Category: Ifoa

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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”

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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.

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Actuaries and equity release mortgages

The Institute of Actuaries’ “Review Team” has launched an Equity Release Mortgages thematic review, “which will consider the work carried out by actuaries in this area – in particular their role in propositions and pricing activity. The market for equity release mortgages continues to grow, and actuaries have an important role to play in this broad and complex area.”

The review includes a questionnnaire for lenders and a questionnaire for consultants. (Academic researchers apparently are not included).

The questionnaires are focused on the governance of ERM work. Example: “In addition to providing documentation, please describe what examples of documentation are subject to APS and/or TAS assessment (in either valuation/capital functions or propositions/pricing functions) at your organisation.”

Which reminds me, if the TAS (Technical and Actuarial Standards) were any use at all, they would have picked up the massively incorrect valuation method used by most (if not all) firms. This suggests they are not any use at all.

Just saying.

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The Hedging Fallacy

In our discussions with equity release actuaries, Dean and I have often come across some recurring arguments.

An example is what we might call the ‘hedging fallacy’ – the argument that we can’t apply B76 (or BS) to value equity release NNEGs because these option price formulas are derived under the assumption that the underlying variable, in this case, forward contracts on residential property, can be hedged. This assumption is obviously empirically invalid, so the argument goes, therefore we shouldn’t use B76/BS. And the argument (often) continues, we should then throw away B76/BS and use the discounted projection approach instead. And thankfully, the discounted projection approach delivers much lower NNEG values. So there is nothing to worry about – all that undervalued NNEG stuff is overhyped.

This argument is false, but it is false in a number of interesting ways.

Continue reading “The Hedging Fallacy”

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The Market Consistent Approach, Updated

Dean and I have updated our work on the MC approach and have just issued a new Discussion Paper on the subject, ‘A Market Consistent Approach to the Valuation of No Negative Equity Guarantees and Equity Release Mortgages’.

To quote the abstract:

This paper provides a new market consistent approach to the valuation of No Negative Equity Guarantees and Equity Release Mortgages. The paper innovates in two respects. First, it provides a new treatment of net rental yields and deferment rates and a proof that the two are equal. Second, the paper provides a new approach to the estimation of the volatility inputs. The proposed approach to volatility produces a volatility term structure that is dependent on the age and gender of the borrower. Illustrative valuations are provided based on the Black ’76 put pricing formula and mortality projections based on the M5 Cairns-Blake-Dowd (CBD) mortality model. Results have interesting ramifications for industry practice and prudential regulation.

The word ‘interesting’ does a lot of the heavy lifting here.

We will be presenting the paper to David Blake’s Sixteenth International Longevity Risk and Capital Markets Solutions conference in Copenhagen in August.

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In Praise of the PRA’s Principles

Dean and I have had a fair bit of behind the scenes back and forth on equity release valuation, and especially on the PRA’s Equity Release Valuation Principles, which continue to be as misunderstood as ever. As someone once said, it can be extremely difficult to persuade people of something that they do not wish to be true, and especially so where their living depends on their not understanding it.

Here is the link to our new Discussion Paper on the subject.

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Honoured in the Breach

The great American jurist Louis Brandeis once wrote:

‘Publicity is justly commended as a remedy for social and industrial diseases. Sunlight is said to be the best of disinfectants; electric light the most efficient policeman. And publicity has already played an important part in the struggle against the Money Trust.’

Which reminds me of the delicate subject of actuarial standards. Here is our take.