# how to calculate the implied interest rates using STIRs futures?

I saw a post of trader sharing his expectations of implied interest rates on different meetings dates of different Central banks using STIRs ScreenShot and am trying to figure out how he did it ? my second question is what are the STIR futures of RBA,RBNZ,BOC,BOJ,SNB

Unlike @Chris Edmonton, I am not sure what the screenshot shows, because in my opinion it does not show if Futures or OIS is used.

In any case, the idea is the same:

• Under the assumption that only central bank actions will impact the effective interest rate of an economy, you can push the expected overnight rates forward and backward through the tenor structure.
• With futures, you get the chain (all tenors) and look at the individual dates. Some contract months will not span central bank meetings, others will. Therefore, you have the future representing the average rate over the period, where it could be higher/lower prior to the meeting date, lower/higher after the meeting date. You can carry the rate forward where there is no meeting - meaning you know the rate prior to the meeting date - and solve the equation $$days_{total}*Future_{meeting_{month}} = days_{prior_{meeting}}*Future_{prior_m} + days_{after}*r_{implied}$$

To provide a specific example, let's look at the FED Funds futures on Bloomberg. In case you have access to BBG, you can look at {WIRP} and {FFA Comdty CT} for the following screens:

Computing the above logic with the market data results in the following lines of

days_total = 31
days_prior = 2
days_after = days_total - days_prior
future_meeting_month = 3.13
future_prior_month = 3.225

r_implied_may = (future_meeting_month*days_total - future_prior_month*days_prior)/days_after


It is reasonably close to the value Bloomberg shows (3.12) for this meeting date. Maybe they use a slightly different logic but the general idea holds (e.g. settlement prices vs Last traded price vs a snapshot of prices at some given time or they adjust for the "basis" between the current rate and the mid between the upper and lower bound or the like).

The CME offers a tool similar to WIRP on BBG - the so called CME FED Watch tool, which provides the probabilities just like WIRP (that's something frequently looked at and discussed in the market, as @KevinT mentioned).

For RBA, you can use the ASX 30 Day Interbank Cash Rate Futures . Bloomberg only displays OIS for the others. Though, I think @KevinT suggestions are sound.

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 $$r_i$$ denoting the expected floating rate on the $$i^{th}$$ day, $$d_i$$ the number of days $$r_i$$ applies for (1 for weekdays, 3 for weekends) and n is the total number of days for the swap. Since r, n and $$d_i$$ is known, you can solve this.

• Hi AKdemy, I actually have a follow-up question on these myself. Recently I did exactly what you suggested here and calculated these "weighted-averages" from the futures for my central bank dates. However, I actually wondered, what exactly are those rates in a more mathematical sense? as this approach is not a classical bootstrap where I solve for the overnight rates, are those actually forward rates from eventdate1 to eventdate2 (like a synthetic FRA between two event dates)? or zero rates from today to the event date? Mar 30, 2023 at 15:54
• I ask because I need to price swaps from a curve that incorporates the jumps at central bank dates and this seems more complicated than I first thought (cause even if it is zero rates, I would then have "roughly" quarterly instead of annual payments, and no proper "coupon" in the classical sense since the implied CB rates are not constant ofc). I could only imagine it works for a single period OIS spanning exactly two CB dates and using the coupon implied from the futures strip. But how about an arbitrary 2y OIS w/ annual fixed rate? I don't see how that could be done quickly... Mar 30, 2023 at 15:57
• Note: I don't have any quotes for dedicated central bank meeting date OISs. Mar 30, 2023 at 15:59

Answering a bit broader / more general: usually, traders deduce the expectations about central bank hikes or cuts from the market quotes of liquidly traded interest rate derivatives. The same holds for the overnight based interest rates -- and in this case, the usual suspects are STIR Futures and Overnight Indexed Swaps (OIS). You specifically asked about the former, so as an arbitrary / meaningless example, let's just say that a 3 month future with September expiry is quoted at 99.0, meaning a 1% (compound or average) interest rate for the reference period (June - September). If your current fixing is at 0.75%, it means the market implies a hike of 25bps for the central bank meeting that falls within this period. (Often traders also express the hikes in terms of "probabilities" of 25bps hikes --> here you'd have a 100% chance / agreement of a 25bps hike).

Lastly, regarding RFR based futures in the markets you asked:

• AUD & NZD: you have 30 Day Interbank Cash Rate Futures that are based on the average RBA Overnight Cash Rate (RBNZ cash rate, respectively). Apparently both can be traded on ASX (see here and here). What might interest you particularly is that the ASX actually developed a webpage called RBA Rate Indicator; it tracks exactly those expectations I mentioned above - see here.

• CAD: you have 3m CORRA futures on the Montreal Exchange (based on the compounded daily Canadian Overnight Repo Rate between two consecutive IMM dates) - see here

• JPY: I don't know that market tbh, but it appears you have some sort of futures based on monthly averages of the overnight based call rate. The longer part in JPY is usually based on liquid TONAR-based OIS, but I really don't know if TONAR and that very "call rate" of the futures are linked/the same.

• CHF: you have 3m SARON futures, traded on both the ICE and Eurex. These are also quarterly compounded rates between IMM dates and based on the SIX publication of the SARON (Swiss Average Rate Overnight).

HTH

To answer your first question, there are markets for forward overnight interest rate swaps (OIS) starting and ending on consecutive central bank rate decision dates. Your screenshot shows quotes for these swaps.