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Interpreting FRA and Interest Rate Futures Implied Rates

Article Quant Q&A · Author: Sourabh Tripathi
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Summary

The document considers whether an FRA rate or an interest rate futures rate is the better proxy for an expected future fixing. The two instruments can imply different values because their settlement structures create a convexity difference. The answers distinguish this mathematical adjustment from the harder question of which market price best represents an unobservable real-world expectation.

One response argues that the true probability distribution cannot be directly observed and suggests treating the more liquid, dominant market as a practical reference. For Euribor, it tentatively favors swaps and FRAs because of their liquidity across maturities, while acknowledging uncertainty and suggesting the latent expectation may lie between the two markets. Another response recommends a convexity-adjusted futures rate when estimating a forward Euribor fixing, provided the futures contract dates match the target period. These are qualified views, not a definitive universal rule; the document gives no volume data or empirical comparison.

Key ideas

  • FRA and futures rates can differ because of convexity effects.
  • The true probability distribution behind market prices is not directly observable.
  • Market liquidity and trading volume may inform which instrument serves as a reference.
  • A convexity-adjusted futures rate can estimate a forward fixing when contract dates align.
  • The preferred proxy depends on the market and the use case.

Tags

Fixed incomeFuturesDerivatives pricingStatistics
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# Expected future interest rate from FRA or IR futures


# Expected future interest rate from FRA or IR futures












I want to know what is expected future rate (fixing, floating rate of fra) in the market. Should i look at the IR futures or FRA rate of the corresponding period? I know they both differ due to convexity in FRAs. But which of the two rates is the correct implied floating/fixing rate?

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/80418

This is quite an interesting question IMO.

The underlying problem is that you have two different instruments which settle to the same index value and yet demonstrate different expectations for their ultimate values. This is due to the deviation in the risk neutral density versus the true density.

The true density is latent. It cannot be observed and we can only speculate as to its value. But we know the convexity of the FRA versus the Future. This is a mathematical quantity derived from some knowledge about the expected volatility of the market and the current market level (and in the market it is often distorted by supply/demand). In a volatile market it is more advantageous to sell futures hedged by selling FRAs in a dynamic delta neutral portfolio, than to buy futures hedged by buying FRAs.

The question then is if we can designate one of these products as the numeraire, i.e. which reflects the true density and the other has a risk neutral adjustment (i.e. a convexity adjustment).

There is another market which has similar concept. The clearing house basis market. To trade a 10Y IRS versus LCH or a 10Y IRS versus Eurex(or CME) is about 3 bps difference. This is big, for the same trade that has exactly the same economics (and this is due to capital and margin costs). But which reflects the true market expectation? Here you have to assert LCH because its volumes are about 100x larger. You have to assume that the dominant market is not dependent upon the much smaller market and reflects genuine expectation, whereas the smaller market can readily treat the dominant market as its numeraire.

For Euribor FRAs and Euribor Futures the difference in volume and which is dominant is not as clear cut. I lean towards swaps/FRAs being the numeraire because it is much more liquid beyond the fronts/reds/greens and tends to have a generally smooth transition from shorter dates to longer dates. But, without seeing any volume data, I would tend to go 75% swaps and dominant and 25% as Euribor, pegging the latent true density somewhere in within the range.

## Answer by user68819 (score 0)

https://quant.stackexchange.com/a/80415

For EUR Swaps for example, the correct "forward EURIBOR rate" to use, would be the convexity adjusted (EURIBOR) futures rate (i.e. the forward rate). Assuming the future has the same fixing/end date as the period you wanted your forward fixing estimation for..

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.