When quoting butterflies and as we'll see next with risk reversals too, the FX option interbank market stays with the principle of quoting in volatility. In the case of butterflies, the volatility quote reflects the spread in volatility between the at the money straddle and the strangle. As you can see here, if we're quoting a 25 delta butterfly, then the average volatility of the strangle strikes is calculated seen here at 10.75 and we subtract the volatility of the straddle 9.5 in our example. This gives a quote for the 25 delta butterfly of plus 1.25 vol. Once a trade has been agreed in vol terms, then the volatility for the straddle and strangle will be fixed with the requisite spread being applied and the strikes of the options set. Quoting in this way allows for the most transparent and easily understood market to be displayed without the unnecessary detail of particular strikes, which then need updating as spot moves up and down. As per butterflies, risk reversals are also quoted in terms of a volatility spread. In this case, it is the spread between the volatility of a call and a put with equal delta. For example, here we have a 25 delta risk reversal where there is a 0.5 vol spread between the call and the put. With the put having the higher vol. In certain markets, it is common to describe risk reversal pricing as call price minus put price. So if the risk reversal price is negative, this indicates that puts are priced higher than calls. In FX you may often see that the risk reversal quote is in absolute terms with an additional description applied to indicate which side is higher. So for example, you may see the above example being quoted at 0.5 puts over or maybe 0.5 in favor of puts or sometimes 0.5 bid for puts. As with everything in finance, if there is any doubt as to what a price means, ask for clarity.

If we're observing an interbank market, quoting straddles butterflies and risk reversals, but what we actually want is to figure out the volatility to apply to a particular strike. Then to help us, we can use the interbank quotes to get the vols for the commonly quoted points that is 25 and 10 delta strikes. To do this, we reverse the logic which took us to the vol spread prices just discussed. For example, as illustrated here, we consider an at the money straddle trading at a vol price of 8 with 25 delta butterflies at plus 0.75 vol and the 25 delta risk reversal at minus 0.5. That is puts over calls. To calculate the volatility for each 25 delta strike, both put and call, we take the at the money vol, add on the butterfly spread, and then for the call we add half of the risk reversal spread. And for the put we subtract half of the risk reversal spread because the risk reversal spread here is negative. Using the convention of call vol minus put vol, this will lead to a lower vol price for the 25 delta call than the put. The result, as we can see here, is a vol of 8.5 for the 25 delta call and 9 for the 25 delta put. We can then repeat this exercise for the 10 delta strikes.

In this way, a trader can calibrate their volatility, smile and skew in order to be able to extrapolate to the correct volatility to be used for other strikes, for example, to be used when quoting specific client trades.