The premium unfortunately gives us another opportunity to confuse ourselves when it comes to FX options. The natural result of putting the details of anx option into a standard option pricer like Black-Scholes is a price in the quoted currency. So for a euro dollar option, the Black-Scholes price would be dollars per euro of notional. In the example here, we consider the price of a three month euro dollar 1.10 call, and we see that we get a price of 0.0166 dollars per euro. This of course, looks like how FX rates are quoted in the first place. Spot euro dollar is quoted in dollars per euro to usually 1 10,000th of a dollar. So here we have an option price quoted in the same way to 1 10,000th of a dollar. And in the spot FX market, we know each 10,000th as 1 pip. So by that logic, our option price here of $0.0166 per euro can equally be expressed as $166 pips. Indeed, this is one of the most common ways of expressing the price. The big advantage of looking at FX options prices in terms of pips of the quoted currency is that it immediately gives us an understanding of our breakeven. In this case, if we ignore discounting, we need the underlying spot rate to be 166 pips above the strike to break even. So for the buyer, adding the premium of a call option onto its strike or subtracting for put gives you an approximate break even rate.

If we compare this with stock options, in our case, our asset is euros and it is priced in dollars. But if we were buying an option on Apple stock, then Apple stock is the asset, and we would expect to see the price of the option quoted in dollars. It would be odd to quote the price in number of shares, although we technically could. But in FX, because our asset is also a currency, we can quote the price in the base currency too. And the conversion, as you might expect, is just done by dividing by the spot FX rate at the time of the trade.

There are actually six valid ways of quoting the price of an FX option, although thankfully, they are not all equally common. The root of all of the prices is the Black-Scholes output in units of the quoted currency for each 1 unit of the base.

The first obvious way of quoting the price is in cash. But to do that, we need a notional amount. So while this method is how the trade price is eventually settled, it is not a common way of quoting the price before we actually do the trade and set the notional amount, the cash amount is arrived at in the quoted currency by multiplying the raw Black-Scholes price by the notional in the base currency. So in this example, that would be the $0.0166 multiplied by 10 million to give a total premium of $166,000. And as usual, if we want the price in the base currency in this case euro, then we divide by spot. The next two formats are the two most common in the market pips of quoted currency and percentage of base notional. Pips of quoted currency we've already dealt with, and in this case is 166 pips. And the percentage of base notional can be easily calculated by dividing the raw price by spot and displaying it as a percentage. The advantage of pips of quoted currency, as we've seen, is the visibility of our break even level. The advantage of percentage of base currency is the simplicity with which it can be converted into a cash price once the base currency notional is agreed.

The remaining two formats are much less common. Percentage of quoted currency and pips of base currency. They are only ever really used when discussing option prices with clients who are talking in non-wholesale market terms, for example, using an inverted exchange rate. The route to calculating all possible prices can be seen in the equations here.