and I lived in the same city. Of course, I called him up to propose a lunch. Lucky for me he said “Yes.” It was before cellphone cameras. To that first lunch I brought a small “point-and-shoot” camera which I asked his assistant to use.

Unfortunately, I did not notice it was set on “Panoramic” which provided a very wide view of many things except, ironically, the heads of the subjects. Harry was 6’4”. For years a picture hung in my office of two hands shaking in front of Harry Markowitz’s belt buckle. Thus began a great friendship.

He towered over me in all respects. He embodied the best of what it meant to be an academic. To those who value rational thinking he was a National Treasure. Every bit equal to his academic accomplishments was his humanity. At that first lunch he described his penchant for putting 25-year-old balsamic vinegar on ice cream. He liked to cook. We exchanged recipes for more than two decades.

His sense of humor was grand. We had heard many of the same jokes but delighted in telling variants of them over again to each other. When, rarely, I had one he had not heard he relished it, doubling over in laughter. It occurred to me that if my greatest accomplishment in academia was making Harry laugh, that would be enough.

Rational in all areas, his health was no exception. For years I would set aside an entire afternoon for our regular lunch, knowing it would be preceded and followed by a long walk. During those walks we discussed all manner of things, academics, mathematics, art and theater, family and, of course, economics.

He shared my bemused interest in politics, wondering right alongside me and everyone else where those whacky ideas came from and who really believed they would work.

His own pure rationality was tempered and tested by his devotion to his wife, Barbara. I was glad to have had the chance to tell him what I admired most in him was his care for her. When the COVID pandrossy ruined plans for their 50th wedding anniversary, I know it was a big disappointment.

He was always writing. He thought he had something to say, and he was right. His view of the world influenced finance; his view of life influenced me. I was so lucky. I heard some of the best things Harry had to say directly from him.

Naturally, we both slowed over the years. I once told him I had made it to the age he was when we first met. He was not impressed. After he turned 90, he was fond of saying that it was too late for him to “die tragically.” The walks got shorter but if the spring in his step lagged, his mind never did. He was always in search of a puzzle, a pun or a way to see life like no one else.

We all should emulate my friend whom I often referred to, in his presence and with a hint of foolishness, as “The Great Man.” The truth is Harry enjoyed being Harry. We are all the richer for it.

Harry’s incredible mind gave us Modern Portfolio Theory. More importantly, his wonderful heart gave rationality a good name.

 

More Trouble at t’ Equity Release Mill

Last week’s (4 October 2022) Daily Telegraph had a nice article by Charlotte Gifford on the impact of higher loan rates and a possible house price fall on the equity release sector:

Equity release market in trouble as rates rise and house prices wobble

‘It will all come crashing down’, warns economics professor

It’s worth a read.

In essence, higher rates and a possible house price fall are not good news for the sector. Says the econ professor “if the Bank Rate hits 6pc and house prices fall by 15pc, then the loss to the lender is … 28 percent of the loan. If house prices fall even more, by 40pc, then the loss would be … 41percent of the overall loan.”

But then again, the ER people are still pretty upbeat, so perhaps it will all go away.

We noticed a couple of flies in the ointment, however.

Continue reading “More Trouble at t’ Equity Release Mill”

Two New Books by EUMAEUS

Two New Books by EUMAEUS

Eumaeus is pleased to announce the publication of two new books published by KSP Books. Regular readers will be familiar with draft versions of both these.

The first is The Eumaeus Guide to Equity Release Valuation: Restating the Case for a Market Consistent Approach, 2nd edition. The second is Can UK Banks Pass the Covid-19 Stress Test? Both were published on June 29th.

We thank Bilal Kargi of KSP Books for publishing these.

More publications are in the works and we will report on them as they come out.

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.

Inflation Returns with a Vengeance

To those who have been watching the broad money supply for the last couple of years or so, it was blindingly obvious that inflation would take off after a decent ‘long and variable’ lag. Well, UK CPI inflation is now 7% and even the Bank of England now admits it could soon hit 10%.

The return of inflation has come as a surprise to many analysts. These include, most notably, especially even the Mystic Moggs at the Bank.

In August 2020, the Bank stated (see p. ii) that

In the MPC’s central [inflation] projection, conditioned on prevailing market yields, CPI inflation is expected to be around 2% in two years’ time. 

 A year later, the Bank stated

3.4: … The MPC expects CPI inflation to rise temporarily to around 4% in the near term, before falling back towards 2%. … Inflation starts to decline in 2022, and returns to the 2% target in late 2023(Chart 3.2).

Those are some specular forecasting failures, even by the Bank’s standards.

To be fair, the Bank is not alone. The Fed has made much the same set of mistakes: first they said there would be no inflation, then they said it would be temporary, then they were looking for it in all the wrong places, and now the dovest of Fed doves are turning into inflation hawks.  See this piece by Steve Hanke and me in the latest National Review: “The Fed Looks for Inflation in All the Wrong Places.”

[DB adds: Andrew Bailey is appearing on Parliament TV this afternoon, so don’t forget to tune in]

Die Scheisse Trifft den Lüfter

There is an interesting piece by David Walker in Insurance Asset Risk on May 5th about German life insurers: ‘German regulator “intensively supervising” 20 life firms.’

The phrase “intensively supervising” got our attention. To elaborate:

Mark Branson, president of BaFin, has revealed about 20 German life insurers are currently under “intensive supervision”, all suffering “legacy issues from earlier guarantee promises”. About 30 pension funds are also being watched closely.

Looks like a lot of German life insurers and pension funds have been using Equitable Life as a how-to manual.

One also has to wonder why BaFin took so long to wake up to this issue – it can’t be that they were too busy harassing FT journalists investigating the Wirecard scandal, because that blew up over a year ago.