Let's take a closer look at gamma.

Here we have reproduced the Black-Scholes risk numbers from when we introduced FX option risk metrics.

In order to focus on the gamma numbers.

The first thing to spot is that the number looks huge.

Gamma tells us how delta changes and the delta of an option can only be between 0 and 1.

So how do we get a gamma number greater than 1? The reason is that gamma is really the local gradient of the delta curve at a particular spot price.

To scale this and apply it to a move of one unit in spot is a massive move.

In terms of the FX rate.

The gamma itself is not constant and so over such a big move, it gives a nonsensical output.

The better way to understand the gamma is to scale it to a realistic spot move and turn it into an equivalent spot.

FX position change. We will do this next.

So here the gamma has been scaled to one big figure by multiplying by 0.01, so the raw Black-Scholes delta of the option will change by 0.06 per big figure movement in spot.

It sounds a lot more reasonable now for the FX trader to understand what this means then, just as we did with delta, we need to scale up the gamma by the notional in the base currency.

By doing this, we get the change in our effective spot position through a one big figure move in the spot rate.

So we can see that with the gamma we have here.

If we own 10 million euro notional of this option, our spot delta position will change by 0.6 million per big figure move in spot.

If one big figure is too crude, the gamma can be calculated per pip or maybe per 10 pips to match.

A more usual short-term movement in spot and maybe a more realistic reeding interval, even better would be to run a scenario table, which shows how your delta changes as spot moves to see the gamma play out.

The advantage of this kind of scenario test is that you can see the effect of non-constant gamma.

To conclude our discussion on gamma, here we have a delta versus spot scenario table.

In this case for a 10 million euro long position in a 6 month 1.10 straddle.

As you can see, assuming we do the initial hedge when spot is at 1.10, then we have a 0 delta there.

The effect of the positive gamma position can be seen if we see how we get long Delta in a rally and short delta in a sell off.

If a trader with this position experiences a one big figure rally from 1.10 to 1.11 to rebalance their delta, they would need to sell 1.2 million euros of spots.