Converting EURIBOR Futures Price Volatility to Rate Volatility

Summary

The document asks how to express the volatility of a three-month EURIBOR forward rate when the corresponding futures price is quoted as a linear transformation of that rate. It distinguishes volatility inferred from options from a historical estimate based on changes in futures prices, and points out that price changes map to rate changes with the opposite sign and a fixed scale factor.

This setup implies that absolute changes in the rate are proportional to absolute changes in the futures price, while relative or log-return volatility need not be the same because the conversion is affine rather than multiplicative. The document itself gives no answer or worked calculation, and it does not resolve which volatility convention should be used for option-implied volatility. Any conversion therefore depends on the chosen definition, quote units, and whether volatility is measured in absolute terms or as a percentage of the underlying. It serves as a focused question about rate-futures quoting and volatility units rather than a complete method.

Key ideas

• The quoted futures price and implied forward rate are linked by a linear transformation.
• A change in the rate is proportional to the futures price change and has the opposite sign.
• Absolute volatility scales under this conversion, while log-return volatility requires separate care.
• The document poses the conversion problem but provides no answer or worked example.

Tags

# What's the link between EURIBOR3M futures volatility and rates volatility?


# What's the link between EURIBOR3M futures volatility and rates volatility?












If I am not wrong, EURIBOR3M futures with maturity $T$, whose price is $F_{T}$, are quoted like contracts which express the underlying forward rates, $r_{T}$, as

$$r_{T}=\frac{100-F_{T}}{100}$$

Now consider a generic Call option, with strike $K$ and maturity $T$, written on EURIBOR3M futures, and its implied volatility, that is $\sigma(T,K)$; you could also consider an historical estimator of $F_{T}$ volatility, like its log-differences rolling standard deviation, which would return $v(T)$.

By the way, here's the question: how would you define the volatility of $r_{T}$ knowing the volatility of $F_{T}$ and their relationship expressed above?

P.S.: it should be a function of $\sigma(T,K)$ or $v(T)$, because, if I am right, it must be

$$r_{T,t}-r_{T,t-1}=\frac {F_{T,t-1}- F_{T,t}}{100}$$

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