Applying basic derivatives pricing to Brexit

Brexit is one of the big issues in the UK today and emotions are running high on both sides of the debate.  This week, HM Treasury released their Brexit analysis, attempting to place a monetary value on the cost of Britain leaving the EU.  The analysis has been pounced on by both the “Bremainers” and the “Brexiters” leading to heated comments in newspaper columns and angry exchanges in the Twittersphere.

This blog from LCP attempts to take some emotion out of the arguments and looks at how market pricing has reacted to the prospect of Brexit. This made me think about derivatives pricing and whether this could provide any insight into the numbers behind the HM Treasury paper.

Derivatives pricing, very crudely, allows you to work out the value of two things:

  • The fixed equivalent of a variable number (think swaps)
  • The premium to protect from certain market events (think options)

These same principles are applied to other, more everyday, things; car insurance for example. The insurance premium a customer pays on their car is made up of the cost of replacing the car in a write off, or theft, multiplied by the probability of that happening plus the cost of repairing the car after an accident multiplied by the probability of needing a repair and so on.  The larger the amount that the insurer could be expected to pay out for a claim, the more the driver must pay for the protection that the insurance provides.

One of the key areas up for debate is whether the “protection” to our economy, that being a member of the EU provides, justifies the costs of membership. Like the car insurance example, is there a way you can crudely price this protection using some basic principles?

One way to do this is to work out the range of potential outcomes – I have thought about it in GDP terms – and then from that work out the probability-weighted value of a given change in GDP. This will give us the “premium” for protecting against GDP being below this level.

The starting point for understanding potential outcomes is to look at the variability in GDP. Historically average UK GDP change year on year has averaged about 2-3% above inflation. Just over two thirds of the time GDP has been within 5% of the average. It is this 5% variability that helps us work out the potential GDP outcomes and implied premium.

The Treasury paper estimates that GDP on leaving the EU could be anywhere between 5% and 10% lower than it would have been if we remained. So for the sake of this example let us work out the premium to protect from GDP falling below its expected future level.

Assuming 2% real GDP growth with a 2% inflation target our expectation at the moment is that GDP will grow at 4% per annum. The Treasury considered a 15 year time period for its analysis meaning that we expect GDP to grow from approximately £1.8trn to £3.2trn in the next 15 years.

Using this assumption and the “variability” input of 5% p.a. discussed earlier we can calculate the premium you would have to pay today to protect yourself from GDP being below £3.2trn in 15 years time. This comes out as approximately £140bn today, or just over £9bn a year – this is not far off (0.1% of GDP) the net annual contribution to the EU of c£7-8bn a year. The “Leave” campaigners would therefore argue that the risk to GDP that the Treasury discusses is broadly equivalent to the cost of the EU and therefore leaving is worth it for the perceived upsides.

On the other hand, as with any model we are heavily exposed to the inputs and assumptions. Remain campaigners would point out that the uncertainty (or variability) of GDP would be significantly higher post-Brexit. If we adjust our assumptions to reflect this, say by doubling our variability to 10% the premium doubles to £240bn or £18bn per annum. And when you look at this output the case for “Remain” is very strong.

The key difference between market pricing and Brexit pricing is that market pricing happens many times a day meaning that if any one person’s pricing assumptions are wildly out of line this anomaly is spotted and removed very quickly.

The challenge with Brexit is that we only have one “trade” so the assumptions either way will never be fully tested.

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