Building a Synthetic FRA with Eurodollar Futures

Summary

The document describes a way to create synthetic forward rate agreement exposure using Eurodollar futures. Its example combines a long position in a contract expiring in 120 days with a short position in one expiring in 30 days to represent exposure to a 90-day forward rate agreement. The question focuses on whether the longer-dated leg must be closed after 30 days to remove exposure over the initial period.

The response emphasizes that the two futures positions together form the synthetic exposure. Closing both legs ends that exposure, while closing or allowing one leg to expire and leaving the other open changes the position into a standalone futures position. This highlights the need to track each leg and its remaining exposure over time. The document gives a conceptual explanation, but does not provide contract specifications, pricing calculations, or a detailed account of futures margining and rate conventions.

Key ideas

• A long 120-day Eurodollar future combined with a short 30-day future represents the described 90-day FRA exposure.
• The synthetic exposure depends on holding both futures legs together.
• Closing both legs removes the synthetic FRA position.
• Leaving one leg open creates a standalone futures exposure.

Tags

# Synthetic FRAs using Eurodollar futures


# Synthetic FRAs using Eurodollar futures












In order to create a synthetic FRA position of 30-day FRA on 90-day LIBOR, the diagram below shows that we can enter into positions by going long a 120-day Eurodollar contract and short a 30-day Eurodollar contract.

Here is a section from Basic of Derivative Pricing and Valuation, Reading 57, a part of CFA curriculum 2019 Level 1

Q: Looking at the diagram, is my understanding correct that what the diagram showing is 30 days from now we have to close the long position of 120-day Eurodollar at T=30 in order to achieve no exposure over 30-day period?

## Answer by David Duarte (score 2, accepted)

https://quant.stackexchange.com/a/53496

You are correct. As long as you have the short and long positions on those future contracts you have a synthetic position in the 90 day FRA.

If you close both positions, it's as if you closed your position in the synthetic FRA. But if you close one leg (or it expires) and you leave the other leg open, then you will no longer have your synthetic position and you will simply have a long position in the 120-day contract.

The impotant concept here is exposure. You are synthetically creating the exposure to a 90 day FRA.

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.