I have to plot the implied volatility surface for EUR/USD.
Searching for informations, I found that I could find call et put volatilities using
Strangle(∆) = 0,5[Call Vol(∆) + Put Vol(∆)] - ATM Vol
Risk Reversal(∆) = Call Vol(∆) - Put Vol(∆)
Call Vol(∆) = Strangle(∆) + 0,5RR(∆) + ATM Vol
Put Vol(∆) = Call Vol(∆) - RR(∆)
However, in my exercise, I have only ATM, 25∆ risk reversal, 10∆ risk reversal, 25∆ butterfly and 10∆ butterfly volatility quotations. So absolutely no strangle data.
With the data I have, is there any way to find the volatilities for both call et put?