Reconstructing FRA History After a Rate Index Transition

Summary

The document considers how to reconstruct historical forward rate agreement (FRA) levels after a Mexican market moved from a 28-day fixing to an overnight index. With the new OIS index published only from September 2024, a direct history for the new-index FRA is unavailable. The answer explains that a 28-day FRA represents a forward projection of rates over a term, while the overnight reference rate is a sequence of one-day rates.

To estimate the term rate from overnight rates, the overnight path over the relevant future period must be forecast and aggregated. The response therefore recommends building a yield curve and deriving FRAs from it for each date. As a rougher approximation, it suggests using the day’s one-month overnight rate and adding the FRA-to-overnight basis. No historical observations or accuracy assessment are provided, and the shortcut depends on the basis estimate; it is not presented as a substitute for reconstructing the curve when greater precision is needed.

Key ideas

• A term FRA summarizes projected interest over its forward period, while an overnight index is a sequence of daily rates.
• Reconstructing a term FRA from overnight rates requires forecasting and aggregating rates over the relevant period.
• A yield curve can be built for each historical date to derive FRA levels.
• A rough approximation uses the closing one-month overnight rate plus the FRA-to-overnight basis.
• The document provides no accuracy evidence for the shortcut or details on estimating the historical basis.

Tags

# Calculating Historical FRA levels after Index transition


# Calculating Historical FRA levels after Index transition












Recently Mexican interest rate market have switched from a 28day fixing to an OIS Index, similar to the transition from Libor to SOFR in US rates.

The OIS Index {MXIBTIEF Index} swap rate for the index started being published as of september 2024 which means also there is no FRA historical data. I am able to calculate the historical adjustment to the spot 28d fix one and extrapolate a historical rate.

Is there a way to reconstruct FRA histories using a formula rather than bootstrapping a yield curve for everyday and calculating the FRAs?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/81397

A 28d Fra is a forward looking projection of a term interest rate at a given time. I.e. it aggregates the 28days worth of interest rates into a single value.

The RFR is a 1d interest rate published at a certain time.

In order to approximate a 28drate with RFR rates you need to forecast all of the RFRs on a curve and aggregate them as of the required forecast date.

This is the same process as US Term SOFR rates. you can read how they constructed.

In short, yes you need to build a curve. If you want an approximatation use the closing 1m RFR rate on any given day and add FRA-RFR basis.

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