How to calculate Bank of Japan rate probabilities from TONA futures

To estimate the probability of a Bank of Japan rate move, take the 3-Month TONA futures price for the contract covering the meeting, convert it to an expected average overnight rate, and isolate the part of that window that falls after the meeting date. The gap between that implied post-meeting rate and today's rate, divided by the size of a standard move, is the market-implied probability of a hike - the same arithmetic the CME FedWatch tool runs for the Fed. What makes Japan its own problem is that TONA futures are quarterly while the Policy Board meets about twice a quarter, so one contract routinely straddles two meetings and you cannot read a single meeting's odds off a single price.

As of late July 2026 the BoJ's guideline for the uncollateralized overnight call rate is around 1.0 percent, raised on 16 June 2026 to its highest level in over three decades. The Board next meets on 30-31 July 2026, and going in, the market had almost no hike priced for that meeting, with the consensus for the next move sitting later in the year. Those are the expectations the tool below lets you read off the curve rather than take on faith.

Why TONA futures, and why they equal an OIS

TONA is the average rate on unsecured overnight lending between Japanese banks, the yen equivalent of SOFR or SONIA. A 3-Month TONA future settles to the daily compounded TONA over its reference quarter, which is exactly how the floating leg of a yen overnight index swap is calculated. That equivalence matters: the future and the matched-maturity OIS carry the same rate expectation, so if the exchange-traded contract is thin on a given day you can cross-check it against the OIS curve. Both are cleaner reads than eyeballing the yen swap curve, because both reference the actual policy-linked overnight rate.

Strip the meeting out of the contract

A futures contract does not price a single meeting; it prices the average rate across every day in its quarter. If a meeting falls partway through that quarter, the contract's implied average blends the rate before the meeting with the rate after it, weighted by the number of days on each side. To recover the post-meeting rate, split the reference period at the meeting date, hold the pre-meeting days at the current rate, and solve for the rate over the remaining days that reproduces the observed futures average. That day-weighted decomposition is the same one FedWatch applies to fed funds futures, and it is the step most homemade versions skip - they treat the whole-quarter average as the post-meeting rate and misstate the odds.

The two-meetings-in-one-contract trap

Here is the Japan-specific catch. The Fed's 30-day fed funds futures give you one contract per calendar month, so a month with one meeting isolates cleanly. TONA contracts are quarterly, and the BoJ meets roughly every six weeks, so a single three-month contract usually contains two meetings and the average rate it prices reflects both moves at once. To pull them apart you bootstrap across consecutive quarterly contracts: use the nearer contract to fix the first meeting's implied rate, then use the next contract to back out the second. The Osaka Exchange publishes its own probability-of-a-rate-hike methodology built on exactly this step-function bootstrap, and it is worth reading as the primary reference before you trust your own numbers.

A worked example

Take an illustrative contract covering a quarter with a single meeting 30 days in, 60 days remaining, with the policy rate at 1.00 percent going in. Suppose the 3-Month TONA future implies an average rate of 1.05 percent across the quarter. The pre-meeting 30 days sit at 1.00 percent; call the post-meeting rate r over the remaining 60 days. The day-weighted average is (30 times 1.00 + 60 times r) / 90 = 1.05, which solves to r = 1.075 percent. Against a standard 25 basis point hike to 1.25 percent, the implied probability is (1.075 - 1.00) / (1.25 - 1.00) = 0.075 / 0.25 = 30 percent. These figures are a textbook illustration, not a live quote - plug in the actual settlement price and meeting calendar on the day you run it.

Read it as cumulative, not a fresh bet

One habit to carry over from the FedWatch reading: these probabilities are cumulative relative to today, not independent wagers at each meeting. A given meeting's hike probability is the chance the rate is above today's level by that date, and it already contains anything priced for earlier meetings. If the July contract implies almost no move and the October contract implies a 60 percent chance of being 25 basis points higher, that 60 percent is the odds of a hike by October in total, not the odds of an October-specific surprise on top of July.

Where Japan breaks the 25bps assumption

The FedWatch arithmetic assumes moves come in clean 25 basis point steps. The current normalization cycle has behaved that way, stepping up to around 1.0 percent, but Japan spent years in yield curve control and negative rates where moves were smaller and less discrete. If you are modeling a regime where the Board might move 10 or 15 basis points, or hold the rate while adjusting another lever, a fixed 25 basis point denominator will misprice the probability. State your assumed step size in the output, and widen it to the moves actually on the table.

The BoJ read completes the set alongside the FedWatch, Bank of England SONIA and ECB ESTR versions - four central banks, one day-weighted method with local wrinkles. Quadesto takes a TONA futures or OIS strip and a meeting calendar and returns the implied path with each meeting's probability labeled and the assumed step size shown. [QUADESTO-EMBED: BoJ market-implied policy path from 3-Month TONA futures, per-meeting hike probabilities, 25bps step, cumulative-from-today]. The free tier embeds it live with a Made with Quadesto credit; Pro (149 pounds a month) removes the attribution and adds branded themes.