## RR vol quote

The

*RR vol quote***(also denoted as**

*σʳʳ***) is used in fx markets in conjunction with the BF vol quote as a market input towards the construction of the volatility smile for various expiries.**

*RR*Its name stems from the fact it is defined through the implied volatilities of the options involved in a Risk Reversal

In spite of the its vol-like symbol,

**is not some sort of vol quote for the price of Risk Reversal, since it is possible for two**

*σʳʳ***to have the same**

*Risk Reversals***but different prices.**

*σʳʳ*For a given expiry

**and a given moneyness**

*T***(for example m = 25),**

*m***is defined as:**

*σʳʳ*σʳʳ = σᶜ - σᵖ

where

**is the implied volatility of a European call that has delta**

*σᶜ*

*Δ = m/100***is the implied volatility of a European put that has delta**

*σᵖ*

*Δ = -m/100*For example, when T = 1 month and m = 25, one may refer to the respective

**as**

*σʳʳ*

*RR (25-Delta 1M)***represents the extra volatility which is added to the call volatility compared to a put volatility which has the same moneyness.**

*σʳʳ*It measures the slope of the volatility smile and also the skewness of the terminal fx rate probability distribution.

The picture below shows the effect of

**on the volatility smile:**

*σʳʳ*The picture below shows the effect of

**on the probability density function of the terminal fx rate:**

*σʳʳ*Most currency markets exhibit a negative

*σʳʳ*