Step-Function Bootstrap from the Quarterly TONA Strip

Instrument. JPX 3-month TONA futures settle on the IMM quarterly cycle (March, June, September, December). Each contract prices 100 − the compounded average TONA over its roughly three-month reference window (third Wednesday to third Wednesday). At current rate levels (~0.5%) the gap between the compounded and the day-weighted arithmetic average is well under a basis point, so we treat the implied rate as the arithmetic average over the window (revisited if rates rise materially).

The identification problem. The monthly PyFedWatch/CME method used for the Fed, ECB and BoE assigns one meeting per contract window. For the BoJ, roughly two Monetary Policy Meetings fall inside each quarterly window, so one contract is one equation in two unknown meeting steps — the per-meeting decomposition is under-determined by about a factor of two.

Model. We treat the overnight path as piecewise-constant, changing only on MPM dates. The level after meeting \(k\) is \(R_k = R_0 + \sum_{j \le k} \delta_j\), where \(R_0\) is the current BoJ policy rate (the money-market anchor for TONA, exactly as €STR anchors the ECB calculation) and \(\delta_j\) is the rate step at meeting \(j\). Each contract \(q\) contributes one linear equation:

The day-weight \(A_{q,j}\) is what carries the timing information: a step early in a window loads that window's average, while a step late in the window barely moves it but appears in full in the next window.

Identification via sparsity. \(A\) is short-and-wide, so we resolve the under-determination with a sparsity prior — iteratively reweighted least squares approximating

This is justified because the BoJ adjusts policy at very few meetings; the \(\ell_1\) penalty recovers a path of a few discrete moves rather than a smeared continuum of tiny changes at every meeting. The recovered per-meeting steps \(\hat{\delta}\) are then quantised onto a configurable increment grid and fed into the same expanding-tree methodology used for the ECB — so the meeting tabs, the granular basis-point outcomes, and the aggregated cut / hold / hike figures are produced by identical downstream code once each meeting's step is known.

Methodological decisions

• Sparsity over plain least squares. Least squares would spread a quarter's implied change across both of its meetings (a phantom "half-move" at each). The \(\ell_1\) prior instead localises the move to one meeting; the cross-quarter timing decides which one.
• Increment grid: 25bp, configurable. Outcomes are quantised to 25bp at launch. Recent BoJ normalisation steps have been ~15–25bp; the increment is a single configuration value and can be changed without altering the tree logic.
• Compounding approximation. Arithmetic average ≈ compounded average at ~0.5% (convexity well under a basis point). Flagged for revision if the policy rate rises materially.
• Honesty guards (no invented data). A stale strip, fewer contracts than the meeting horizon, or a degenerate fit (large residual \(\lVert A\hat{\delta} - b \rVert\)) each yield no per-meeting probabilities rather than a forced decomposition. Meetings beyond the coverage of the available contracts receive no figure.
• Anchor. \(R_0\) is the BoJ policy rate from our rate data, keeping the absolute-rate ladder consistent with the policy rate shown above.

Contrast with the ECB. The €STR calculation reads one meeting per monthly contract directly. The BoJ calculation adds exactly one stage in front — the quarterly-strip bootstrap that recovers each meeting's step — and is otherwise identical.

Monetary Policy Framework Analysis

The Bank of Japan operates under a unique policy framework combining short-term rate control with yield curve control (YCC). The Policy Board, consisting of the Governor, two Deputy Governors, and six ordinary members, conducts Monetary Policy Meetings (MPMs) eight times annually.

Current Policy Structure:

• Short-term Rate: Current account balances at BoJ (IOER) set at 0.5%
• Long-term Rate: 10-year JGB yield targeted "around 0%" with flexibility
• YCC Framework: BoJ purchases JGBs to control yield curve shape
• ETF Purchases: Discontinued regular purchases as of March 2024

Reference Rate Transition: Japan has successfully transitioned from JPY LIBOR to TONA (Tokyo Overnight Average Rate) as the primary risk-free rate, supporting the OIS market development.

Policy Rate Framework

Current Settings (as of December 2025):

• Short-term Policy Rate: 0.50% (applies to current account balances at BoJ)
• 10-Year JGB Yield Target: "Around 0%" with flexibility (actual market yields may vary within tolerance band)
• Policy Stance: Gradual normalization from ultra-accommodative monetary policy
• Last Change: July 2025 (maintained at 0.50%)

TONA Reference Rate: Tokyo Overnight Average Rate currently trading around 0.08%, reflecting the transmission of policy rate through money markets.

MPM Framework & Communication Strategy

Systematic approach to monetary policy communication and market guidance.

Macroeconomic Assessment

Key Economic Indicators (December 2025):

• Core CPI (ex-fresh food): ~2.8% YoY, driven by services inflation and energy base effects
• Core-Core CPI (ex-food, energy): ~2.6% YoY, indicating underlying inflation momentum
• Wage Growth: Shunto spring wage negotiations resulted in ~4% base pay increases for major firms
• GDP Growth: Modest expansion around 1.0-1.5% annualized, below potential but positive
• Unemployment Rate: Historically low at ~2.5%, supporting wage pressure arguments
• JPY Exchange Rate: Trading around ¥148-152 per USD, policy divergence with Fed a key driver

Policy Considerations:

• Inflation Sustainability: BoJ focused on whether 2% inflation is sustainable without monetary accommodation
• Wage-Price Spiral: Monitoring for virtuous cycle between wages and prices
• Global Uncertainties: US economic trajectory, China slowdown, geopolitical risks
• YCC Exit Strategy: Managing gradual normalization without market disruption

Adapted Taylor Rule for Japan

Modified Taylor Rule accounting for Japan's unique monetary environment:

• Neutral Rate: 0.0% (based on Fujiwara et al 2016, BoJ research)
• Inflation Response (α): 1.2 (higher than standard 0.5, reflecting deflation history)
• Output Gap Response (β): 0.2 (lower than standard 0.5, reflecting cautious approach)
• Inflation Measure: Core CPI (ex-fresh food)

Policy Communication Analysis

Comprehensive coverage of BoJ statements, Governor speeches, and market-moving announcements with technical analysis.

Macroeconomic Modeling Framework

The BoJ employs a suite of models approach for policy analysis, forecasting, and risk assessment. Primary models include Q-JEM for operational forecasting and various DSGE models for theoretical consistency.

Primary Sources & Data

Direct access to BoJ publications, data, and research: