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?


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.


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