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insomniac


Total Posts: 148
Joined: May 2006
 
Posted: 2008-03-07 09:38
I apologize in advance if this sounds like a stupid question.

Apart from the mathematical interpretation, I suppose one way of thinking of gamma is how much a delta hedged position will gain/lose with a change in the underlying price for instruments that show convexity.

Any instrument that shows convexity would have its hedge broken after a shift in the underlying price. Why then do we hear so much about "delta-neutral" positions and very little about gamma-neutrality?



ficsur


Total Posts: 13
Joined: Feb 2008
 
Posted: 2008-03-07 10:31

Executing the delta hedge is a discrete process that lags the movement of the underlying. In practice you are therefore bound to realize the gamma.

Edit: apologize. wrong answer to a different question Head against Wall


hakapveszi ha kap veszi

FDAXHunter
Founding Member

Total Posts: 8356
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Posted: 2008-03-07 10:32
Two reasons:

First reason: Delta-neutrality is a first order hedge. It should cover a good fraction of your risk (though by no means all of it, and depending on the position, you could have massive exposures in other greeks (like vega, for example)

The main reason is cost. It's usually very cheap and very easy to hedge with the underlying (although sometimes not). Hedging your gamma is more expensive:

Gamma neutrality is a second order hedge. Say you are a market maker and you sold the 100 March 08 Call. To go gamma neutral, you will have to buy some option around the 100 strike in March (or April). So, you're going to have to buy that. Assuming that no customer is willing to sell you any, you will have to go to another market maker and ask him to sell it to you. That costs obviously (you're paying his spread). It's much cheaper to hedge the delta first and then slowly try to either buy the 100 Call back or wait till someone else sells you a similar option.

Long-story short: Delta hedging allows you to warehouse a trade cost effectively for a period of time.

Second Reason: The concept of delta-neutrality is the main driver in a lot of trades: Anything that actually trades realized vol vs. implied vol will only be hedged on a delta-neutral basis.
Hedging the gamma as well would remove the potential of the trade to make money should the underlying move.... which would be self-defeating. A lot of delta hedging is actually related to traders "distilling" the underling's volatility, rather than trying to maintain a flat book.

The Figs Protocol.

insomniac


Total Posts: 148
Joined: May 2006
 
Posted: 2008-03-07 13:01
Thanks for the answers, FDAXHunter.

Coming from the credit world, it would seem that gamma hedging would be a pretty good strategy for structured products. If I've sold protection on a bespoke CDO, I should be able to hedge price convexity by buying back protection on a liquid tranche.

The reason I ask is because I'm wondering how effective delta hedging would be in such a case. Every time underlying credit spreads would move, the delta hedges would need re-balancing.

Also your second reason begs another question: in what situation, and for what instruments, would gamma hedging be an effective strategy?



FDAXHunter
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Posted: 2008-03-07 13:15
It's always a matter of cost and/or risk appetite. Is the additional cost that you incur by buying convexity worth the reduced risk and cost of re-balancing your deltas.

I don't think there's a straight forward answer to that question.

The second part of your question doesn't seem to make sense (or my explanation didn't). You need delta hedging to be able to capture the trade.
It's like this: If you buy the variance swap at a 30% annualized vol and delta hedge because you think that volatility is actually going to be higher, then hedging your gamma (i.e. selling a variance swap) will just flatten your position....

The Figs Protocol.

kr
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Posted: 2008-03-08 08:35
There is a lot of chatter about tranche gamma hedging right now. It sounds like a good idea in theory, but practice is a completely different issue. Yes, the client is buying something that only exists through replication - so the only way it's going to be created is by somebody either running all the greeks into the market or owning the other side of the trade. Some element of both is done. In general, the desk would really prefer not to run dynamic greeks because the ability to lose money while running them will show up as a limitation in taking P/L... and if you can't take the client's money while you are definitely on the desk - that is, on the trade date rather than waiting for 5 years - then it may not make economic sense to do the trade. Those limitations come from the following:

- CDO is a bespoke product, so who is going to back you up when you say the client's trade is worth X? If it's just you and your model, there will be problems

- Just b/c the model says to run greeks on 100 different names doesn't mean you will, because you will be killed by transaction costs. For example, single-name CDS bid-offer is at least 5 and often 10bps, whereas index will be 1-3bps. This is a problem if you are only paying the client maybe 50-60bps! So, even if you had a theoretical model, you probably don't live true to it.

- Liquidity and interactions with gamma are a big problem. You don't want to be always buying a rising market and selling a falling market, especially when that market tends to overshoot. But this is the gamma profile of many CDO products. The result is that the credit index volatility has grown hugely as credit has widened and deltas have gone up thru gamma effect. To give you an idea how serious this is, the volume of index hedging activity is so great that it would be creating room for index arb - i.e. single names trading maybe 3-5bps different on average than the index itself - which is only beaten back through OWIC/BWIC on big notional to beat the single-name bid-offer.

- One more issue about model quality is that if you are really costing up your rebalancing, then you better hope that your market vol is itself not volatile. Now one thing about CDO tranche models is that they do not really model the rebal costs (because spreadvol is not a factor), so the gamma produced by such a model is totally suspect. But even if it were ok, the problem is that the vvol is huge, i.e. index vol a multiple of what it used to be - maybe 2-3x.

my bank got pwnd

insomniac


Total Posts: 148
Joined: May 2006
 
Posted: 2008-03-10 14:05
Thanks for the reply, kr. To address your last point: I don't understand why gamma not being a function of spread vol makes it suspect. The fact that is doesn't depend on vol (just like the tranche delta doesn't depend on vol) is simply a function of the model.

My understanding of gamma is as first derivative of delta, so if the delta is kosher then the gamma should be too, right?

granchio


Total Posts: 1540
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Posted: 2008-03-10 23:12
kr, am really intrigued:

from the first few sentences: do i infer that some desks did the trade and just sit on it, without dynamic rehedging ? to avoid awkward questions?


>...better hope that market vol is not volatile
are these things priced with just one flat vol? no volvol? no skew etc (sorry to use equity vocabulary)

> interaction of liquidity and gamma
oh yes. i confirm... coming from EQ derivs, well known problem when pricing large corporate deals on single stocks... one normally tries to apply some rules of thumbs to incorporate the feedback, or put limits to the size based on the liquidity available. from what you say, and what i see, it sounds like it did not happen in this products (also, it often does not happen in EQ)

"Deserve got nothing to do with it" - Clint

djanklod


Total Posts: 57
Joined: Jul 2007
 
Posted: 2008-03-11 21:45
insomniac
what has been said above is true and in a way deeper/better than my own take below, which I'm posting in the hope that it might be useful for you to get another perspective.

Seems to me you're thinking too much in terms of maths and not enough in terms of what trades and what you're trying to achieve.

If you're a market maker you'll try to hedge your book as best as you can, but as explained by FDAX you won't find gamma hedges at prices that you like. And you have models that tell you that you won't lose your edge is you delta hedge, so that's what you do.

If you're buying options with a view on the market, the last thing you want it to be flat risk. In such a case what you choose to hedge depends on what you have a view about. In particular if your view is about realized vol vs implied, the only way to monetize it is to run a gamma position (but you don't want the delta if you don't have a view about where the underlying is going)

Hope this helps.

Granchio: you'd be even more scared by multi credit "models" if you looked closer...

dongta


Total Posts: 5
Joined: Jun 2007
 
Posted: 2008-03-22 16:05
This is an even more silly question: why do you delta-hedge if you want to make some money? What do you gain in this game?

baraider
Banned

Total Posts: 53
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Posted: 2008-03-22 16:32
If you work at a bank, you need to hedge unless you want to lose your shirt and you want the control office, compliance folks eat you alive.
If it's your money then you can do whatever you want: all in or nothing.

Baltazar


Total Posts: 1764
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Posted: 2008-03-22 20:24
dongta
option price do depend on the stock/index/whateverunderlying level but also on dividend/volatility/time/interset and so on.

If you want to trade dividend through option, you'd rather by neutral with the underlying and volatility moves, hence you will hedge stock moves with delta/gamma and volatility by other options/var swaps,

if your play on dividend was rigth you will gain money.

Qui fait le malin tombe dans le ravin

jaiman


Total Posts: 248
Joined: Oct 2004
 
Posted: 2008-03-26 18:42

This is an even more silly question: why do you delta-hedge if you want to make some money? What do you gain in this game?

It depends, a prop trader looking to take a directional view wouldn't hedge delta and then has to deal with the consequences of his view being wrong.

A market maker, though, is basically in the business of manufacturing and selling options. The input costs on an option would be your hedging costs (delta, gamma, vega, etc) so as long as you are selling the option for more than it cost to manufacture you're making money.


kr
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Posted: 2008-03-26 23:05
to that end, any trader worth his salt will bet on outcomes where signal-to-noise is at least semi-decent - and in most cases, the place where that's worst is in the outright market direction, so in that case being delta flat is a good start. To some extent that is because either liquidity or being a price-maker means that it is easier to take money out of something other than market direction outright. I.e. if I am in the business of replication then I will just overcharge for gamma to the best of my abilities, since I will never be able to undercut the index trader.

my bank got pwnd

Jurassic


Total Posts: 55
Joined: Mar 2018
 
Posted: 2018-05-15 23:35
>A market maker, though, is basically in the business of manufacturing and selling options.

Does this argument that market makers are manufacturers work outside options?

day1pnl


Total Posts: 20
Joined: Jun 2017
 
Posted: 2018-05-17 00:17
yes, it does work outside options. more crudely you could say a derivative is manufactured simply by holding a collection of proxy-hedges. But there are some caveats to any choice of the collection of proxy-hedges as hinted above

katastrofa


Total Posts: 415
Joined: Jul 2008
 
Posted: 2018-05-17 02:04
A more "social" explanation of the term "manufacturing" is that people working on those desks like the idea that they're actually producing something.

ronin


Total Posts: 266
Joined: May 2006
 
Posted: 2018-05-17 10:59
> more crudely you could say a derivative is manufactured simply by holding a collection of proxy-hedges

You could say it, but it wouldn't be correct. A derivative is a contract for some exchange of payments. It is created when the contract is executed. Either side can hedge it, not hedge it or mishedge it - doesn't affect the derivative contract in the slightest.

It doesn't really work outside derivatives. You can't just create another share of IBM or a UST. And you definitely can't create oil or gold. On the other hand, you can create shares in ETFs. So there.

"People say nothing's impossible, but I do nothing every day" --Winnie The Pooh

day1pnl


Total Posts: 20
Joined: Jun 2017
 
Posted: 2018-05-17 14:37
Sure, but then an options isn’t “manufactured” by the buying or selling of delta either... but that is to my understanding what is meant by the term, no? Or perhaps i simply (incorrectly) do not distinguish between the terms “manufacturing” and “replication”... ive always heard the terms used interchabgeably

ronin


Total Posts: 266
Joined: May 2006
 
Posted: 2018-05-17 17:05
Options can be created, extinguished and replicated.

If you and I trade an option between us, we "created" it. One or both of us may be hedging it, so the payoff is "replicated" on that side - but it doesn't have to be. At some point in the future, one party can ask the other to get out of the option in exchange for some cash changing hands. If the other party accepts, the option is duly "extinguished".

The expression "manufacturing" is a bit strange. I would understand it to mean "creating" an option. I can see how in a certain context it could mean "replicating" an option as well.

That's the problem with language. Words can mean different things to different people in different contexts.

"People say nothing's impossible, but I do nothing every day" --Winnie The Pooh
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