who gets the gamma?

[Mr Doe]

Suppose the spot is trading at 100, atm implied vol at boring 15% (assume a skew across the surface), and a large order comes in to buy 1,000,000 contracts of 6 months put options struck at 50. Market maker sells them for expensive implied vol - relative to previous. But now the market maker is stuck with a huge short gamma position. Suppose, he decides he will (dynamically) hedge some of it, but the rest will be covered by spreading across strikes and expiration

Now some food for thought; if the market maker decided to hedge it dynamically he would have to chase the market as it ticks up or down, hence amplyifing the whipsaws - furthermore, he will pay for the spread and lose money on misshedges. Even if he does some spreading he will transfer the short gamma position to someone else, so the person selling him will have to do the same thing.
The question is - how gets the "bad" gamma? The short gamma from the large bet still has to be in the market; is it stuck with the trader how sold the puts and the guys how participated in the spreading, or is it embedded in the implied volatility surface (i.e. the market maker doing the spreading has to buy options of different strikes/expiration, thus lifting the implied volatility)?
Does anybody have exprience how does a large bet influence the spot and vol. surface? Any academic work?

I hope I made myself clear. Any comments are appreciated.

 

[financeguy]

So first of all, and I'm sure this is just a stupid detail, but I'd think that a 6m 50 strike off spot 100 and 15% atm vol would be extremely low delta and is not incredibly short dated and therefore the market maker wouldn't be as short gamma (locally) as you'd think. Also, because the market maker is selling a low strike on a vol higher than 15%, i.e. the smile is bid for puts / low side options, he will earn more decay for less short gamma - the risk being that getting killed if spot dumps is a real possibility as why else would the skew be bid for low side. Anyway the other point to make is that its short gamma, not necessarily "bad" gamma. If you're short gamma, yes, you stop out on spot as you get longer delta as spot goes down and shorter delta as spot goes up, but you of course receive time decay for that. So, as long as the theta you receive each day is greater than the amount you spend each day stopping out on spot, it's actually a good position. Likewise, if you're long gamma and you don't make as much money taking profit on spot as you pay away in theta each night, you've got a bad position. Obviously you can imagine situations where you're short gamma and get murdered by spot as well. Anyway onto your question...

So say a market maker gets paid for a huge amount of low side gamma by a customer. He can buy options back from other market makers (there are broker markets as well as direct interbank markets for this sort of thing), he can try to get other customers to give him gamma (a lot of customers like selling options), or he can just trade the gamma and receive his time decay. If it's a truly huge size, it's very likely the market maker will buy something back from somewhere and keep a fraction of the short gamma on his books - it's a personal decision. Now he might have to pay some spread away to buy back some gamma, but this should be less spread than he charged the customer on the way in - after all the market maker should have greater access to liquidity for generic gamma than the customer. Net on net, the market maker after reducing his own gamma position to a point at which he feels comfortable should still be up money on the trade. I'm not sure what you mean by mishedges really and why the market maker must lose money on them. One of the reasons why greeks such as gamma are so useful is that you can aggregate positions based on them and hold strike mismatches until they become very short dated, at which point if they're really a problem you can try working out of them.

Every now and again big money customers will come in and rip supply out of the market which is what I think your question is ultimately trying to address. So say this customer pays a market maker for an incredibly large amount of 6m vol (I'd keep calling it gamma but 6m is vol really and not gamma). The market maker would in turn start buying up 6m vol in the interbank markets, thus pushing the prices of 6m options higher (well not just 6m but you know what I mean). At the end of the day behind all the greeks and the math, it's just another market. If some big hedge fund went out and bought a hundred million shares of Apple stock, you'd expect the price of AAPL to go up. If some big player bought a ton of 6m vol, you'd expect mid-date options to become more expensive.

 

[Devdeep]

Anyway the other point to make is that its short gamma, not necessarily "bad" gamma. If you're short gamma, yes, you stop out on spot as you get longer delta as spot goes down and shorter delta as spot goes up, but you of course receive time decay for that. So, as long as the theta you receive each day is greater than the amount you spend each day stopping out on spot, it's actually a good position.

Precisely! Thank you for such a great explanation, @financeguy. I have a small question. Let's say that the market maker reduces his own gamma position to a point at which he feels comfortable and starts enjoying the positive theta. Assuming that the underlying is still at 100 after 4 months (it is now closer to the expiry), would it make sense to get to a more short-gamma position to enjoy further and steeper positive theta? Or is it that the deep out-of-the-money put would not have much juice with only 2 months remaining?

 

[Mr Doe]

Thanks guys for the comments.

What I wanted to ask is; how does a large (non-hedged) bet influence price discovery is spot/forward? From what you said, it seems that is only gets transfered to higher implied volatility.

 

[financeguy]

Precisely! Thank you for such a great explanation, @financeguy. I have a small question. Let's say that the market maker reduces his own gamma position to a point at which he feels comfortable and starts enjoying the positive theta. Assuming that the underlying is still at 100 after 4 months (it is now closer to the expiry), would it make sense to get to a more short-gamma position to enjoy further and steeper positive theta? Or is it that the deep out-of-the-money put would not have much juice with only 2 months remaining?

His book would likely not trade short gamma at that point due to that option, as it would be very out of the money as you point out. What delta the option has is a good way to describe how out of the money it is. The delta of a vanilla option will, give or take, describe the percent chance that option will expire in the money. So while the 6m option may have been something like a 15 delta option, in 4 months time keeping everything else constant the now 2m option is probably more like a 3 delta option (I don't know exactly, just sticking a finger in the air). And 3 delta options carry very little gamma. Something to keep in mind is that because the option he's short is deeply out of the money on the high side of the risk reversal, he'll be receiving a bit of extra decay for that. The way that is just a bit less intuitively expressed is that he'll actually get a little long gamma from it without paying much if any decay for it. This is called being long smile gamma (i.e. long gamma resulting from being marked to a smile in excess of your black-scholes gamma). In vanillas you generally get long smile gamma by selling the front end risk reversal, or some component of it as in this case. You get long gamma without having to pay for it locally, but the risk is that if spot goes to where the risk reversal says it's most volatile and it in fact realizes that volatility, you could end up with a big problem being short gamma there.

Thanks guys for the comments.

What I wanted to ask is; how does a large (non-hedged) bet influence price discovery is spot/forward? From what you said, it seems that is only gets transfered to higher implied volatility.

If I understand you correctly, I think you are asking something like "if a big customer pays the market for this 6m low strike, does this have a downward influence on spot since the customer is after all sort of selling spot by buying an out of the money low side option and not hedging it?" If that's what you're asking, the answer is, generally speaking, no. Usually the effects of this purchase would be limited to the options market, so 6m vol and particularly low strikes would become more expensive. Very occasionally people will point out if some really good fund is looking at low side spot and maybe it will get people to think about it more and maybe in the end they'll end up doing it as well, so maybe there's an argument that that could happen, but that certainly isn't a knee jerk reaction to the purchase of the options. Also the options market maker on the delta hedge at onset of the trade would have to sell the spot in the market if the customer isn't hedging his delta (and therefore would not exchange the delta with the market maker), which would put some downward pressure on spot - that could be another argument. But the spot market is much more liquid and vast than the options market and can generally do a better job of absorbing a one time delta hedge done in the market than the options market can do of absorbing a big options trade.

 

[Devdeep]

Thanks a bunch!

His book would likely not trade short gamma at that point due to that option, as it would be very out of the money as you point out...
But the spot market is much more liquid and vast than the options market and can generally do a better job of absorbing a one time delta hedge done in the market than the options market can do of absorbing a big options trade.

 

[Mr Doe]

Financeguy, thanks for the explanation; I really enjoyed the discussion .

I did found one example of derivatives driving the spot: i.e. "tail wagging the dog" (though indirectly);

“It all began in late November [1994] when ... [James] Leiter’s LM International pur-
chased $500 million of ‘knock-in’ put options from Merrill Lynch and other dealers, for
his own funds and those he managed for Steinhardt Management ... If the price [of
the underlying bonds] never broke 51 the knock-ins would expire as worthless ... After
buying the put options ... the hedge funds carried out two maneuvers ... apparently
designed to drive up the price of the Venezuelan bonds ... [buying] call options [which]
in turn forced the sellers to buy roughly $150 million of the underlying bonds ... [and]
accumulating holdings valued at between $800 million and $1 billion – or about 13% of
the total face value outstanding [ofthebonds].”
“By early December, the battle over the drive to push the Venezuelan par bonds to
51 erupted into open warfare ... On Dec. 9 the bonds surged 10%, from about 45 to
nearly 51 ... The hubbub continued the following Monday and Tuesday. EuroBrokers’
screens ... indicated that one or more firms — traders say it was Merrill Lynch — were
offering to sell unlimited amount of the bonds at up to 50.875.”— from the Wall Street
Journal, February 16, 1995, pages 9 and 20.

 

[financeguy]

Financeguy, thanks for the explanation; I really enjoyed the discussion .

I did found one example of derivatives driving the spot: "tail wagging the dog" (though indirectly);

“It all began in late November [1994] when ... [James] Leiter’s LM International pur-
chased $500 million of ‘knock-in’ put options from Merrill Lynch and other dealers, for
his own funds and those he managed for Steinhardt Management ... If the price [of
the underlying bonds] never broke 51 the knock-ins would expire as worthless ... After
buying the put options ... the hedge funds carried out two maneuvers ... apparently
designed to drive up the price of the Venezuelan bonds ... [buying] call options [which]
in turn forced the sellers to buy roughly $150 million of the underlying bonds ... [and]
accumulating holdings valued at between $800 million and $1 billion – or about 13% of
the total face value outstanding [ofthebonds].”
“By early December, the battle over the drive to push the Venezuelan par bonds to
51 erupted into open warfare ... On Dec. 9 the bonds surged 10%, from about 45 to
nearly 51 ... The hubbub continued the following Monday and Tuesday. EuroBrokers’
screens ... indicated that one or more firms — traders say it was Merrill Lynch — were
offering to sell unlimited amount of the bonds at up to 50.875.”— from the Wall Street
Journal, February 16, 1995, pages 9 and 20.

Ah ok well this is something very, very different. There are tons of examples of when people try to push the market in favor of their positions (and these don't necessarily have to be derivatives positions), but in order to do that people deal in large amounts of SPOT in order to make the derivatives gain in value. The important point is that the derivatives themselves aren't the instruments pushing the market - the enormous buying or selling of spot is what's doing it and the derivatives are what's being pushed. This happens a lot with barriers in the market. If one bank stands to gain a lump of money when a certain trigger level in spot trades and one bank stands to lose, you can expect (depending on the asset class and time to maturity, the shorter the more likely) a bit of warfare in the spot market. Sometimes there are customers who will try to defend (more frequently) or push barriers as well. Again, the ammo used to fight this battle is from the spot market not the options market.

Since we're on the topic of barriers, here's a simple example of when barriers triggering can influence the spot market other than interbank warfare. Consider if a bank is long a barrier to a customer, say in GBPUSD on the high side at 1.70 (I find the FX market most intuitive for explanations, and these sorts of exotics are common there as well). This is common because customers often buy options with knock outs from banks, which leave the banks long barriers and customers short them. Further suppose the customer doesn't delta hedge but the bank, of course, does. So as spot moves up and gets closer and closer to 1.70, the bank is selling more and more GBPUSD as being long a high side barrier makes the bank long delta. Then spot deals at 1.70 and the barrier level triggers. The long delta position the barrier had given the bank disappears and all that's left is the bank being short spot from all the spot it sold against the barrier, which means to get back to a delta neutral position the bank has to buy back all the spot it sold before the barrier triggered. The customer had never delta hedged so it doesn't have any spot to sell. If this is a common barrier in the market, and lots of banks are long it to lots of customers, all the stop losses in the market to buy back GBPUSD after 1.70 trades can push the exchange rate much, much higher. In any case a lot of this craziness is associated with exotic options rather than vanillas.

 

[Tsotne]

Ah ok well this is something very, very different. There are tons of examples of when people try to push the market in favor of their positions (and these don't necessarily have to be derivatives positions), but in order to do that people deal in large amounts of SPOT in order to make the derivatives gain in value. The important point is that the derivatives themselves aren't the instruments pushing the market - the enormous buying or selling of spot is what's doing it and the derivatives are what's being pushed.

Quite long ago (I believe 2-3 months back) we had a discussion on this forum with one member trying to evaluate the importance of economic/financial (qualitative) experts. And he raised an important arguments that they "predict" "loudly" the market in order to make others follow his lead and gain advantage of such activities. I wonder what your ideas and opinions are regarding this issue. As you mentioned, how do people push market in favor of their position??????

http://www.quantnet.com/forum/threads/financial-analyst-opinions.5504/

 

[financeguy]

Quite long ago (I believe 2-3 months back) we had a discussion on this forum with one member trying to evaluate the importance of economic/financial (qualitative) experts. And he raised an important arguments that they "predict" "loudly" the market in order to make others follow his lead and gain advantage of such activities. I wonder what your ideas and opinions are regarding this issue. As you mentioned, how do people push market in favor of their position??????

Hmm well this is outside of my immediate area of expertise, but from what I've seen in my market is that money talks. Sure, people put out research and express opinions that support the positions they've put on - but what else would you expect them to say? They've put on the positions, surely they truly do think positively of them. From what I've seen, someone taking a very large market-moving position along with making some reason for it public can influence others to follow along. But if it's a guy that doesn't have a great reputation in the market (and people do remember track records), then it'll probably go ignored. So I think my response would be that generally, only people that have tended to be right in the past will be listened to. If you scream about something and it goes wrong, no one will listen to you next time - and will probably take you down. I have to believe you can't be successful in profiting off a self fulfilling prophecy every time and that traders would catch on and run you over. On the trading floor from time to time you hear conversations like "this guy just paid the desk for 50 but he's an idiot - yours 100". You also hear the opposite. Certainly it's plausible that in equities you could imagine someone taking a position in a stock, starting a rumor about the company, then offloading that position at a profit, but I've never seen anything like that - but then again I don't look at individual stocks.

 

[Tsotne]

I also meant experts having a good reputation. Institutional investors are less likely and almost never follow their opinions. I agree with your points.

 

[Mr Doe]

Thanks again for the comments!

@financeguy: What is your experience with pin risk? Do you think that a large open interest can influence the spot? My thinking about that is that it might be easier for the m.m. to move the underlying out of the money, than to fight with 0 or 100% delta. I read recently that gold might get pinned around 1500 or 1520 strikes (next week exp.), so I would be interested to hear your thoughts about it.

Also, I was thinking about portfolio insurance and 87 crash; it was a negative gamma trade (they were replicating a put, right?) and same as in my example the gamma had to be stuck with someone. Would you argue that it was a liquidity problem or a massive short gamma issue?

Again, thanks for an illuminating discussion.

 

[financeguy]

Thanks again for the comments!

@financeguy: What is your experience with pin risk? Do you think that a large open interest can influence the spot? My thinking about that is that it might be easier for the m.m. to move the underlying out of the money, than to fight with 0 or 100% delta. I read recently that gold might get pinned around 1500 or 1520 strikes (next week exp.), so I would be interested to hear your thoughts about it.

Also, I was thinking about portfolio insurance and 87 crash; it was a negative gamma trade (they were replicating a put, right?) and same as in my example the gamma had to be stuck with someone. Would you argue that it was a liquidity problem or a massive short gamma issue?

Again, thanks for an illuminating discussion.

I don't think having "pin risk" would influence the market all that much. All pin risk is short gamma on day of expiry, which is just translated into a delta position with a discontinuous jump around the strike. In vanillas, if you're delta hedging, it doesn't matter if it's an in the money call or an out of the money put, it's all the same (put-call parity, etc.). You're either long a strike or short a strike. So say you're short a 1500 strike in 100, that just means if XAUUSD spot on expiry is around 1500, a hedged position would be to run your deltas such that you are long 50 XAUUSD below 1500 and short 50 above. If spot starts moving away from the strike you just stop out your position and hopefully it doesn't cross back over the strike the other way. It's very unlikely that a bank would try to move gold spot away from 1500 just because it has strikes there. The market is so big you could lose more money trying to push spot around than if you wind up pinning a big strike. Also remember if you pin a short strike overnight you earn a lot of time decay as well. If you push the spot away from the strike, then after you don't earn your decay spot runs back and pins the strike again, that would kind of suck for you right? So my answer all in all is no I don't think market makers will push around gold spot in order to avoid pinning strikes. Of course if everyone is short the same 1500 strike and everyone is trading their deltas at the same time, that could influence the flow of the spot a little away from the strike (as it's stopping out).

As for '87, obviously I wasn't trading options then. I mean if you had sold a lot of low side options to customers who wanted insurance on equity positions, you'd have a massive short gamma position on lower spot. So if every delta hedging bank was short these options, they'd have to sell all at the same time as the market declined, which en masse would push the market further down, and which would of course then force them to sell even more, again at the same time, etc. In any case low side equity options trade at a smile premium now partly because of that crash so at least that is priced in. But yes if a bank sells an option to a customer who doesn't delta hedge, the bank gets short gamma and the customer gets long gamma (but doesn't really care most likely) and you can't just remove that from the market unless another customer who doesn't delta hedge wants to sell that option as well.

 

[Mr Doe]

Thanks again for the comments. Regarding XAU/USD, I dont know what the hell happened in the past two days, it went up to 1520, then got smacked down bellow 1500, just to skyrocket to all time high today. Honestly, I cannot say that it is somehow related to options; it is clear it external events might be the cause for the extreme price action (i.e. todays FOMC). Still, I think that its more convenient for m.m. to not have the options in the money - no hedging, no volatility exposure, nothing; just collect the premium.
Its interesting how you explained hedging on expiry, I always thought the point is to smooth the P&L, so my thoughts where that one would have a "waterfall compartment" method, where you would gently work the delta around the strike. Then again, since the price would wipp more often, you would suffer more costs due to the short gamma position.
I recall that implied volatility was flat(ish) before the '87 crash, think Rubinstein did some work on it (but cant find the article, sorry, will try to find it). Do you think that after the crash there was a colective wake-up call to guys who sold derivatives?
Furthermore, I do know of Phibros' manipulation is silver markets when they exercised out of the money calls, and then drow the price to get the payoff. Dont know how often, or isolated this kind of events are.

Sorry for shooting all over the place with the questions.

 

[financeguy]

Thanks again for the comments. Regarding XAU/USD, I dont know what the hell happened in the past two days, it went up to 1520, then got smacked down bellow 1500, just to skyrocket to all time high today. Honestly, I cannot say that it is somehow related to options; it is clear it external events might be the cause for the extreme price action (i.e. todays FOMC). Still, I think that its more convenient for m.m. to not have the options in the money - no hedging, no volatility exposure, nothing; just collect the premium.
Its interesting how you explained hedging on expiry, I always thought the point is to smooth the P&L, so my thoughts where that one would have a "waterfall compartment" method, where you would gently work the delta around the strike. Then again, since the price would wipp more often, you would suffer more costs due to the short gamma position.
I recall that implied volatility was flat(ish) before the '87 crash, think Rubinstein did some work on it (but cant find the article, sorry, will try to find it). Do you think that after the crash there was a colective wake-up call to guys who sold derivatives?
Furthermore, I do know of Phibros' manipulation is silver markets when they exercised out of the money calls, and then drow the price to get the payoff. Dont know how often, or isolated this kind of events are.

Sorry for shooting all over the place with the questions.

To be clear the method of delta hedging on expiry I've mentioned IS to smooth P&L. Also the market maker will hedge options whether or not they are in the money. Furthermore, due to put-call parity, in the money vs out the money makes zero difference when you delta hedge options, all that matters is if you're long or short the options. I have no idea why you think "no hedging, no volatility exposure, nothing" - that's just plain wrong. What is a pain is when spot crosses the strike on day of expiry but if you have your deltas running in the way I've described above and stop out appropriately as spot moves away from the strike hopefully you don't get killed. Not really sure how you think you can work deltas gently on day of expiry, and no clue what this waterfall compartment method is you speak of.

And yes implied vols across strikes were flattish pre '87, and yes, it seems it was a wake-up call to options writers who then demanded higher premiums for low strikes in equities. No clue on the Phibros stuff.