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vplanas
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market maker's dynamics

November 8th, 2004, 10:22 am

Is there any model that consider market makers behaviour that justify the random hypothesis of the stocks prices and the log-normal returns?Can a market maker control the price of a stock? How many market makers are there for a particular asset?I would really appreciate some light in this subject, and some references about the subject. Thanks.
 
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Aaron
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market maker's dynamics

November 8th, 2004, 1:32 pm

You don't justify a hypothesis. You make it, deduce the implications and test them. If the implications are true or useful, the hypothesis is useful.There are models of market makers, this field of study is called market microstructure. However it's hard to generalize about this area. There are many kinds of market makers in different markets.In stocks, you have specialists on the New York Stock Exchange who follow one set of rules. Over the counter you have market making firms with different rules. The number depends on the trading interest in the stock.Although it's hard to answer in general, I would say for the most part the market maker does not control the price of the stock, it (or he or she) only mediates the execution while the market price adjusts.
 
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Aaron
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market maker's dynamics

November 8th, 2004, 1:32 pm

Repeated post deleted.
Last edited by Aaron on November 7th, 2004, 11:00 pm, edited 1 time in total.
 
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vplanas
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market maker's dynamics

November 8th, 2004, 2:30 pm

By 'justify' I was meaning that there's a more fundamental (at the microstructure scale) model whose consequences implies for instance, the hypothesis of random assets behaviour, probably as a limit case or under reasonable simplifications and approximations. In the same way as statistical mechanics 'justify' the thermodynamical laws. Maybe it wasnt the very appropriate word.Do you know where could i find a good reference for such models.Is this an active research area. Is this interesting for practitioners or just academis?Thanks again.
 
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ScilabGuru
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market maker's dynamics

November 8th, 2004, 7:03 pm

To what I remember this idea can be derived from utility function theory. Every participant (investor ) on the market has it's own utility function that he tries to maximize. The general properties of these functions induce stochastic behaviour of the market ( like in statistical mechanics). Additionally, it justifiesbidask spread even in the simplest case when the intermediate party does not take any commission. Unfortunately I don't remembert the references. But utility function here is the key.
 
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exotiq
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market maker's dynamics

November 8th, 2004, 10:20 pm

I think one possible word you might have been thinking of is "explain" rather than "justify".Theoretically, market makers have no market views, are the most risk averse (using in ScilabGuru's utility terms), and act as pure reactionaries to the market and manage inventories to be as flat as possible. Market makers who don't just run a single stock inventory but instead hedge, say, a vega book of options and arbitrage with forwards, variance contracts, and options of different strikes, the inventory management problem is more interesting. That market makers have no interest in pushing price one way or another, and their inventories are either non-public or reflected in price is an efficient market theorist's evidence of how these guys simply facilitate the random walk.There has been a good deal of research in Microstructure dealing with the informational content of order flow, especially in decentralized markets like FX.The agents whose dynamics interest me are not the market makers, but the speculators and natural investors, since they have a reason to influence market direction. For any agent the dynamics influence the price like the water molecules' influence on the particles Brown observed his namesake motion on...
 
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vplanas
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market maker's dynamics

November 9th, 2004, 8:22 am

My problem with utility functions is that I see these theories as mathematical 'tricks', that gives sometimes right answers, but I dont believe in a heuristic interpretation (or even pragmatic) at a fundamental level.They dont help me to 'understand' the market, they just tell me that there's a set of function such that if i maximize certain combination and i do certains operation i get some result that could be interpretate in a market/macroeconomic setting.Maybe this is more a philosofical problem of mine, I would feel more confident with a microstructure theory that i can understand and accept, but of course each of us would prefer different theories as the explanation.Exotiq, very interesting your comments. Maybe a theory of investors and speculators in which market makers are just the intermediate agent.
 
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Aaron
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market maker's dynamics

November 9th, 2004, 5:56 pm

I think you meant "justify." In my terminology, you aren't interested in hypotheses, you want to know the truth. Modern finance has made most of its progress by making hypotheses that are clearly false; but lead to useful implications. "Securities are priced as if the market incorporates all information," rather than "the market incorporates all information." This is not a theory of what's inside investors' heads; it's a theory of security pricing.Newton explained Kepler's laws by making a bunch of false hypotheses: all celestial objects are incompressible perfect spheres of uniform density, planets have no gravitational influence on each other, neither larger (other stars) nor smaller (moons, asteroids, etc.) objects affect orbits, there's no such thing as relativity or quantuum mechanics; and so on. In the context of 16th century physics, it made little sense to investigate these hypotheses. Some everyone knew were false, others people couldn't understand, still others were impossible to test.Personally, I think finance is too young for investigation into the depths of its hypotheses to be useful. Assumptions should be challenged always, conclusions also, but there is a time and place for challenging hypotheses. However, I'm often wrong and you may do some useful work this way.
 
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vplanas
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market maker's dynamics

November 9th, 2004, 9:08 pm

QuoteOriginally posted by: AaronI think you meant "justify." In my terminology, you aren't interested in hypotheses, you want to know the truth.I couldn't have said it better, Aaron.My interest in finances is academic with an eye in applications, so i want to know (at least) some truth.However, I'm not particularly interested in write down an abstract model whose conclusions give right and usefuls answers. There are much smarter and pragmatic people than me to do that.My objective is to interpretate the real world (market makers, speculators, etc) in terms maths (equations) and models for which we can recover the usefuls and pragmatical models that people use.Thermdynamics is a theory that gives right and usefuls answers almost all the time. You define Entropy, Entalpy, etc. Well, I like statistical mechanics.Anyway, i look with admiration people can be more practical than me.
 
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farmer
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market maker's dynamics

November 9th, 2004, 9:21 pm

The problem with modeling market-maker behavior is that they are at a unique information vantage point.There is nothing complex about what they do, once you know what they see. So it is an information-gathering problem, not a problem of how to behave once you have the information.Even when they are at a relatively symmetric market-facing vantage point - as with some types of options market-makers - they will face their own subset of customers or clients. So while two different market makers might both be eager to sell at $1.25, the one with the sales force will get the sale. He will then become the high bidder in the exchange to offset this sale.Or, when such a market-maker has a proprietary customer order in hand unfilled, he can treat it as an option, and lean on it to take a position in the central marketplace.I can only guess that market-makers are a bit like John Zogby. Once they have spoken to three of their customers, they can pretty well predict what the fourth guy who calls in is likely to say.
 
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vplanas
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market maker's dynamics

November 10th, 2004, 8:41 am

So, if I understood, the role of market makers is basically to adjust the prices using their information about supply and demand. At the end, that affect the prices is (as exotiq said) investors and speculators, being the market makers the tool of the system to materialize the change in value of a asset.If it's something like that, then the markov property of the classical theories is not justifiable ( in my sense). Am I wrong here?
 
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DominicConnor
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market maker's dynamics

November 10th, 2004, 10:04 am

I think the Markov property is justified, since it reflects some of the "truth" you are seeking, providing you make some (roughly) realistic assumptions.In modern markets, a customer will know about as much as the MM about currrent conditions and the recent movements in price.I don't think history is thus directly a driver of the next price.The driver is the flow of orders, which you can choose to model as a bog standard Poisson process, (as in your icon But if you're after "truth", I assume you want mechanism ?The thermodynamics you love makes false but useful assumptions about the nature of matter, and one can get good approximations out of it.You want to be able to say "trades per second = f(price) - q(market state) * t (market users)"I've played with this, and although at one level it is "mathematical", it isn't really what you're looking for, indeed it is evidence that you can't get it.What I've done is create an array of market users, each with different criteria for buying and selling.Some have to buy/sell at certain times, others trade at pre defined levels, others look at recent history.You can play with the parameters, and get all sorts of results. Add in random inputs to simulate exogenous information, and you get some fun results.With sufficient computing power you can tune these market users to give the sort of results you see in real life. but it takes quite a while.
 
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vplanas
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market maker's dynamics

November 10th, 2004, 11:09 am

QuoteOriginally posted by: DCFCWhat I've done is create an array of market users, each with different criteria for buying and selling.Some have to buy/sell at certain times, others trade at pre defined levels, others look at recent history.You can play with the parameters, and get all sorts of results. Add in random inputs to simulate exogenous information, and you get some fun results.With sufficient computing power you can tune these market users to give the sort of results you see in real life. but it takes quite a while.That exactly the kind of models i had in mind. I'm not looking for an equation/relationship between a few variables, but a mechanism using market users of the kind that you describedand then run simulations imposing some heuristic rules in their behaviuours.But for me is quiet clear (probably i'm wrong...) that in the game of buy and sell it's important the history of the price. (do we agree that many people buy and sell because of the history of a particular asset?) Then, even if thes relevant history goes to 1-2 days as much, a continuous model (taken as a limit process of one of these mechanisms) will probably give us a pde with delay.Let's suposse, for a moment, that what i get is a BS with delay. Under normal condition solutions can be very similar, but under unexpected movements in one or other direction, this special nonlinear term can lead to important bifurcations in the 'dynamics'.That i expect is an amplification of bad events, (catastrophe and bifurcation theory) due to the (small) delay efect.The problem is of course how to write the model, how to choose the parameters and how to try to figure out a continuom limit, using which variables, etc.By the way, Did your model work, I mean, do you get something like a log-normal random walk for a stok? I'm very interested on it.
 
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DominicConnor
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market maker's dynamics

November 10th, 2004, 12:03 pm

[But for me is quiet clear (probably i'm wrong...) that in the game of buy and sell it's important the history of the price.In one sense pretty much all models of MMs use some sort of "history". It can be a subtle point.Take volatility, in >90% of what you read about the standard models, volatility is assumed to be an instantaneous quantity, ie measurable at a point, and models like Black-Scholes assume you know what it is going to be. But of course neither are true.MM models frequently use volatility to predict rational behaviour, since it is intuitive that bid-offer spreads are driven at least in part by the volatility.Forward volatility is usually taken some function of recent history.However "history" shows little predictive power, thus although individuals may use it to determine trades, the actual price is usually pretty independant of history. This is not always intuitive. (do we agree that many people buy and sell because of the history of a particular asset?)Some people do.However, it is frequently the case that the reason people can make money from an "efficient" market is that people can act stupidly even if it is a rational view. That i expect is an amplification of bad events, (catastrophe and bifurcation theory) due to the (small) delay efect.Dealys are something I care about actually, since my job involves prices moving physically around the market.You also need to look at relativity here, yes really. Prices do not reach everyone at the "same time", they are not processed at the same speed, and often it is the case that the person who reacts first get the whole amount available at that price.By the way, Did your model work, I mean, do you get something like a log-normal random walk for a stok? I'm very interested on it.It could be made to do that, though it was harder than you might expect. However to get any sort of LNRW I had to alter it with the goal of making it that way, rather than just toss in parameters. If LNRWs were only to be found in a a few markets, then I'd be tempted to assert that LNRW was some sort of coincidence, but we observe that most markets are at least mildly LNRW.The mechanism I belive can be seen if you imagine a market that was not LNRW.Perhaps this might be because one common type of customer had to buy at a certain time.However, people would notice this effect, and two things would happen.Firstly, those who didn't have to sell then would avoid doing so, since they'd get inferior prices.MMs would learn and thus take positions ahead of time to exploit it. This would of course result in rational bubbles.Doesn't have to be t ime driven , if an effect is driven by any visible signal then people will exploit it, and by doing so erode it almost away. This is pretty much a mainstream view of why the efficient market hypothesis works (mostly).
 
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Aaron
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Joined: July 23rd, 2001, 3:46 pm

market maker's dynamics

November 10th, 2004, 1:33 pm

The problem with this approach, in my opinion, is it treats the financial markets as given, and tries to deduce price behavior. I think it's the other way around. Only certain kinds of price behavior lead to stable financial markets, market makers adapt to provide that price behavior.Biology is a better model than physics. Selection pressure is applied to price behavior, which kills some kinds of microbehavior and allows other kinds to flourish. The surviving microbehavior is complex and difficult to relate to the macro causes; just as you wouldn't know from chemistry why one arrangements of atoms is a gene for blue eyes and another is a gene for brown.Another approach is to consider the financial markets products of conscious human design. Why are securities defined and traded the way they are? Why do we have markets for pork bellies and crack spreads, but not divorce rates? Why do different markets have different rules for matching orders, none of which are the theoretical rules that economists devise? From this view, explaining price movements from microstructure is like saying the roof of a house is angled the way it is because of the thread spacing on the drywall screws.
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