RR vol quote


The RR vol quote σʳʳ (also denoted as RR) 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.
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, σʳʳ is not some sort of vol quote for the price of
Risk Reversal, since it is possible for two Risk Reversals to have the same σʳʳ but different prices.
For a given expiry T and a given moneyness m (for example m = 25), σʳʳ is defined as:
σʳʳ = σᶜ - σᵖ
where
σᶜ is the implied volatility of a European call that has delta Δ = m/100
σᵖ is the implied volatility of a European put that has delta Δ = -m/100

For example, when T = 1 month and m = 25, one may refer to the respective σʳʳ as RR (25-Delta 1M)

σʳʳ represents the extra volatility which is added to the call volatility compared to a put volatility which has the same moneyness.

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 σʳʳ on the volatility smile:


The picture below shows the effect of σʳʳ on the probability density function of the terminal fx rate:


Most currency markets exhibit a negative σʳʳ