Delta hedge workout.

This workout tells us that a trader sells a three month 35 delta euro US dollar call in 15 million euro. And the question is, what is their initial delta hedge? Now remember to convert the Black-Scholes delta into an FX spot position. We multiply the option delta by the notional in the base currency. So in this case the delta is 0.35 and the notional is 15 million.

And so that equates to 5.25 million euro.

As the trader has sold the euro dollar call, the delta hedge is to buy 5.25 million euro dollar spot.

Next, we are told that they run their gamma and see that it equates to approximately a 100,000 spot euro dollar per 10 pip movement in spot. If spot now rallies by one big figure, what rebalancing trade do they need to do to restore a delta neutral position? The trader has sold a call and so if spot rallies, the gamma per 10 pips we told is a 100,000 but we're gonna make that negative 100,000.

The spot move in terms of pips, we are told that the rally is one big figure and a big figure is 0.01. So 0.01 times 10,000 gives us 100 pips.

So if we have a gamma of minus 100,000 per 10 pips and spot moves 100 pips, the change in delta is going to be the negative 100,000 divided by 10 multiplied by 100, and that gives us negative 1 million. So the rebalancing trade here is to buy 1 million euro dollar spots.