# How to Calculate (month by month) what hikes are priced into OIS?

I am looking to see on a monthly basis, what the market is pricing in in terms of rate hikes in the OIS.

Would it be sufficient to look at fed funds futures at those monthly dates? My gut says not.

It would be great to understand better how the OIS (and OIS futures curve?) could be used to see how many hikes are priced in at any frequency out to any horizon

• See also quant.stackexchange.com/questions/18890/… especially Helin Gai's answer. There are a lot of assumptions and choices involved, and therefore limitations on what you can "see". Mar 23 '17 at 15:41

## 2 Answers

Fed funds futures are nearly sufficient. You need to know the precise way in which Fed Fund futures are calculated for settlement purposes - e.g. that it is an arithmetic average of the fed funds fixings where a fixing is weighted by the number of days between the fix and the next fix (i.e. a Friday fix will be weighted 3 times if there is no holiday on Monday).

OIS curves are great too. Easiest thing to do would be to assume that on average, the fix will be constant between CB meeting dates (or the effective dates of rate changes really - In Europe, the effective date can be 6 or 7 days after the meeting, but otherwise effective date is usually the next day).

Also, good to keep track of where the fixes are relative to the benchmark rate as there can be a few bps difference at times.

Then if you make the assumption that there will be no inter-meeting rate changes and that rate changes can only be 25 bps (for the US) - then if the forward rate between a given central bank meeting date and the next meeting date is $n$ bps higher than previous such forward rate, you might say that the market is implying an $n/25%$ chance of a rate change during that meeting.

In EUR, GBP, AUD, NZD, and CAD, there are reasonably liquid forward OIS contracts that do exactly this - they start on one meeting date and end at the next meeting date so they purely capture the central bank's implied prob without you having to do any interpolation or handling of the evil interest rate conventions,

We have an elaborate discussion of different OIS in our paper (link). In short, the OIS can give you the risk-neutral expectation of what the cumulative overnight rate is going to be in, say, 6 or 9 months. Bad news is, you cannot go further without assumptions: that the overnight rate is the same as the policy target rate, that the risk-neutral and natural expectations coincide in this case, and that the variance of the overnight rate is known. Good news is, many of these assumptions are not as restrictive as they seem! You can work off the formula in the paper, modifying it to the multi-period setup.