The objective of this post is to establish speculation as an artistic activity. This obviously does not mean that speculation can only be practiced as an art; just as one can paint, sculpt or write with no artistic ambition, it is obvious that one can speculate with no artistic concern whatsoever. My point is rather to say that it is possible to develop an artistic mastery in speculating just as it is possible to develop one in the other arts. In particular, I wish to investigate how such a mastery is conducive to successful trading.
In order to do that, I shall first consider some traditional features of art and build some analogies with speculation. That will hopefully open new perspectives to thinking and practicing speculation
I-CONSTRAINING THE ART
Let me start by a quote from Baudelaire’s Salon of 1859:
“Car il est évident que les rhétoriques et les prosodies ne sont pas des tyrannies inventées arbitrairement, mais une collection de règles réclamées par l’organisation même de l’être spirituel. Et jamais les prosodies et les rhétoriques n’ont empêché l’originalité de se produire distinctement. Le contraire, à savoir qu’elles ont aidé l’éclosion de l’originalité, serait infiniment plus vrai. » [ Salon de 1859- Le gouvernement de l’imagination]
Which, in english, gives :
“Since it is clear that rhethorics and prosodies are not arbitrarily invented tyrannies but a collection of rules required by the very organization of the spiritual being. And never did the prosodies and rhetorics prevent originality to get produced distinctly. On the contrary, to say that they nurtured the occurrence of originality would be infinitely truer.”
Such a remark was inspirational for Raymond Queneau and Francois Le Lyonnais when they founded the Oulipo in 1960. This movement may be superficially seen as a reaction against the trend of discarding traditional rules such as versification in poetry, figuration in painting or common practices (tonality, contrapuntal forms,…) in music. In this sense, it would closely relate to Baudelaire’s point in reasserting such rules on the ground that they coincide with “the very organization of the spiritual being”. Such is not the goal of the Oulipo however, it is, in fact, more in line with the questioning of the traditional rules and their replacement or improvement, as can be seen in the efforts of Schoenberg in music or in those of Kandinsky in painting. In my understanding, the Oulipo’s project is, first of all, to assert the necessity of constraints, and secondly, to reflect upon the nature of these constraints.
According to this conception, Art is not to be freed from arbitrary constraints and led to develop from a pure constraint-free intuition as some may have thought wrongly in the 20th century (with experiments such as some kinds of stream-of-consciousness, automatic writing, …); on the contrary, Art needs constraints, for intuition and imagination to be productive. The fundamental problem then becomes one of knowing which constraints are relevant, or even whether this question is meaningful at all.
In practice, Oulipo’s artists have often been led astray from their original goals by surrealistic believes, but these early objectives do retain, in my view, all their relevance. The presence of mathematicians, such as Francois Le Lyonnais and Claude Berge, among the founders, tends to credit the central concern about structures that underlies the whole enterprise. Many Oulipo’s constraints came therefore to be inspired directly from mathematics. The Oulipo’s work may then seem to be acquainted with what TA is doing in relation with speculation, provided that speculation is indeed an art.
II-THE BEAUTILESS ART
When considering art, we routinely turn our attention to beauty, as art is widely defined as the making of beautiful things. However, there is no beauty to be found in speculation, the speculator does mot produce any masterpiece that can be looked at and admired in an aesthetic perspective, the only judge of the value of a speculator’s action is the profit or the loss he made, and this judgment is as unaesthetic as can be since it solely is based on immediate usefulness. Art, from the romantic period onwards, is not considered as a mean for a material gain, or it becomes devoid of content and is abased to mere propaganda. Art is believed to be an end to itself (which was translated by Duchamp as “Art for art’s sake”), in that the search for beauty, is not the search of an external object in order to acquire or even unveil it in a mundane sense, it is more about creating beauty.
Speculation cannot be said to create anything beautiful, it merely is useful for the speculator and the system which it brings to existence: the market. However, art may also be said to be useful, just not directly so, I admit that art is an end to itself (but I contend that speculation is also an end to itself) but its creations have a purpose and even a cognitive content, the beauty is enlightening, it says some truth, albeit not one as formed and determinate as is normally considered to be a true statement.
I have written earlier that the market is evolving faster than mundane reality, and it is in this difference of speed that we must look for the reason of the absence of beauty in speculation. I believe that beauty simply has not the time to form in the market place, speculation can only display its utility, its efficiency, the enlightenment of the speculative art is at best confined to the mind of the speculator, and even there, it is only present for a fraction of a second, and it leaves no trace whatsoever. The closest to the art of the speculator is the performance of an amnesic improvisator with no public.
In that, I think I can say that speculation is an art, at least that it can be considered as an art in the way a speculator wishes to approach this activity, the speculator can, and I believe must, be an artist, even though he will never be recognized as one by any public.
III-THE FALSEHOOD OF TECHNICAL ANALYSIS
Baudelaire, again in the “Salon de 1859”, wrote this at the end of section 8 “Le Paysage”:
“I would rather return to the dioramas, whose brutal and enormous magic has the power to impose on me a useful illusion. I would rather go to the theater and feast my eyes on the scenery, in which I find my dearest dreams artistically expressed and tragically concentrated. These things, because they are false, are infinitely closer to the truth.”
[translation from “The Arcades Project”, p.536 (Q4a,4), Walter Benjamin, First Harvard University Press, 2003]
Similarly to the dioramas, it is because TA is false that it may bring us closer to the truth of speculating, which is itself a production of truth (and that is similar to the status of truth in art as well). Many Technical Analysts are looking for low-lagging tools, conceiving no-lagging tools as the ideal they should aim at, but this is a mistake, the ideal TA tool is not one with no lag at all, since if such a tool were existing, there would be no market in the first place, the ideal TA tool is one that has a lag adapted to the given speculator and particularly to his relation to the conditions of the market (its speed). The TA tools therefore are not there to tell some truth about the market but rather, like the dioramas for Baudelaire, to “artistically express and tragically concentrate” the reality of a relationship between the speculator and the market conditions (the speculator’s dream), which, when witnessed by the speculator will allow him to be attuned to the market.
The point of the Oulipo’s constraints is exactly that as well, it is to pull the mind of the artist from the unconstrained immediacy of nothingness, from the passivity of contemplation, in order to force him to reconquer this immediacy by displaying his creative power to overcome the constraints. Like an Oulipo’s constraint incites/challenges the artist to create in order to overcome it, TA incites/challenges the speculator to speculate also in order to be overcome.
That view, in some way, gives credit to the contrarian philosophy, a speculator speculates against TA. Speculation to qualify as the activity I expose here, must always be done at variance with the market and with what the market is saying; speculation is the counter-proof of TA, and it is through this double-negation of the market (TA negating the market and speculation negating TA), that the speculator becomes the market (see The Logic of Place: not-not-a = A).
Showing posts with label Technical Analysis. Show all posts
Showing posts with label Technical Analysis. Show all posts
Sunday, May 22, 2011
Monday, April 18, 2011
The possibility of cognition
The most fundamental question raised by “The Blank Swan” may be that of the level of cognition of the market an individual can acquire, and the usefulness of such a cognition if it is, at all, possible. Such a matter is obviously paramount to the validity of Technical Analysis. The untotalization of possibilities Elie Ayache shows with regard to financial markets, seems to invalidate most of the current attempts at thinking this market in explicit terms, as most, if not all, of these attempts are ultimately based on probabilities computation (and therefore on unwarranted, even false, assumptions about the totalization of possible states), and this is indeed the case for Technical Analysis, though I believe that the fractal analysis I have endeavored to develop in this blog provides for an untotalization by means of an implicit multifractal model, where Hurst exponent keeps being recomputed (I however start thinking this model still falls short of being efficient at a theoretical point of view). In this post, I therefore intend to examine, from the standpoint of such a critic of probability theory, whether some kind of cognition is still possible as to what the market is going to be.
I-READING A BOOK BEFORE IT IS WRITTEN
The best way to read a book before it is written is to write it, and that is, to some extent, what Elie Ayache is proposing us to do in The turning. There he shows how the market can be dealt with, not by predicting it by computing some probabilities artificially attached to possible states of the world, but rather by writing contingency, i.e. writing contingent claims. However, the book of the market is not written by any single individual (or even any single intentional entity), as is clearly said on page 43:
“The place of the contingent claim is nobody’s place in particular. It falls to no subject to assign a price to the contingent claim or to reflect it in his mind.”
Writing a contingent claim, therefore, does not quite amount to write the book of the market. It does amount, however, to protect one’s financial interest from the uncertainty of the market, from its contingency. In this sense of one’s direct financial interest, as being under the threat of contingency, writing of contingent claims indeed appears as the means to “mediate contingency”. The question which interests me, at the level of Technical Analysis, is whether we can mediate contingency beyond this direct financial interest, and still do that in a speculative manner (in the philosophical sense of the term “speculative”), in other terms, can we speculate (financially) speculatively?
As to read the book of the market before it is written, it obviously is not possible, as such a thing would clearly come down to write it, and as such, it would make it redundant, and therefore destroy it. If the book of the market was to be written by one subject (or if its writing could be seen as being the work of one subject), it would immediately cease to be a market, as a market can only be a place of exchange, necessarily supposing the presence of at least two independent subjects.
Nonetheless, speculative knowledge is not perfect knowledge of the phenomenon under inquiry, on the contrary, speculative knowledge is precisely imperfect, partial, fragmentary, as such a knowledge is rooted in the necessity of contingency, which implies the knowledge that perfect knowledge is illusory (not in an epistemological sense but in an ontological one).
As a consequence, we will not be able to read the book of the market before it is written, we will not be able to predict it in a deterministic way, nor will we be able to predict it in a probabilistic way, what we could endeavor to know however is the language of the market, and from knowing its grammar, we may be able to infer something about the market and its dynamics, just like a knowledge of a natural language allows us to expect a verb after a subject (or the reverse, depending on the language we consider). Such a knowledge may not be enough to diminish the absolute contingency of the market, but it should be sufficient to provide a basis for a speculative speculation, or, as Nishida calls it, an action-like intuition.
II-ACTION-LIKE INTUITION (行為的直感, KOUITEKI CHOKKAN)
Robert Wilkinson presents the concept of Action-like Intuition, that he calls Action-Intuition, in the following manner:
“We must experience the world in order to act on it, and we learn to perceive the world better by acting on it. Just as he [Nishida] insists that practical reason is more profound than the theoretical, so he insists that our natural mode of being-in-the-world is not contemplative but active, an aspect of the constant mutual interaction between individual and the world. The idea that experience is a passive reflection of the world he regards as entirely false: ‘intuition, separated from action, is either merely an abstract idea, or mere illusion’(Intelligibility and the Philosophy of Consciousness, p.208). Action-intuition, like any other form of action in Nishida’s late thought, is a mutual relation of forming and being-formed: ‘Action-intuition means our forming of objects, while we are formed by the objects. Action-intuition means the unity of the opposites of seeing and acting.’(ibid, p.191)
[…], the philosophy of pure experience leads Nishida to take a view of concept formation diametrically opposed to that to be found, for example, in the classic empiricists, according to whom concepts are arrived at by some process of abstraction based on noting common elements in numerically disctinct perceptions. Concepts are not formed in this way in Nishida’s view. We form concepts in the course of action-intuition: ‘Conceiving something through action-intuition means: seeing it through formation, comprehending it through poiesis.’(ibid, p.210)
The basic thesis of the philosophy of pure experience is that the world is a construction from such pure experience, and manifestly such construction has to have some method: action-intuition is the basic formative operation by means of which this construction is carried out. […]. Cognition has to be understood as a form of dynamic, reciprocal expression”
[Nishida and Western Philosophy, Robert Wilkinson(2009),p.120-121]
While Nishida obviously considers these remarks to apply to the whole of reality, and while such a stance may be argued against, I believe there is not much argument as to the relevance of his remarks when it comes to the market. Cognition, in this domain, can only “be understood as a form of dynamic, reciprocal expression”, and concepts formation, according to Nishida, can only occur within a poietic attitude, that is an active one, and not a detached, analytical one. This dimension is well-established by Elie Ayache in “The Blank Swan” with regards to the writing of contingent claims, and particularly with the logic of inverting dynamic replication with the view of implying volatility. When it comes to Technical Analysis, what Nishida is saying, also has an interesting consequence, in that it tells us, that, in order to grasp the market, we must grasp the grasping itself. We therefore need a Technical Analysis tool that is essentially self-referential, there is however a difficulty in understanding this sentence, that lies in the difference of velocity between the processes in historical reality, which are the ones Nishida is treating, and the processes in the market which are the ones interesting us.
The remarkable characteristic of the market is its proximity to the virtual (wherein speed is infinite), a consequence of this proximity is its very high speed, and its emancipation from causality. This high speed also accounts for the absence of a subject-object distinction because such a duality does not have the time to accrete. We are therefore confined, within the market, in a relatively unfriendly environment when it comes to scientific investigation (even a probabilistic one). In this context, self-reference itself becomes an ill-defined notion, since we don’t even know on which entity to apply such a self-reference. Of course, we may say that the market is self-referential, in some sense, but since we don’t know what the market is, since we can’t reduce it to a subject or an object, we have no direct way to comprehend such a self-referentiality in order to translate it in a cognition (be it a partial one) of how the market may evolve. This ambiguity is enough to invalidate a TA tool that would simply be self-referential since such a tool could only be efficient if every market-actors were to use this specific tool, which is obviously impossible. What we need is a tool that is self-referential in the way the market (whatever it is) is self-referential, we therefore need a TA tool that accounts for the very grammar the market is writing itself in.
III-THE GRAMMAR OF THE MARKET
What I call the grammar of the market, extending the analogy made by Elie Ayache between the market and a book, asks for a little precision here. As said above, the velocity of the virtual is infinite (because the virtual is not situated in time), and the market inherits some of this velocity more directly than history, as such it appears much faster than history and mundane life (this high speed also contaminates real history and accelerates it in some way, this is particularly visible in recent times). Natural languages also happens in history and as such, their grammar seems relatively constant to us, nonetheless, natural languages change, and so do their grammar, we must therefore expect the grammar of the market to change faster than the pace we are accustomed to with natural grammar.
In order to elucidate what we can know of this grammar (that can only amounts to some structure of it, and therefore to a meta-grammar), we must first look at the market globally and that leads us to recognize that it has fractal features. This, in itself, is already a very interesting finding, one from which I have tried to develop some TA tools , but many unknowns remain, such as the adequate period for calculation, the real meaning of fractal dimension, the scope of the probabilistic model (Fractional Brownian Motion) used,…,and the mathematics that sprang from the fractal theory seem relatively limited to clarify these unknowns. The holistic approach of Fractal Theory only provides a very global view of the price dynamics, and Mandelbrot himself even excluded its possible application either to investing or to trading; in his view, Fractal Theory only served to invalidate probabilistic and statistical inference from the market.
However, to obtain a model that would provide a higher interest in building TA tools, we need to start considering a reductionist approach at some level. Again here, I must insist, it would be absurd to look forward obtaining a precise account of the working of the market, when I am talking of reductionism, it must be clear that I mean a very partial one, that will inevitably fall short of elucidating the processes of the market. Reductionism may indeed not be the right word, what I am intending to look at, is something in between holism and reductionism. Despite such reserves, I believe there may be something valuable to find and to explicit about the market, and that this something may lead to a deeper understanding of the whole reality.
IV- FRACTALS AND P-ADIC FIELDS
I said earlier that the fundamental properties I wish to look at are to be found at a topological level. One way to study such properties is to find a space homeomorphic to the one we wish to investigate, and that is simpler to manipulate.
When it comes to self-similar fractals, which are typically build by IFS (Iterated Function Systems), it is known that we can find a map ψ so as to assert the homeomorphism of some self-similar fractals with a space of p-adic integers:
From this map, we can obtain the fractal dimension of the constructed self-similar set:
For b=3 and p=2, we get:
Where this homeomorphism is actually mapping the ring of 2-adic integers onto the Cantor Set
Alain M. Robert provides a more detailed discussion of these maps in "A course in p-adic Analysis"(pp.8-17)
Of course the fractals we wish to investigate in Finance are not as simple as those built by IFS, in particular, the self-similarity is not strictly true. Nonetheless, I think such a direction may lead to some interesting results. The ideal objective would be to establish a general procedure to find a map between a set of arbitrary fractal dimension and a subset of the space of p-adic numbers. I believe such a question is still an open one, and I am not sure of the advancement of research in this area (or even whether there are any), as I am just starting to look at this question.
The fields of p-adic numbers also present another interesting feature when it comes to account for the process of decision-making at an atomic level. The market is clearly the product of multiple decision-making processes, and as such they are all, individually, rooted in a valuation of reality. While we are well-acquainted with the classical absolute value that leads to the intuitive definition of distance (metric), p-adic fields are equipped with an ultrametric that satisfies the strong triangle inequality.
Whereas a metric satisfies the following triangle inequality:
An ultrametric satisfies the following:
Such a feature leads to rather counter-intuitive results, when we try to visualize them in geometric terms, such as the following formula, known as "The strongest wins":
However, if we think in terms of decision making, we will indeed tend to ignore menial parameters to base our decision on the one parameter we consider as the most relevant. In that, we seem to be closer to an “ultrametric mode” of thinking.
These considerations are still far from exploitable intuitions, and I myself am not very sure whether they will lead anywhere. Once again, I am only in the process of learning about this problematic, and anybody is welcome to criticize or comment, either positively or negatively, on such ideas.
I-READING A BOOK BEFORE IT IS WRITTEN
The best way to read a book before it is written is to write it, and that is, to some extent, what Elie Ayache is proposing us to do in The turning. There he shows how the market can be dealt with, not by predicting it by computing some probabilities artificially attached to possible states of the world, but rather by writing contingency, i.e. writing contingent claims. However, the book of the market is not written by any single individual (or even any single intentional entity), as is clearly said on page 43:
“The place of the contingent claim is nobody’s place in particular. It falls to no subject to assign a price to the contingent claim or to reflect it in his mind.”
Writing a contingent claim, therefore, does not quite amount to write the book of the market. It does amount, however, to protect one’s financial interest from the uncertainty of the market, from its contingency. In this sense of one’s direct financial interest, as being under the threat of contingency, writing of contingent claims indeed appears as the means to “mediate contingency”. The question which interests me, at the level of Technical Analysis, is whether we can mediate contingency beyond this direct financial interest, and still do that in a speculative manner (in the philosophical sense of the term “speculative”), in other terms, can we speculate (financially) speculatively?
As to read the book of the market before it is written, it obviously is not possible, as such a thing would clearly come down to write it, and as such, it would make it redundant, and therefore destroy it. If the book of the market was to be written by one subject (or if its writing could be seen as being the work of one subject), it would immediately cease to be a market, as a market can only be a place of exchange, necessarily supposing the presence of at least two independent subjects.
Nonetheless, speculative knowledge is not perfect knowledge of the phenomenon under inquiry, on the contrary, speculative knowledge is precisely imperfect, partial, fragmentary, as such a knowledge is rooted in the necessity of contingency, which implies the knowledge that perfect knowledge is illusory (not in an epistemological sense but in an ontological one).
As a consequence, we will not be able to read the book of the market before it is written, we will not be able to predict it in a deterministic way, nor will we be able to predict it in a probabilistic way, what we could endeavor to know however is the language of the market, and from knowing its grammar, we may be able to infer something about the market and its dynamics, just like a knowledge of a natural language allows us to expect a verb after a subject (or the reverse, depending on the language we consider). Such a knowledge may not be enough to diminish the absolute contingency of the market, but it should be sufficient to provide a basis for a speculative speculation, or, as Nishida calls it, an action-like intuition.
II-ACTION-LIKE INTUITION (行為的直感, KOUITEKI CHOKKAN)
Robert Wilkinson presents the concept of Action-like Intuition, that he calls Action-Intuition, in the following manner:
“We must experience the world in order to act on it, and we learn to perceive the world better by acting on it. Just as he [Nishida] insists that practical reason is more profound than the theoretical, so he insists that our natural mode of being-in-the-world is not contemplative but active, an aspect of the constant mutual interaction between individual and the world. The idea that experience is a passive reflection of the world he regards as entirely false: ‘intuition, separated from action, is either merely an abstract idea, or mere illusion’(Intelligibility and the Philosophy of Consciousness, p.208). Action-intuition, like any other form of action in Nishida’s late thought, is a mutual relation of forming and being-formed: ‘Action-intuition means our forming of objects, while we are formed by the objects. Action-intuition means the unity of the opposites of seeing and acting.’(ibid, p.191)
[…], the philosophy of pure experience leads Nishida to take a view of concept formation diametrically opposed to that to be found, for example, in the classic empiricists, according to whom concepts are arrived at by some process of abstraction based on noting common elements in numerically disctinct perceptions. Concepts are not formed in this way in Nishida’s view. We form concepts in the course of action-intuition: ‘Conceiving something through action-intuition means: seeing it through formation, comprehending it through poiesis.’(ibid, p.210)
The basic thesis of the philosophy of pure experience is that the world is a construction from such pure experience, and manifestly such construction has to have some method: action-intuition is the basic formative operation by means of which this construction is carried out. […]. Cognition has to be understood as a form of dynamic, reciprocal expression”
[Nishida and Western Philosophy, Robert Wilkinson(2009),p.120-121]
While Nishida obviously considers these remarks to apply to the whole of reality, and while such a stance may be argued against, I believe there is not much argument as to the relevance of his remarks when it comes to the market. Cognition, in this domain, can only “be understood as a form of dynamic, reciprocal expression”, and concepts formation, according to Nishida, can only occur within a poietic attitude, that is an active one, and not a detached, analytical one. This dimension is well-established by Elie Ayache in “The Blank Swan” with regards to the writing of contingent claims, and particularly with the logic of inverting dynamic replication with the view of implying volatility. When it comes to Technical Analysis, what Nishida is saying, also has an interesting consequence, in that it tells us, that, in order to grasp the market, we must grasp the grasping itself. We therefore need a Technical Analysis tool that is essentially self-referential, there is however a difficulty in understanding this sentence, that lies in the difference of velocity between the processes in historical reality, which are the ones Nishida is treating, and the processes in the market which are the ones interesting us.
The remarkable characteristic of the market is its proximity to the virtual (wherein speed is infinite), a consequence of this proximity is its very high speed, and its emancipation from causality. This high speed also accounts for the absence of a subject-object distinction because such a duality does not have the time to accrete. We are therefore confined, within the market, in a relatively unfriendly environment when it comes to scientific investigation (even a probabilistic one). In this context, self-reference itself becomes an ill-defined notion, since we don’t even know on which entity to apply such a self-reference. Of course, we may say that the market is self-referential, in some sense, but since we don’t know what the market is, since we can’t reduce it to a subject or an object, we have no direct way to comprehend such a self-referentiality in order to translate it in a cognition (be it a partial one) of how the market may evolve. This ambiguity is enough to invalidate a TA tool that would simply be self-referential since such a tool could only be efficient if every market-actors were to use this specific tool, which is obviously impossible. What we need is a tool that is self-referential in the way the market (whatever it is) is self-referential, we therefore need a TA tool that accounts for the very grammar the market is writing itself in.
III-THE GRAMMAR OF THE MARKET
What I call the grammar of the market, extending the analogy made by Elie Ayache between the market and a book, asks for a little precision here. As said above, the velocity of the virtual is infinite (because the virtual is not situated in time), and the market inherits some of this velocity more directly than history, as such it appears much faster than history and mundane life (this high speed also contaminates real history and accelerates it in some way, this is particularly visible in recent times). Natural languages also happens in history and as such, their grammar seems relatively constant to us, nonetheless, natural languages change, and so do their grammar, we must therefore expect the grammar of the market to change faster than the pace we are accustomed to with natural grammar.
In order to elucidate what we can know of this grammar (that can only amounts to some structure of it, and therefore to a meta-grammar), we must first look at the market globally and that leads us to recognize that it has fractal features. This, in itself, is already a very interesting finding, one from which I have tried to develop some TA tools , but many unknowns remain, such as the adequate period for calculation, the real meaning of fractal dimension, the scope of the probabilistic model (Fractional Brownian Motion) used,…,and the mathematics that sprang from the fractal theory seem relatively limited to clarify these unknowns. The holistic approach of Fractal Theory only provides a very global view of the price dynamics, and Mandelbrot himself even excluded its possible application either to investing or to trading; in his view, Fractal Theory only served to invalidate probabilistic and statistical inference from the market.
However, to obtain a model that would provide a higher interest in building TA tools, we need to start considering a reductionist approach at some level. Again here, I must insist, it would be absurd to look forward obtaining a precise account of the working of the market, when I am talking of reductionism, it must be clear that I mean a very partial one, that will inevitably fall short of elucidating the processes of the market. Reductionism may indeed not be the right word, what I am intending to look at, is something in between holism and reductionism. Despite such reserves, I believe there may be something valuable to find and to explicit about the market, and that this something may lead to a deeper understanding of the whole reality.
IV- FRACTALS AND P-ADIC FIELDS
I said earlier that the fundamental properties I wish to look at are to be found at a topological level. One way to study such properties is to find a space homeomorphic to the one we wish to investigate, and that is simpler to manipulate.
When it comes to self-similar fractals, which are typically build by IFS (Iterated Function Systems), it is known that we can find a map ψ so as to assert the homeomorphism of some self-similar fractals with a space of p-adic integers:
From this map, we can obtain the fractal dimension of the constructed self-similar set:
For b=3 and p=2, we get:
Where this homeomorphism is actually mapping the ring of 2-adic integers onto the Cantor Set
Alain M. Robert provides a more detailed discussion of these maps in "A course in p-adic Analysis"(pp.8-17)
Of course the fractals we wish to investigate in Finance are not as simple as those built by IFS, in particular, the self-similarity is not strictly true. Nonetheless, I think such a direction may lead to some interesting results. The ideal objective would be to establish a general procedure to find a map between a set of arbitrary fractal dimension and a subset of the space of p-adic numbers. I believe such a question is still an open one, and I am not sure of the advancement of research in this area (or even whether there are any), as I am just starting to look at this question.
The fields of p-adic numbers also present another interesting feature when it comes to account for the process of decision-making at an atomic level. The market is clearly the product of multiple decision-making processes, and as such they are all, individually, rooted in a valuation of reality. While we are well-acquainted with the classical absolute value that leads to the intuitive definition of distance (metric), p-adic fields are equipped with an ultrametric that satisfies the strong triangle inequality.
Whereas a metric satisfies the following triangle inequality:
An ultrametric satisfies the following:
Such a feature leads to rather counter-intuitive results, when we try to visualize them in geometric terms, such as the following formula, known as "The strongest wins":
However, if we think in terms of decision making, we will indeed tend to ignore menial parameters to base our decision on the one parameter we consider as the most relevant. In that, we seem to be closer to an “ultrametric mode” of thinking.
These considerations are still far from exploitable intuitions, and I myself am not very sure whether they will lead anywhere. Once again, I am only in the process of learning about this problematic, and anybody is welcome to criticize or comment, either positively or negatively, on such ideas.
Tuesday, October 14, 2008
The weight of news
The following article from the Federal Reserve addresses the matter of the effects news announcements have on some assets price (taken in a general sense):
http://www.ny.frb.org/research/current_issues/ci14-6.html
It's a purely statistical approach and therefore lacks any model to really make sense of the data. In particular, the sample of data does not reflect the difference that may exist between a bull market reaction and a bear market reaction.
Some interesting comments however on the type of assets that are the more reactive, on the indices that elicit the most volatility, on the timing of the most significant reaction.
http://www.ny.frb.org/research/current_issues/ci14-6.html
It's a purely statistical approach and therefore lacks any model to really make sense of the data. In particular, the sample of data does not reflect the difference that may exist between a bull market reaction and a bear market reaction.
Some interesting comments however on the type of assets that are the more reactive, on the indices that elicit the most volatility, on the timing of the most significant reaction.
Saturday, June 7, 2008
About technical analysis
Let me start by precising how I understand Technical Analysis, its value and limitations.
I don't believe Technical Analysis alone encompasses all that there is to know about trading. Foremostly, to me, TA is a tool, that provides the trader with some kind of knowledge, and this, in turn may help him to decide about what trade to take and when to act upon it (when to enter it and when to exit it).
On this site, I want to explore the value of this knowledge, and how to make the best use of it.
Ultimately though, the decision taking is a psychological process, TA can just amount to a valuable input in it, along with knowledge of relevant fundamentals, as well as some level of intuition.
TA, clearly, is subjective, and as such, there certainly is a lot to discuss as to what one can gain (and how can he gain it) from its practise.
One last precision: As a FOREX trader, I don't really care about Volumes, which are an important component when it comes to stocks, but have much less relevance in an OTC market.
I don't believe Technical Analysis alone encompasses all that there is to know about trading. Foremostly, to me, TA is a tool, that provides the trader with some kind of knowledge, and this, in turn may help him to decide about what trade to take and when to act upon it (when to enter it and when to exit it).
On this site, I want to explore the value of this knowledge, and how to make the best use of it.
Ultimately though, the decision taking is a psychological process, TA can just amount to a valuable input in it, along with knowledge of relevant fundamentals, as well as some level of intuition.
TA, clearly, is subjective, and as such, there certainly is a lot to discuss as to what one can gain (and how can he gain it) from its practise.
One last precision: As a FOREX trader, I don't really care about Volumes, which are an important component when it comes to stocks, but have much less relevance in an OTC market.
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