## Delta and Gamma Hedging

AdrianWS Posted 17 Feb. in #Eurusd #Fx #Fx Options #Gamma #Delta #Spot #Forwards4/29

Ranking

After discussion in a recent webinar on the price action of the GBPUSD we stumbled across a huge aspect of the market that is barely touched upon (or even known) about from a retail perspective. That is Delta and gamma hedging in the spot FX market. Firstly we need to define these, and in the least mathematical way (to keep it simple)

Delta - the change in value of the derivative compared to the change in price of the underlying asset. Delta can be expressed in a few ways, but in the FX markets it will normally be represented as a % of the notional position. For example, if I have an option position in EURUSD worth €1,000,000 and a delta of 25% then my option increases or decreases in value at 25% of what the EURUSD moves. I.e. If the EURUSD rises 1%, then my option rises by 0.25% etc

Gamma - this is the second derivative, so this is the change of delta for a change in the underlying. Delta is not constant, and as the EURUSD rises the delta changes (this relationship is defined by gamma). Once again quoted in %. For example the same option above with a delta of 25% (€1,000,000 value) might have a gamma of 10%. This means that for a 1% change in the EURUSD the delta changes by 10%. So if the EURUSD rises by 1% the delta moves from 25% to 35% for example.

I stress this is a moderately simplified version, but it covers enough to understand how important delta/gamma hedging is in the foreign exchange marketplace.

This is an excerpt from the BIS triennial survey, and it shows the breakdown of various derivatives by volume in the FX markets. As we can FX swaps are by far the largest (no surprise), spot closely follows, and then outright forwards. But at 6% in 2013 we see FX options, a small portion it seems. What is most frustrating about this, is how it is completely misquoted - many merely suggest that FX options are not important for the actual exchange rate, yet if they knew about gamma and delta hedging they would understand that it plays a significant part.

So lets consider a normal At-the-money (ATM) straddle for the EURUSD, this means you buy or sell both a put and call at the current spot rate, which is currently 1.3700. For an ATM straddle the positive delta and negative delta cancel each other out, and as such it should be pretty much delta neutral at the start of the trade. We can see this below for the €200,000 (2 lot) ATM straddle with a delta of about €-600 which is insignificantly small for a €200,000 trade.

What is crucial here is the left hand column, as this shows the net effect of both the put and call leg.What we can also see a little below the delta is the gamma. Remember this shows how our delta changes for a 1% rise in the EURUSD. This means that if the EURUSD rises by 1% our delta will be €-45,000.

Below shows the hypothetical scenario that we do in fact move up around 1%, to a nice round number of 1.3850 in fact.

What we can see here is out delta is in fact around €-45,000, not exactly but close enough. This means that we are now in effect short the EURUSD by 0.45 lots without having any spot position. A lot of options traders are purely trading the volatility and have no directional bias and so don't ever want to be exposed either bullish or bearish. As such a trader with a 1.37 straddle will look to "hedge" this options trade. This will be done by buying €45,000 in the spot market so as the delta column equals 0. It is also key to bear in mind that the gamma is still very high at this point (€37,000) this means if the EURUSD rises another 1%, the options trader needs to buy another 0.37 lots and so on and so forth.

Now lets consider if the market fell - so we are trading 1.3550 (~1% lower this time)

So in this instance, the delta on the options position is now +€45,000 or so, this means we are now long the EURUSD by 0.45 lots, once again very few options traders want this and so will hedge this delta away by selling €45,000 in EURUSD at the spot rate so to bring the delta to 0 again. Like above, if the EUR kept on falling, the trader would have to keep on selling to remain hedged.

So broadly speaking someone who is short gamma when entering a trade such as in the example above will need to sell the low and buy the high. sounds pretty silly, and well it goes against most speculation but we have to remember that this keeps them delta hedged and they are trading volatility and not spot. But in practice this does explain some of the recent price action in the GBPUSD. The market is strongly short gamma (according to a few major banks) and as such to keep hedged, the traders need to keep buying the GBPUSD as it moves higher and higher, that is why there have been very few dips, and shallow at most over the last few weeks on the move higher. However, this works the other way too, when the market changes direction, those short gamma, will need to sell the lows and there will be very short rallies.

It is almost impossible to tell when the market is long or short gamma but the price action tells us quite easily in hindsight. if the market reverses sharply from the highs or lows then the market is long gamma as they need to buy the lows and sell the highs for example.

While there isn't a concrete trading plan within this, watching the price action will help determine the market positioning which will ultimately help us decide whether to play the range or buy the dips etc etc.

Also, looking at the DTCC data from today (options trades with a US bank) we can see maybe less than 10% of the FX options trade volume for today (a very quiet day with US banks on holiday!)

Yet there is some major sized trades here, many well over 100,000,000 USD - you can only imagine the volume in delta and gamma hedging when you look at this. That is why options are so, so important!

In conclusion - this is merely a short introduction into hedging in the options markets, and hopefully if you do ever read the market is "short gamma" or "heavy gamma supply at 1.70" you hopefully will understand what this means a little better. Also, if you ever have wondered who on earth buys at the high? well at least now you know!

As always if there are any questions, just ask

thanks, Adrian.

Delta - the change in value of the derivative compared to the change in price of the underlying asset. Delta can be expressed in a few ways, but in the FX markets it will normally be represented as a % of the notional position. For example, if I have an option position in EURUSD worth €1,000,000 and a delta of 25% then my option increases or decreases in value at 25% of what the EURUSD moves. I.e. If the EURUSD rises 1%, then my option rises by 0.25% etc

Gamma - this is the second derivative, so this is the change of delta for a change in the underlying. Delta is not constant, and as the EURUSD rises the delta changes (this relationship is defined by gamma). Once again quoted in %. For example the same option above with a delta of 25% (€1,000,000 value) might have a gamma of 10%. This means that for a 1% change in the EURUSD the delta changes by 10%. So if the EURUSD rises by 1% the delta moves from 25% to 35% for example.

I stress this is a moderately simplified version, but it covers enough to understand how important delta/gamma hedging is in the foreign exchange marketplace.

This is an excerpt from the BIS triennial survey, and it shows the breakdown of various derivatives by volume in the FX markets. As we can FX swaps are by far the largest (no surprise), spot closely follows, and then outright forwards. But at 6% in 2013 we see FX options, a small portion it seems. What is most frustrating about this, is how it is completely misquoted - many merely suggest that FX options are not important for the actual exchange rate, yet if they knew about gamma and delta hedging they would understand that it plays a significant part.

So lets consider a normal At-the-money (ATM) straddle for the EURUSD, this means you buy or sell both a put and call at the current spot rate, which is currently 1.3700. For an ATM straddle the positive delta and negative delta cancel each other out, and as such it should be pretty much delta neutral at the start of the trade. We can see this below for the €200,000 (2 lot) ATM straddle with a delta of about €-600 which is insignificantly small for a €200,000 trade.

What is crucial here is the left hand column, as this shows the net effect of both the put and call leg.What we can also see a little below the delta is the gamma. Remember this shows how our delta changes for a 1% rise in the EURUSD. This means that if the EURUSD rises by 1% our delta will be €-45,000.

Below shows the hypothetical scenario that we do in fact move up around 1%, to a nice round number of 1.3850 in fact.

What we can see here is out delta is in fact around €-45,000, not exactly but close enough. This means that we are now in effect short the EURUSD by 0.45 lots without having any spot position. A lot of options traders are purely trading the volatility and have no directional bias and so don't ever want to be exposed either bullish or bearish. As such a trader with a 1.37 straddle will look to "hedge" this options trade. This will be done by buying €45,000 in the spot market so as the delta column equals 0. It is also key to bear in mind that the gamma is still very high at this point (€37,000) this means if the EURUSD rises another 1%, the options trader needs to buy another 0.37 lots and so on and so forth.

Now lets consider if the market fell - so we are trading 1.3550 (~1% lower this time)

So in this instance, the delta on the options position is now +€45,000 or so, this means we are now long the EURUSD by 0.45 lots, once again very few options traders want this and so will hedge this delta away by selling €45,000 in EURUSD at the spot rate so to bring the delta to 0 again. Like above, if the EUR kept on falling, the trader would have to keep on selling to remain hedged.

So broadly speaking someone who is short gamma when entering a trade such as in the example above will need to sell the low and buy the high. sounds pretty silly, and well it goes against most speculation but we have to remember that this keeps them delta hedged and they are trading volatility and not spot. But in practice this does explain some of the recent price action in the GBPUSD. The market is strongly short gamma (according to a few major banks) and as such to keep hedged, the traders need to keep buying the GBPUSD as it moves higher and higher, that is why there have been very few dips, and shallow at most over the last few weeks on the move higher. However, this works the other way too, when the market changes direction, those short gamma, will need to sell the lows and there will be very short rallies.

It is almost impossible to tell when the market is long or short gamma but the price action tells us quite easily in hindsight. if the market reverses sharply from the highs or lows then the market is long gamma as they need to buy the lows and sell the highs for example.

While there isn't a concrete trading plan within this, watching the price action will help determine the market positioning which will ultimately help us decide whether to play the range or buy the dips etc etc.

Also, looking at the DTCC data from today (options trades with a US bank) we can see maybe less than 10% of the FX options trade volume for today (a very quiet day with US banks on holiday!)

Yet there is some major sized trades here, many well over 100,000,000 USD - you can only imagine the volume in delta and gamma hedging when you look at this. That is why options are so, so important!

In conclusion - this is merely a short introduction into hedging in the options markets, and hopefully if you do ever read the market is "short gamma" or "heavy gamma supply at 1.70" you hopefully will understand what this means a little better. Also, if you ever have wondered who on earth buys at the high? well at least now you know!

As always if there are any questions, just ask

thanks, Adrian.