# 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

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

• Just a note I have to mention, if you are referring to the Euribor options the vol is quoted onj the implied rate, not the future price, so both your terms is the same – Abrag Mar 3 '14 at 6:42