Inferring Central Bank Rate Expectations from OIS and Futures
Summary
The document asks how to infer market expectations for a future central bank decision from overnight indexed swaps or short-term interest rate futures. It introduces an OIS relationship that equates the fixed leg’s accumulation with compounded daily overnight rates, accounting for how long each daily rate applies, including weekends. The central question is how to isolate the expected rate around a meeting when overnight rates vary over time.
It also gives an illustrative setup with a one-year OIS quote and a meeting before maturity, then asks how a three-month futures quote might indicate the expected policy move. No worked solution or answer is included, so the document does not specify the assumptions, curve inputs, or decomposition needed to extract a meeting-implied rate. OIS and futures cover accrual periods that can span multiple policy decisions, and the note alone does not explain how to separate those effects or account for contract conventions and risk premia.
Key ideas
- An OIS fixed rate reflects compounded overnight rates across the swap’s accrual period.
- The daily rate applies for its relevant calendar days, so weekend accrual differs from weekday accrual.
- A swap spanning a central bank meeting does not directly isolate the rate expected at that meeting.
- Short-term rate futures also require accrual-period and contract-convention analysis to interpret as policy expectations.
- The document poses these inference questions but provides no worked answer.
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# Calculating Implied rates from OIS and Futures
# Calculating Implied rates from OIS and Futures
I've been trying to figure out how to calculate the implied rate for interest rate decisions by central banks using OIS and came across an explanation that I can't quite wrap my head around:
> Apart from futures, you can also look at OIS swaps, which for some countries even have directly quoted central bank meeting date swaps. If not, you can still rely on the following equilibrium:
> $1 + \frac{r*n}{360} = \prod_{i=1}^n \left(1+ \frac{r_i*d_i}{360}\right)$
> where the left hand side is the fixed part (r is the quoted OIS price / fixed rate), and the RHS the floating part, with ri denoting the expected floating rate on the ith day, di the number of days ri applies for (1 for weekdays, 3 for weekends) and n is the total number of days for the swap. Since r, n and di is known, you can solve this.
Let's say I have a OIS contract with a duration of 1 year and the OIS rate for that duration is 3%. The current interest rate is 2.5%. The next central bank meeting is in 30 days and I want to figure out what the market is pricing in for the implied rate of that meeting? According to the explanation I can calculate ri for the ith day but isn't ri changing every night depending on what the overnight market does? What would the calculation look like for deducing what the implied rate (and hence the central bank decision) would be at that date? Please show your working out as that is where my understanding gets me lost.
Moving onto a different example with the 3 month short-term interest rate futures. Current interest rate is 2.5%. The next central bank meeting is in 30 days. Let's say the 3 month STIR future is currently priced at 3%. What would the calculation look like to try and find what the market expects the central bank to do with interest rates in 30 days?
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.