FX Options Valuation

How are FX rates quoted?

Let's look at one of the main currency pairs, GBP/USD, commonly known as Cable. The key thing to remember when looking at currency pairs, is that it is the currency on the left that is being bought or sold, so GBP in this case and the currency on the right is the one that the price is in terms of, in this case, USD. 

If GBP/USD is currently 1.3474, and GBP was to strengthen (appreciate), this number will go up, as it requires more USD to buy one GBP. 

How do you value and FX forward?

FX forward trades are similar to spot FX trades, but rather than settling in 2 days, they settle at some point in the future. 

Assume the 3-month forward price on GBP/USD is 1.3485, how has this price been determined? The cost represents the costs and benefits of holding a position in GBP/USD for 3 months. If we were to buy £1 for the spot price of $1.3474 we would then be long GBP and short USD. To hold that position for 3 months we would need to pay interest to borrow the USD and receive interest on the GBP. 

Therefore, the forward price is calculated as Spot price + cost of financing USD – benefits of holding GBP. The USD costs equate to S x r-USD x t and the GBP benefits equate to 1 x r-GBP x t, which in USD terms is F x 1 x r-GBP x t. 

So Forward = Spot + (S x r-USD x t) – (F x 1 x r-GBP x t) or rearranged to Spot x (1 + r-USD x t) / (1 x r-GBP x t). 

What are FX options and what is the market terminology? 

Now we can price FX forwards, we can look at FX options. You can trade options on FX, exactly the same as any other option. 

Take the following example: 

EUR/USD spot is at 1.3474.  The 3-month forward is quoted as +11 pips which gives 1.3485.

So the 3-month 1.3485 Euro call–dollar put would be at the money forward. This is just one option, to buy euros and sell dollars, even if the name sounds like it might be two options. This trade may also be known as just a Euro call.