nikol
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I observe both measures: RN via options, RW via econometrics or similar.
What are model types to mix them?
Is this blending useful at all for a purpose of trading? Or
May be, is it better to observe degree of their discrepancy as a trading signal?
PS. or the answer "depends on"?
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... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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deeds
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most literature i have seen discusses separate analysis.
scenario analysis is a place where they are forced to interact.
have seen three approaches
Nice discussion of elementary risk neutralizing in a toy problem in Rubinstein's "On Derivatives" set out a little more nicely in a basic paper by Gaia Barone-Adesi...looks at earthquake probabilities and then adjusts a la BS framework
Market price of risk (Sharpely speaking) type adjustments use current market information more specifically, can see this in papers on interest rates and other non-tradeables and/or incomplete markets (where we are invited to think about the two worlds)...this is not apparent in BS for publicly traded equities because we start with fair value equity price, no adjustment necessary (kind of the thrust of the whole BS theory)...a place where this has reappeared as a significant question is in the treatment of contingent payments in M&A where we have options over revenue/earnings...this is now routinely adjusted by financial statement valuation jockeys in a slightly dodgy calculation based on (perhaps required) imprecise interpretation of finance and option pricing theory...there is (somewhat dodgy) guidance about this from AICPA
Timothy Falcon-Crack (and others) will show you how to create real world prob analysis for options
There are some unexplored leads here, e.g. using implied trees and other approaches
lmk if you don't see any of the sources, may be able to send snips (all are pdfs floating on the detritus of the web)
EDIT: another good source of literature is the credit world...moody's default estimates and other sources on one hand, indices and CDS on the other
EDIT2: apologies, immersed in a different kind of BS. Stephen Ross's Recovery theorem is the recent gigantic result in recovering real world probabilities from risk neutral market indications.
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nikol
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BS (Bayes?) completely forgot. Kind of blackout. :(
However, one concern. Simple illustration:
If Prior ~ Norm(m1,s1) and Data(m2,s2), then Posterior ~ sigma weighted Norm()
which means that BS is nothing else but pure blend of distributions. No magic.
Will take a look into other ideas. Thank you! |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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TonyC
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| Nuclear Energy Trader |
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deeds wrote:
"EDIT2: apologies, immersed in a different kind of BS. Stephen Ross's Recovery theorem is the recent gigantic result in recovering real world probabilities from risk neutral market indications."
if you search around the web you'll come across a video of Peter Carr giving a lecture at MIT where he goes over what is required to use Ross's (is that enough "s"-es?) method of mapping the risk neutral distribution/vol-smile to an implied physical distribution
I remember thinking at the time that I actually understood it, which gives you some idea of just how clear Peter's explanation really was |
flaneur/boulevardier/remittance man/energy trader |
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Baltazar
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| I haven't looked in a long time but I think Ait Sahalia did something like that too. |
Qui fait le malin tombe dans le ravin |
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deeds
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i guess the notion of using 'real options' in business strategy and finance falls under the same category...often mix risk neutral commodity prices (gold is classic example, oddly have done a lot of work with salt and natural gas in other settings) and subjective probabilities...not sure why i didn't include in the first place...
@nikol - please update with pointer/reference if you see something unmentioned or new |
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ronin
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> Is this blending useful at all for a purpose of trading?
At the risk of stating the obvious:
- RN means "the cost of hedging this"
- RW means "the value of this, in my opinion"
Some things you hedge, some things you run.
You decide on the mix based on, well, all sorts of things. Risk to reward, limits, targets, other business reasons, operational considerations, etc.
The answer is pretty much "it depends", yes.
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"There is a SIX am?" -- Arthur |
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nikol
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@deeds
No need to popup. I have taken already what I needed.
@ronin
It is valuable!
When writing "it depends" I had in mind this:
- separate consideration is needed to capture signals, maybe directional or even market making
- blended distributions can be used for risk. However, indeed, I ask myself what if I observed big/significant difference between RW and RN, how can I use this for risk eval?
Btw.
Are there models to imply measure from LOB? Does it make any sense? |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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ronin
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Right, but the decision process is then:
- if I hedge this, these are my possible scenarios
- if I don't hedge this, these are my possible scenarios
If not hedging is attractive in risk neutral terms, if you like it and you can afford to run it, run it. If any of those is no, then don't.
I'm not sure the rest makes sense. Blended distribution for risk - well, if you hedge, you have a bigger universe because you have your hedging instruments. So it's more complicated than just a copula between an option derived distribution and a distribution that you convinced yourself to believe in.
There is always a significant difference between risk neutral and real world. That's just how things work - nobody would buy stocks if their expected return was flat.
This is fairly vanilla stuff if you are dealing options on stuff on which there is no meaningful options market. Fund derivatives desks end emerging markets desks do that sort of thing all the time. |
"There is a SIX am?" -- Arthur |
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chiral3
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| I'll state the obvious also: if you're hedging it becomes real in time. Simple example would be being short BSPut(S,K,...,sig', r') and delta hedging receiving some r and sig such that r'>>r and sig'<< sig....P&L < $0. To paraphrase ronin, it's taking a view. |
Русский военный корабль, иди на хуй! |
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deeds
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@nikol - (maybe mistakenly) had thought of this thread as a commons where everyone considering the question could benefit from leads.
That (maybe mistaken) view was also behind my request.
live.
and learn. |
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deeds
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@chiral3 - well said and quicker than numbersix's massivity (though i think the point is the same)
and explosive intersections...gamestop. gamma play. viacom? the PnLs and projections of SPACulative companies, and before them OTC biotech, crammed with contingencies both financial and fully diversifiable. the convexity of melt-up per carson block / muddy waters.
i think the boundary has large analytical opportunities, also where the completeness/tradeableness of assets/markets is evolving dynamically...
Fully concur that real options models and market price of risk adjustments are number play typically. but in the right setting...
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ronin
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> Are there models to imply measure from LOB? Does it make any sense?
That is actually pretty interesting, and I did spend some time looking at that.
The short answer is no. The reason why option prices imply a distribution is because you can construct digital bets. "I pay 20 cents now, and I get a dollar if the price ends up above strike." Which is basically probabilities.
You can't do anything like that with the LOB. You can't use it to derive outcomes. It isn't even particularly forward looking - the LOB could look completely different in minutes, or even seconds.
The only thing the LOB tells you is how big a gap will be opened when given quantity crosses the spread. Any prediction is pretty much as good as the next trade, or maybe a handful of small trades. And that is assuming they arrive now.
You can still use it to form some biases in the short term. Look up microprice. But it is of limited use. Microprice based signals were old and too simplistic to work ten years ago. |
"There is a SIX am?" -- Arthur |
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nikol
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> The short answer is no.
Really strange. LOB is formed by ensemble of opinions optimised on top of future price prediction, own account and price of risk (bellman program). Why I cannot invert that?
With options my best visual example is to poll crowd of people to vote for series of statements "do you think the asset will cost more than X at time T?". The result of that is CDF(X). Integral of that is option price. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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ronin
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> "do you think the asset will cost more than X at time T?"
Yes, on the hand-waving level, limit orders are just like options. But when you get down to details, they are not.
Fist, there is the "time T" bit. Limit orders don't have that. So things to do with the LOB are at best instantaneous. And this isn't some theoretical cop-out - liquidity is always there until you need it, and then it isn't.
Then, you don't have the other side. If the stock goes up, you are eating into the ask book. But you have no idea what happens with the bids.
So, no. You can estimate some extremals, as in "over the traded quantity Q, the price will stay within the [L(Q),U(Q)] range, assuming the orderbook doesn't change shape". And you can map L(Q) and U(Q). You can also map the mid of L(Q) and U(Q), which is the microprice for Q.
And, that's it. That's as far as you can go. If you can make money with that, good luck.
But then, say I am also trading that book. I want to sell. And I notice you running in the direction of the orderbook gradient.
So I put some volume into the bid side. Away from the touch, so the risk of fill is low. You see thick bids, thin asks. Your microprice is flashing a buy signal. You quickly buy before it goes up. You fill my asks, which is what I wanted in the first place. I then safely cancel my bids. Everything is back to where it was, only I sold a bit above mid. You bought a bit above mid.
And it cost me nothing. Putting things in and out of the book is free.
The gaps in the reasoning are what I said. There was no obligation on me to keep those bids for any specific amount of time. I cancelled them when I no longer needed them. And, you assumed that new bids would follow your buying. But they didn't, because the pressure was artificial. |
"There is a SIX am?" -- Arthur |
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nikol
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@ronin
The scenario "flash my bid, to improve my offer" seems to be described everywhere as an example. Does it still work? What-if flash order is hit?
Regarding "LOB implied pdf". By comparing digital (aka binary) cash-or-nothing and one touch/no touches with vanilla gamble bet I come to different conclusion than yours - pdf info is stored inside LOB. |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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ronin
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> By comparing digital (aka binary) cash-or-nothing and one touch/no touches with vanilla gamble bet I come to different conclusion than yours - pdf info is stored inside LOB.
I'm pretty sure there is a gap in your reasoning. And, I'm pretty sure it's because you are making an implicit assumption of no cancellations, or something very close to that.
> The scenario "flash my bid, to improve my offer" seems to be described everywhere as an example. Does it still work?
The point isn't really whether it works or not. The point is that an order has no information value. A flash order is the prime example why.
> What-if flash order is hit?
That is an information event. You know more after it than you did before. It may be 'there is an idiot there chasing every flash', or it may be 'there is lots of sell volume'. It might take more than one fill to work out which. Either way, it does not change the utility of the fact that an order was placed in the book, which is zero. |
"There is a SIX am?" -- Arthur |
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nikol
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binary bets - I think I get the flavor.
You mean that with option I pay premium and expect payoff later, i.e. by paying premium I already engage into "the game". While will flash order I am not.
> The point isn't really whether it works or not. The point is that an order has no
> information value. A flash order is the prime example why.
if it has zero information value, then why should you expect that bid flash increases "offer lift rate"?? |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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doomanx
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@nikol the point ronin is making is that microprice/weighted mid alone isn't terribly good on it's own anymore because it is easily fooled. That being said the idea isn't useless and everyone and their grandmother still looks at the metric, you just need to think about the problem a bit more.
Take a hard look at the orders - how long have they been there? What was the queue like when they joined? How big are they? Did a lot of other orders follow the order? Profile the orders, then combine with micro/weighted mid and you'll do better. |
did you use VWAP or triple-reinforced GAN execution?
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nikol
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@doomanx
In my defense, my Honor.
I wondered if LOB contains distributional info.
Since "naive" Amihud/Mendelson papers (80'), the shape of LOB does not depend on mid-price, only on shape of Demand/Supply and the traded volume is optimized by hit rate of dealer's orders via maximization of PnL. So, the market making is about interaction between the two, D/S and hit rates.
http://people.stern.nyu.edu/lpederse/courses/LAP/papers/InventoryRisk/AmihudMendelson80.pdf |
... What is a man
If his chief good and market of his time
Be but to sleep and feed? (c) |
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doomanx
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@nikol no need to defend it, asking questions/discussion is not dishonourable ;)
'The shape of LOB does not depend on mid price'
I agree. I mean by definition it's almost the other way around.
'On shape of demand/supply'
Right, so you can interpret what I am talking about as identifying the 'true' supply/demand among noise by filtering out those orders that don't contain information. And really a lot of it is noise.
Also notice I didn't mention other information in the book (like trade impulse and such), but we're discussing limit orders only here. |
did you use VWAP or triple-reinforced GAN execution?
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