Skip to content
All library documents

Mapping Inflation and Yield-Curve Risk in Brazilian Bond Markets

Article Quant Q&A · Author: SuavestArt
Read the original

Summary

The document discusses market factors for mapping the risk of Brazilian commodity swaps exposed to commodity forwards, BRL interest rates, and the IPCA inflation index. It outlines common Brazilian curve proxies: DI futures for the nominal swap curve and NTN-F bond yields or their spreads to DI for sovereign-versus-swap risk. It also describes using NTN-B yields as inflation-linked bond factors, with an alternative of modeling spreads between nominal and inflation-adjusted curves.

IPCA is a monthly consumer price index with a daily estimate, and NTN-B cash flows are indexed to its level relative to the bond's starting index. These practices are reported as market conventions rather than a prescribed model for the swap in question. The document does not provide calibration details, factor sensitivities, or validation results; it points to a reference on Brazilian derivatives and securities for further study.

Key ideas

  • DI futures are used to represent Brazil's nominal swap curve.
  • NTN-F yields or spreads to DI can represent sovereign yield and treasury-swap spread risk.
  • NTN-B yields are commonly used as market factors for inflation-linked risk.
  • Spreads between nominal and inflation-adjusted curves are a possible alternative representation of inflation risk.
  • IPCA is published monthly and has a daily estimate used in indexed bond cash flows.

Tags

Fixed incomeCommoditiesRisk managementStatistics
Full text
# Risk mapping for Brazilian IPCA bonds


# Risk mapping for Brazilian IPCA bonds












On Jorion's 'Value at Risk' chapter about risk mapping, interest rate swaps are decomposed in a portfolio of forward contracts so they can be mapped into risk factors. I'm trying to implement this for some commodity swaps which P&L depend on three risk factors: the commodity forward price, the BRL risk free rate, and the Brazilian official inflation index (IPCA).

Is there any reference on how IPCA is modelled into risk factors? I can't find anything, even in Portuguese, and have never seen this implemented.

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/74332

Brazil markets have some conventions different from other countries. Some things look very different at the first sight, but are somewhat similar to other countries. A good book is cited in Trying to understand brazil derivatives market

Brazil's equivalent of the nominal swap curve is built from the exchange-traded DI (Interbabk Deposit) futures.

Brazil treasury issues fixed-coupon bonds called NTN-F (Notas do Tesouro Nacional - Série F). Some people treat their yield curve as market factors. Others prefer to treat the spreads between the DI curve and the NTN-F as market factors, so if you're long an NTN-F bond, you can attribute your mark to market changes to the swap curve and to the treasury-swap spread.

IPCA is Índice Nacional de Preços ao Consumidor Amplo - the Extended National Consumer Price Index, very similar to the CPI in the US and other countries. It is published monthly, but, like in some other countries with a history of high inflation, they also publish a daily estimate.

Brazil treasury issues inflation-linked fixed-coupon bonds called NTN-B's. They are mostly similar to TIPS in the US. A cash flow is some fixed number times the (daily) index at the time of the cash flow divided by the index at the inception of the bond.

Everyone I know just uses the yields of the NTN-B bonds as the market factors. But you could instead try to use the spreads between the nominal curve and the inflation-adjusted curve as some kind of inflation curve.

Brazil conventions for quoting bond prices (PU) are unusual, but don't worry about them, just use yields.

Brazil has other inflation indices and used to issue bonds linked to another index, but you're unlikely to encounter that.

## Answer by Rodrigo (score 1)

https://quant.stackexchange.com/a/74343

Brazilian Derivatives and Securities: Pricing and Risk Management of FX and Interest-Rate Portfolios for Local and Global Markets: 2016, Marcos Carreira

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.