# How do markets price an interest rate rise?

It is common to see phrases like

Markets priced in a 68 per cent chance of a rise in UK interest rates at the next meeting, up from 48 per cent before the June decision was announced

This example came from the Financial Times last week.

How does the mathematics work behind this? Can someone give a basic example how such numbers can be computed?

• Jun 25, 2018 at 21:13
• The original paper which develops this methodology is Geraty (2000). Nov 22, 2018 at 22:05

In financial markets there is an interest rate index called the OIS fixing (the overnight index swap fixing). In different currencies it is calculated slightly differently, but the general principle is that it is a notional weighted average of traded overnight loans between banks. The price fluctuates very little and it is common to stably fix either a few basis points above, or below the central bank rate.

For example in EUR if the central bank deposit rate is -0.40bps then the OIS might be -0.36bp. Interest rate markets have derivative products known as overnight index swaps (OISs) which trade against this index over a specific period. About 13 years ago the market evolved to price these swaps between central bank meeting dates, so that speculation about central reserve periods could be explicit.

So as a concrete example if EUR OIS normally fixes 4bps above the central bank deposit rate and the next ECB meeting period is priced in the market at -0.31bps, this suggests the market expects the deposit rate to be -0.35bps in that period, which is generally interpreted as a 50% chance of no change and 50% of a 10bps hike.

Note that the bayesian probabilities are not complete since there might be a chance of say a 20bps hike, or a 5bps hike, but it is impossible to make this distinction so a binary outcome is usually what's quoted.

OK, so IG will quote me 99.240 as the mid-point for the Dec19 Short Sterling contract (L_Z19 in bloomberg, ie space not _).

This is 0.760% in expectations for GBP 3m LIBOR in December (ie 1 minus divided by 100). As compares to current 3m LIBOR of 0.8095%. So that's a 5bp dip = a 20% "chance" of a 25bp reduction. These things always assume nice, clean 25bp changes ;-)

https://www.global-rates.com/interest-rates/libor/british-pound-sterling/gbp-libor-interest-rate-3-months.aspx

Interest rate purists can perfectly correctly observe that LIBOR is not the same thing as the policy rate. And so OIS is indeed the better-matched benchmark, especially if you are a journalist in search of "truth". Except the Brevan Howards and associated punters who punt these things don't really trade OIS swaps in size. They do Eurodollars (for the \$/Fed), EURIBOR (for the E/ECB) and Short Sterling (for the £/BoE); where the open interest literally runs into the trillions (don't worry - they really don't move that much, so the notional is not as extreme as it might otherwise sound).

The direction of travel will be the same, irrespective of the finer points of the measure chosen...