Trading FRA–Eurodollar Futures Convexity and Implied Rate Volatility

Summary

The document considers a position that is long a forward rate agreement and short a Eurodollar futures contract with matching fixing dates. It characterizes the position as having positive convexity because the FRA has positive convexity while the futures contract is treated as having none. The discussion frames the difference as exposure to interest-rate volatility rather than a direct arbitrage by itself.

Under an assumed convexity-adjustment relationship between the FRA and futures rates, the observed rate difference and time to fixing can be used to infer implied volatility for the reference rate. A trader who believes actual volatility differs from that implied by market prices could take a long or short convexity position accordingly. The document gives no market data, transaction costs, or conditions establishing a risk-free arbitrage, so the proposed trade is a volatility view and depends on the stated adjustment assumption.

Key ideas

• A long FRA paired with a short Eurodollar futures contract is described as positive convexity exposure.
• The convexity adjustment between FRA and futures rates can encode implied interest-rate volatility.
• A volatility view can motivate taking either the long or short side of the convexity exposure.
• The discussion does not establish a risk-free arbitrage or quantify trading costs.

Tags

# Long Forward Rate Agreement, short Eurodollar futures


# Long Forward Rate Agreement, short Eurodollar futures












For this question

> If you are long a FRA and short a ED future with the same fixing dates, do you have positive convexity or negative convexity?

The answer is positive convexity, because a Eurodollar future has no convexity and the FRA has positive convexity. What are the implications of this from a trading perspective? Specifically, under what conditions does this lead to an opportunity for arbitrage?

## Answer by Nicholas (score 3, accepted)

https://quant.stackexchange.com/a/22380

hypothetically if we assume that $R_{fra}=R_{fut}-\frac{1}{2} \cdot \sigma^2\cdot T^2$ holds (convexity adjustment) and you are able to observe $R_{fra}$, $R_{fut}$ and $T$ then you can extract implied volatility of reference interest rate. If your view on volatility is different then you can make a bet: long convexity position (if you expect volatility should be higher); or short convexity position (if you expect volatility should be lower).

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.