Three-Currency HJM for Brazilian Credit Markets

Raphael Coelho · arXiv:2605.29376

Overview

This paper introduces a three-currency Heath–Jarrow–Morton framework that treats corporate credit as a distinct economic sector, linked to the nominal and real economies via synthetic inflation and credit "exchange rates." It jointly models Brazilian nominal rates (DI), real rates (NTN-B), and corporate credit spreads (JGP Idex) under no-arbitrage restrictions across all three curves. Calibration uses only curve histories and spread data — no option prices — making the methodology accessible for emerging markets where derivatives data is limited.

The triangle-consistency identity

The model's central testable prediction is that an issuer's credit spread over the inflation-indexed (IPCA+) risk-free curve equals its spread over the nominal (CDI+) curve plus the model-implied breakeven inflation forward at the same maturity, up to a tenor adjustment χ:

sIPCA+(t, τ)  =  sCDI+(t, τ)  +  BE(t, τ)  +  χ(τ)

All quantities below are in basis points. Adjust the inputs to see the implied IPCA+ spread.

Implied sIPCA+(t, τ) 850 bps

Empirical finding

Applied to Brazilian debenture markets (January 2021 – February 2026), fifteen large issuers placing bonds in both CDI- and IPCA-indexed segments exhibit a three-year tenor residual averaging 640 basis points, with a cross-sectional standard deviation of just 26 bps that stays stable through monetary cycles. A retail post-tax indifference benchmark anchored on Lei 12.431 accounts for most of the residual.

Citation

@article{coelho2026threecurrency,
  title  = {Three-Currency HJM for Brazilian Credit Markets},
  author = {Coelho, Raphael},
  year   = {2026},
  eprint = {2605.29376},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/2605.29376}
}