# How to derive appropriate volatility for a binary option (with strike/term) from market data?

I am valuing a binary FX option (european) with a defined strike and term (2Y). I'm using a closed form solution based on Black-Scholes framework. How can I derive the appropriate volatility to use from the market data I have?

Market Data (all quoted in implied volatility):

ATM
25D Risk Reversal
25D Butterfly
10D Risk Reversal

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If you just need a Perl formula: github.com/barrycarter/bcapps/blob/master/bclib.pl#L1214 or in Mathematica: github.com/barrycarter/bcapps/blob/master/nadex.m#L64 –  barrycarter Oct 15 '11 at 19:33

It might be easier to use the Black-Scholes formula for binary options:

then add the distributions for each leg:

and then use numerical methods to calculate what volatility makes the legs match the quotes prices.

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