I knew it, dear T4A, one day you and I will have to publish all this in the form of a Platonic dialogue of some sort!Probably better not to burden your post with quoting each section of mine; sections numbers will do, don't you think? The logic of succession still works, no?Or should I stop calling them numbers, logical steps, transitions between states, etc., and start calling them "prices", or "points", or "prizes"? Or just, "contingent claims"?Cheers,EA

I really think that a new book could be write with your posts It's interesting to follow this debate. I'm a bit lost sometimes but I found highly enjoyable to compare your both point of view.

OK, I will use numerical references to the sections/points/ticks/timestamps/differentiated points of your grand textured textual surface. There may be a couple of days latency, but I will offer my bid on your contingent claims with some contingent (hopefully coherent) claims of my own. I look forward to our continued swapping of integrative, derivative, and primitive claims across (and about) the duration of the market's existence.Cheers,T4A

Numbersix,Here's my point-by-point thoughts on your interesting chain of statements.Cheers!Re §1:§1.1. Agreed. We all want to know the future.Re §2:§2.1. Although contingency is real, I'm less confident that it is independent of state or time. Is not inevitability the antithesis of contingency and don't some states and times lead to inevitability? Don't procyclical economic structures and policies lead, inevitably, to bubbles and crashes so that violent price movements are inevitable, not contingent?Re §3:§3.1. If "state" is derivative, what is it derived from? I agree that the world, as perceived by an entity, starts as undifferentiated fog and that only through effort of repeated sensing and model-based processing, might that entity differentiate the world into discrete objects in discrete states. Note that philosophers of a more holistic mindset would deride the differentiation process as being reductionist (and I would partially agree that reductionism brings some dangers). Others would point out that we have many possible models for state identification of which tree-based financial models are but one.Re §4:§4.1. This issue of "being" vs. the passing thought of a "mark" may be where you and I start to diverge. For me (as someone who studied zoology and artificial life) "thought" is a hyper-derivative process with perhaps half a dozen layers of derivation between thought and the underlying primitive physical world. In many regards, thought sits on the extreme derivative end of the primitive-derivative spectrum. That fact make me extremely reluctant to consider any thought-like phenomenon (e.g., marks or strikes) to be anywhere near raw material or some primitive notion of being or contingency.Re §5:§5.1. Although the strike of contingency certainly leaves a mark on the surface, that does not imply that all "visible marks" on the surface arise from the strike of contingency. First, the surface may have some non-contingent structure whose features might be confused for contingency-induced marks. Second, misperceptions by the mark reader would appear as marks in that reader's mind but they would be marks that have no real underlying because they lie inside the reader, not on the real surface. This second phenomenon is one of the root causes of tree-taint. In essence, a volatility surface is a composition of the price surface and the tree-based model. As such, any marks on volatility surface may represent real phenomena or they may be a mirage induced by the tree-model.Re §6:§6.1. Let me see if I understand your counter-intuitive conversion of the gaze. Would it be fair to say that instead of saying simply "this is this" you would say "this is not that but could have been that?" Is any given "this" intertwined with all the could-have-been-different "thats" that it could have been? If so, I agree that we can look at things by their complements and should look at things by their complements if we wish to understand and manage risk.Re §7:§7.1. A mark on a surface actually has four interpretations, not just two: 1) an uninformative accident or blemish in the surface; 2) a positive bit of information about the world; 3) a negative bit of deception by which the mark maker wishes to induce an action for their own profit; 4) a mirage in the mind the mark-reader. Note that case #1 and #4 are quite distinct because even if they seem "random" because, in case #1, all readers observe the same mark and may have the same reaction to that mark whereas, in case #4, different mark readers see different marks. Case #4 also includes mirage marks induced by the false-models used by the reader. This last case can be rather dangerous because, to the extent that most readers use the same flawed model, those readers will all agree that the mirage mark exists -- the model creates a shared delusion.Re §8:§8.1. I agree with your forward and backward views on functions but would add two observations. First, y=f(x) also defines a coupling between two "could have been different" spaces. The first derivative, f'(x), defines a relative scaling for the relative amounts of difference in x and y. To the extent that f'(x) becomes 0, +INF, or -INF, it places a constraint that one variable or the other couldn't have been different. Second, any real-world y=f(x) comes with: 1) empirical limits on observed x and y (and the implication the y != f(x) outside the observed range); 2) theoretic models that predict potential distortions of f at extreme values of x; 3) dynamical models that reflect distortions or lags in y(t) = f(x(t)) for extreme dx/dt.Re §9:§9.1. The reverse direction, involving recalling the function, also raises the problem of the contingency of the function. That is, we see the y and attempt to recall an f, but the f could have be g or something different. Any inversion process will have this problem of adding contingency to the inverted quantity. That is, we start with a real y, invert through a could-have-been-different f to resolve a could-have-been-even-more-different x.Re §10:§10.1. Perhaps "contingent claims are written only insofar as they will be exchanged in the market," but I see two quibbles and a whopper of a problem. First, why are material marks inseparable from the material sheet? In your statements §5 and §7 you speak of the distinction of the mark/strike/trail on the undifferentiated surface/sheet. Second, exchange may be sufficient, but it is not necessary. I would strongly argue that the act of bidding/offering a contingent claim contract on a market, even if it is not exchanged, is an act of writing. People do use the current bid and offer, not just the historical ticks of exchanged transactions. In fact, for thinly traded instruments, the transaction data is too sparse and quotes must be used.§10.2. This leads to the much more serious issue of whether prices are real or not. Do price quotes mean much? Do traded prices mean much? Two phenomena suggest that prices, even the prices on trades, are less real than we might think. First, although a financial market might, in the long-term, generate efficient prices, the same cannot be said of each individual trade. The arguments underpinning EMH assume that irrationality is steadily removed from the system by reversion of pricing, transfers of wealth from irrational participants to rational ones, and by averaging processes. But none of those processes provides an instant remedy for or proof against real-time mis-pricing. In fact, any auction-like pricing mechanism will suffer from distortions -- see the "winners curse" for why exchange prices can be totally unreal under some conditions.§10.3. Second, market makers and any other hedged market participant do not care if prices are real -- they are insulated from contingency, including much of the contingency inherent in the errors in their methods. Hedged participants don't need EMH and don't need to spend time attempting to compute true prices in the way that unhedged participants do. This insulation from risk attenuates the processes that create efficient prices by making some participants cavalier about the specific price -- they don't care about the price and trade regardless of price. And as the percentage of hedged, cavalier participants in a market increases, the likelihood that two cavalier participants consummate an exchange grows. And if exchanges occur between cavalier participants, then arbitrary price excursions, unhinged from any fundamental rationale for price change, can occur.Re §11:§11.1. Hmmm... The differential view makes sense to me (see my response to §8). Clearly, we can go from y = f(x) to ∆y = f'(x)*∆x to consider the relationship between contingency in an observed value versus contingency in an underlying value. But I can't see why you say "probability is but an integral." Technically, probability is NOT the integral, but the integrand. That is, we integrate probability to estimate an aggregate expectation. That implies that probability is a derivative of expectation.Re §12:§12.1. I fear this statement has lost me -- perhaps I need to see your statements 12a., 12b., 12c., etc. My first fragmentary reaction is that exchange places are integrative both on the level of integrating the arrivals of buyers and sellers and in the sense of integrating price increments generated by those participants who compute prices in relative terms (e.g., those who think "(price(t)=X + news(t+1)=good) implies (price(t+1)=X+∆X)" ). My second fragmentary reaction is that any chain of logic involving the "body of the trader" must exclude hedged participants (e.g., hedged market makers) because hedged participants are pass-through entities that connect trading in one instrument to trading in other hedging instruments without, themselves, taking a net position in any instruments. The body of a hedged trader absorbs nothing.Re §13:§13.1. Perhaps the contingent mark is not computable but....... see my "future" remark on §17 (which was written before this remark! ).§13.2. I, personally, wouldn't say that the function is "forgotten" as much as say that the function is inaccessible to us mere mortals who are endogenous to the system. We humans comprise a growing portion of the function and to the extent that no one human is smart enough to know the behaviour function of all humanity, then no one human can know that function. Moreover, the act of trying to remember or reconstruct the function changes the function if we use it.§13.3. How are contingent marks affected by those that have the hubris (or foolishness) to think they know the function? That is the mechanism by which tree-tainted arrogance leads to tree-tainted contingent marks and tree-tainted market dynamics.Re §14:§14.1. Agreed. Counterfactuals are an absurd game because we don't know the true coupling of components in the world or what was contingent, co-contingent, or inevitable.Re §15:§15.1. I agree that the future world is also real and unpredictable with the proviso that people can and do influence the future world to varying degrees of success. Thus the world is partially uncontrolled in addition to being unpredictable. This is the crucial difference between the roulette table and the markets. Equating markets with games of chance gives rise to the dangers of the ludic fallacy. This is why I wholehearted agree with you about the morbidity of tree-based thinking.§15.2. What fascinates me about the contingency of the markets is the vague sense that some of the most contingent events (e.g., large price movements) may be far less contingent than we think. The very fabric of modern economies and financial systems contain deep pro-cyclical causal links that inevitably induce cycles of boom and bust. This is why I've always felt that Nassim doesn't go far enough with his ideas about black swans and why I do like your ideas about contingency.Re §16:§16.1. Is the market real? Given the association between markets and animal spirits and sayings such as "Markets can remain irrational longer than you can remain solvent," or "you can't fight the tape," I have a hard time agreeing to the reality of the market. Given the pressures on market participants as well as the biological quirks of human cognition, I would say that the market reflects "a" future which might well be an efficient expectation (i.e., anticipation of the actual future reality) or it could be a shared delusion or even an intentional fraud. Any valid theory of contingency-based logic must be able to account for bubbles, crashes, Ponzi schemes, pump-n-dump, Central Banker puts, political witch hunts, etc. Re §17:§17.1. Although I agree that price is non computable that doesn't stop players from computing it. In the same way that gamblers have algorithmic systems that they believe will maximize their roulette winnings, so, too, speculators, investors, and market makers have algorithmic systems that they believe will maximize their trade winnings. These algorithms contain de facto computations of price, either as a point value to be submitted as a limit order or as a half-space threshold for a trade/no-trade decision on hitting a quoted bid or offer. Whether these algorithms compute prices accurately is a separate question whose answer I think we tend to agree on. §17.2. My concern is that whereas gamblers interact with a system whose outcomes are wholly independent of the gambler's wagers (the ball is neither attracted nor repelled by the depth of the chip stack associated with wheel's numbers), the markets are strongly coupled to the wagers of the participants. In fact, it is the participants' wagers that exactly determine the quotes and prices that are then fed into other participants' algorithmic systems. Only at the moment of expiration of a finite duration contract does the "real world" enter into the pricing. But it's worse than we might think because the participants' wagers determine capital flows in the broader economy (e.g., look at the effects of CDS on rates paid by sovereign entities and the impact of those rates on the contingency of default). We may think that equity prices, for example, derive from the economic fundamentals of the underlying companies, but we face a world in which the economic activities of the companies derive from the underlying prices of equities and other instruments. This difference between exogenous contingency (e.g., a game of chance) and endogenous contingency (e.g., a complex adaptive system) colours everything about the ontology and epistemology of markets.Re §18:§18.1. Very true, indeed! Making one market begets making other exotic markets. But it's far more insidious that you suggest. Not only must the market maker factor in (or synthesize) the price of all the ancillary replicating instruments, but he must use the most popular model to do it. Any market maker using an odd-ball model will find themselves strongly long or strongly short with a high volume of hits on his bids and offers. The simple fact that the aggregate capital in the market exceeds the capital available to any one participant implies that no one individual can maintain both bids and offers while being to far from the consensus. Use a strange model, and everyone will think you've mispriced the instrument and apply their capital to the discrepancy. The point is that the price surface recapitulates the endogenous consensus algorithms of the participants rather than reflecting, sampling, or marking an independent exogenous contingent reality. Keynes Beauty Contest trumps both logic and empirical results (although we would hope that both logic and empirical results influence the beauty contest judges!)Re §19:§19.1. Aye, there's the rub, me laddie! §19.2. One common (if kludgy) approach is to define a second-order confidence value to all probability-related statements. This distinguishes between the case of asserting P(event)=0.5 exactly (e.g., a known fair coin) and saying P(event)=0.5 but we're not sure (e.g., a coin of dubious provenance). Although some might counterargue that these two statements are the same or that the probability of the latter should be changed, the rationale for second-order measures of uncertainty come from outcomes that are nonlinear in the real P. This approach is commonly used in safety engineering in which engineer's assessments of the reliability of key components may be backed by data of varying levels of confidence.§19.3. A second approach is to define instruments in ordinal scale terms without assigning an quantitative measure of likelihood or an interval scale of encompassed states. For example we know that an in-the-money expiration of a deep OTM option implies an in-the-money expiration of all shallower strikes. We don't know how diffferent it could have been, but we can say that if it is different enough to trigger instrument B, then it must also trigger instruments {C, D etc.} and if it is different enough to trigger instrument A, then it must also trigger instruments {B, C, D etc.} . This, in turn, sets a ranking of the prices of instruments, but doesn't provide numerical estimates of the prices.§19.4. I don't know that either of these methods is "competitive" with tree-based methods even if both methods are better on theoretical grounds. The first method complicates the calibration process. The second method is much more correct on theoretical grounds but is wholly inferior to trees because it doesn't compute a unique price.Re §20:§20.1. I agree with your distinction -- the tools may be tree-shaped, but the process is not. Yet the distinction doesn't imply that the overall process avoids the taint of the component tree-shaped parts. In particular, the use of tree-tainted probabilistic tools infects the total process in two ways. The first source of tree-taint is in each dynamic increment in which the tree is used as an approximation for the actual unknown ("forgotten") function. This first source introduces potential biases that decline with increasing re-calibration frequencies -- calibrate often enough and the tree-taint diminishes to zero. The second source of tree-taint is in the interpretation of the calibration -- e.g., the tree-tainted interpretation that judges a mark on a volatility smile to be incorrect. The second introduces biases that do not decline with frequency -- the tree-using market maker stubbornly and persistently remarks the price to a tree-tainted value because they stubbornly and persistently assess the surface with a tree-tainted lens.§20.2. Dynamic replication does more than pull the future into the present, it also spreads the gyrations of each instrument into adjacent replicating instruments. Each trade by the dynamic replicator induces trades in the replicant instruments. Each change in price in any instrument also induces re-hedging trades in the replicant instruments. The result is a self-consistency in the markets which sounds great but it's a self-consistency as defined by tree-based methods and tree-based interpretations of all the instruments.§20.3. And I agree that dynamic replication is a game changer, but in more frightening ways that one might think. The act of replication is an act of pass-through in which the replicator nullifies their position through clever combinations of other instruments. This replication and hedging disconnects the replicator from any pressures of correct pricing. They become free to float on an irrational surface because hedging insulates them from the capricious flux of contingency. That's great for the replicator, but terrible for anyone else that depends on prices written by the replication-using market maker.§20.4. Although I would not go this far (really! really! really!), some might argue that hedging by a market maker is unethical because it means the market maker has no skin the game, no motivation to price instruments correctly, no concern for fellow market participants because the hedged participant does not share the risks or contingency of price movements in all but extreme conditions. In essence, a hedged participant is like the U.S. mortgage brokers who had no motivation to correctly price mortgages because these brokers were never exposed to the risks of those mispriced mortgages. As long as mortgage brokers and hedged market makers are compensated for deal flow (the volume times spread), they have every incentive to make trades happen but no incentive to make them happen at "correct" prices. Please know that I'm not casting aspersions on market makers' morality, only noting the disconnect that it replication creates.Re §21:§21.1. The entitlement of the market maker to use a tree-based pricing tool would seem to hinge on one key question. Does the tree-based logic of the pricing tool affect the price offered by the market maker or the hedging ratios employed by the market maker? If tree-based logic is wrong and it affects the market maker's work product, then they aren't entitled to use tree-based logic for the pricing tool. Although replication may insulate the market maker from the errors in their tools, replication doesn't insulate the market from those errors.Re §22:§22.1. I disagree entirely that "recalibration is what constantly undermines any tendency that the tree would have had to extend its branches and probabilistic transitions again". Although periodic recalibration clips the tree, it does not entirely avoid the tree's taint if that taint exerts a bias. If the truck of the tree pulls the market to the right, reclaibration may limit the radius of that right turn, but it won't prevent the market from inexorably pulling to the right. If the tree-based method constantly underprices deep OTM options by 10%, how does recalibration fix that?Re §23:§23.1. I suspect that one large difference between you vs. I is one of description vs. prescription respectively. Your's seems like a prescriptive argument for why people should not think of the markets in certain highly popular ways (and a apologia for why market makers are entitled to think that way). In that regard, I agree with your first point and want to push the argument further -- that even market makers shouldn't think in trees. In contrast, mine is a descriptive argument which says, in a nutshell, that if people use the logic of probabilities to price instruments and manage contingency, then the shadow of that logic will affect instrument prices, trading volumes, open interest, capital flows and the contingencies themselves. Rather than use independently realized empirical outcomes to scientifically drive theory, I see that our modern financial system using theory to unwittingly drive empirical outcomes.Re §24:§24.1. Yes, what is the market of reality at large? Do prices reflect the future as we expect it is, as we think it should be, as we think it could be, as we wish it to be, as we fear it to be, as we ......? I think the answer varies with the market and with the times. But the more interesting issue, especially with respect to those that live in moment on the surface is: who is this "we" that is doing all this thinking about markets and the future? At the very best, the "we" is that subset of people with the cash, instrument holdings, attention, and decision rights to both watch and transact in the market. This is already a tiny fragment of the total market, the total body of expertise, and even the total set of people who have incentive to watch the market. In the context of prices, the we is even narrower than that and this is where we must drop all the aggregate arguments about equilibrium prices, market efficiency, and collective intelligence to recognize the individuality inherent at the microstructure level. A price quote represents the idiosyncratic thoughts of one single trader. Moreover, an open quote implies that no currently vigilant counterparty agrees to take the other side (i.e., there's no "we" in the we at all). Even a consummated exchange represents the thoughts of only only two parties with a high potential of an asymmetric consensus (i.e., a wide variety of reasons of why either buyer or seller think the traded price could have, maybe should have, been different.) The point is that prices, at the real-time level, don't represent a global reality but an extremely local one that might be subject to all manner of delusions (including delusions that dynamic calibration makes things OK).

Traden4Alpha,Thank you for this patient, thorough, and -- as always -- very instructive response. In this game of action and reaction and push and pull, it might be a good idea to reconsolidate the argument and pull it together from time to time, instead of ramifying it forever. So I will not individually comment on your comments on my individual points, but I will rather try, at this juncture, to converge back to my essential divergence, if I may say so; that is to say, to go back to my single most radical step away from the received view of markets and its traditional logic (and the corresponding metaphysics).My whole elaboration in terms of the antecedence of the mark, or strike, of contingency to the subsequent being and in terms of this primitive contingency continuing itself naturally in price and in the market, as further stages of the differentiation of the surface, instead of following the logic of the well-rounded identified states and of probability, which only reflect the integrative reflex of thought pulling in the opposite direction, aims, as you may have guessed, at insulating the reality of contingency and of the market from the fiction (and infection) of possibility, of state, and of probability.This is part of a much more general and ambitious overturning of the order of thought that I see happening today both in the philosophy of physics and in metaphysics. I am not alone in my criticism of the notion of "state". You can read Michel Bitbol's most recent book (his magnum opus of over 700 pages: De l'Intérieur du Monde: Pour une Philosophie et une Science des Relations, Paris: Flammarion 2010) as a systematic and tightly argued charge against the pervasiveness of the notion of state both in our ontology and in our language, with quantum physics acting as the guide. As for metaphysics, I cannot insist enough on reading Quentin Meillassoux's After Finitude: An Essay on the Necessity of Contingency (London: Continuum 2008), in which the primitive and absolute status of contingency is established and beingness is derived from it. Contingency in this sense is a very abstract category. As a matter of fact, it is supposed to compete with being at this level of philosophizing, even to take precedence over it. For instance, I keep saying that time is inevitable and that we all seem inevitably to live in time; however, time might be contingent, for all we know. Time and space (where states lie) might just be symmetry-breaking contingent events that have occurred at some point in the otherwise intensive dimension of virtual space and virtual time. Read Manuel DeLanda's Intensive Science and Virtual Philosophy (London: Continuum 2002) or, for that matter, read The Blank Swan: The End of Probability (London: Wiley 2010).As far as the market or the future (of which the market is the material technology) are concerned, my claim is simply that printed money, written contingent claims and prices constitute the material chain that should replace, respectively, time, possible states and probability. It is in this sense that the market is real. This is a sense of reality that is supposed to bypass the fiction of states, even to some extent the fiction of being. By contrast, you seem to want to understand "real" only in the sense of prices being the reflection of some underlying objective reality or fundamental value. You still haven't managed to shake the remaining scales of the physicist's (received) view off the metaphysical eye that I can only hope you will open fully one day. Probability is an integral because it presupposes the integrality of possible states to which it applies. When confronted with a multi-valued function, our first integrative reflex is to compute its average; then we compute the higher-order moments, etc. Yes, probability is but an expectation. It says nothing of the future state-to-be; it is only attached to the present state. (Hence the whole predicament of objective vs. subjective probability; hence the inability of any thinker of probability to say how probability really "acts" in the interval or transition between the possible and its actualization.) The present state is the arch-integrative state. It is a logical (not chronological) stand, if you will. It replaces the multiplicity of the multi-valued function with a logic of succession. Instead of thinking of all the states and all the values all at once, we make it easier on thought by simulating something like a succession between a present state and a probable future state. Probability is an integral because it integrates the thought of the probability p=1 that the future state-to-be will get with the thought of the probability p=0 that the states-not-to-be will get. Read Peter Whittle's Probability via Expectation (New York: Springer 2000). And what would be the generalization of probability if the notion of "states-to-be" (not the mention the integrality thereof) were unavailable? Price and written contingent claims perhaps?All we have are written contingent claims and a place where we exchange them against money. Now, we happen to have contingent claims that are written on other traded contingent claims, the so-called derivatives. This is what makes probability theory and stochastic calculus inevitable, to my mind. Probability is fascinating, and worth studying, only to the extent that it derives from the contingent claims. (This makes it doubly contingent, mind you, although it is inevitable). Stop believing in an underlying objective reality (i.e. in some metaphysical truth lying there underneath the market) and you will stop speaking of the hedged market-maker as being unethically insulated from the market's reality. On the contrary, dynamic hedging is needed only to the extent that the whole range of states on which the probabilistic model is based needs to be surpassed, for the market-maker to then trade the derivative outside that range, precisely inside the reality of the market. "If the tree-based method constantly underprices deep OTM options by 10%", as you say, then recalibration fixes that by precisely recalibrating against the market price of that option. Unless what you meant by "underpricing" was that the market itself was mispricing that option relative to the metaphysical truth lying down there?

Numbersix,A quick question - perhaps it is that I do not understand the ramifications of your book - but has this book and the thought process changed the way your pricing tools work in ITO33 ? If yes, how, if not, why not?Any insight appreciatedThanksRHCP

1. My pricing tool does not work in ITO 33 but in the market.2. My whole book is only the explanation of how my pricing tool, the regime-switching model, works in the market, and how any pricing tool worthy of that name should work. This is its revolutionary side.3. Therefore my book cannot change the way my pricing tool works. Rather, it attempts at understanding, through the way in which the pricing tool works in the market, what the market is. This is its speculative side.4. Traden4Alpha would argue here that my pricing tool, and generally pricing tools, change the way the market works. Maybe so.5. To which I would add that, when it comes to the book, the book can change the way the market works even less than it can change the way the tool works. 6. In fact, the book is more ambitious than this. Through speculation on what the market is (its ultimate goal), my book changes the meaning of the word is. This is its deepest metaphysical insight.7. In a word, it changes the world. Happy?

QuoteOriginally posted by: numbersix1. My pricing tool does not work in ITO 33 but in the market.That is what i meant - it was a question on design.I'm afraid, I am still lost - if the market is a given, the tool is a given, then by extension the world is a given at any point - so how is the world changed? Also - since markets are, underneath all that mathematics and numbers, essentially about the behaviour of the masses/herd at any point in time - what does this philosophy bring to the table that the behaviorists have not thought about... and I ask this not as a critic, but as a merchant of the markets - one of the masses/herd. If we start from the end of your comment - i.e. the book changes the world .... models/pricing tools are supposed to represent the state of the world, and therefore should change as well ? (which brings me back to my original question). If I extend this thought using point 4 - pricing tools change the way the mkt works - this could be in the direction the book aims to, so, not a bad thing ?In passing - I would agree with point 4 - we have seen this happen in our near history - (the rise and fall of CDO's).

RHCP,Thank you for your continued interest. My few esoteric bullet points make sense, I can assure you -- I only arranged them this way as a further variation on how to best condense my line of thinking -- so if I may now elaborate:All I meant is that the pricing tool we have developed at ITO 33, the regime-switching model, was designed prior to writing the book; so it is not the book that has changed the way we design the tool, but rather the opposite, i.e. the design, purpose (and beyond that, the essence of the derivative pricing technology) that has changed the way that I think derivatives book (or more generally, books designed to illuminate the market from the point of view of the pricing of contingent claims) should be written.Of course, the tool was not designed from scratch or by chance. The main insight is due to the designer of the tool -- my partner in ITO 33, Philippe Henrotte -- whose credo, which I share, is that derivative pricing and hedging as technology makes sense only to the extent that it is calibrated and recalibrated to the market of derivatives. From prices to prices, with probability theory, stochastic processes and dynamic replication acting only as an intermediary, or inner episode of the tool. It is sufficient to give it a minute of thought (I can refer you to the whole history of this thread or indeed to the lecture I have given at my book signing event, whose audio-video is linked to the Wilmott website) to realize that this new logic ("from prices to prices"), whose other name is recalibration, is incompatible with probability theory and the fixed and delimited states of the world that lie at its foundation. Ever since he graduated as a PhD in Finance and through his teaching years as professor of finance at HEC, the French business school, Philippe's main criticism against the Arrow-Debreu paradigm was that prices that come out as the result of probabilistic computations based on "abstract" states of the world, according to Arrow-Debreu, will themselves constitute new states of the world (of the market). Hence a contradiction, or at least a perpetual breaching or non-closure of the ontological circle.The regime-switching model has the unique feature that the regimes have no particular given names (of variables that are specifically stochastic -- such as stochastic volatility, stochastic jumps, hazard rates, etc.) but adopt only the names that calibration assigns to them, hence it is always indistiguishable whether a given instance of the regime-switching model is a case of calibration or of recalibration. Now imagine that the given sequence of recalibration is only an "accident" of time (because we all happen accidentally to live in time) and doesn't reflect the real essence of the market (which says, in essence, that no contingent claim, no matter how complex, should be redundant); imagine, in other words, that the real process doesn't take place in time but on the "spot" (what I like to call "in place"), and then the structure of the market, or its real process, will have no other place to go but into a dimension that has to be real although it is not actual -- because actualization is what gives the actual prices you calibrate against in time. This combination of reality and non actuality is what I have discovered philosophically, and what motivates writing the book. As I have said repeatedly on this forum, my book is a book of metaphysics, so I guess it can have no causal agency of any sort and cannot change anything, except the way you think. It certainly cannot change the market, the tool, or the world, for that matter. What I have discovered philosophically is the Bergsonian-Deleuzian virtual, which is the name Bergson and Deleuze after him have given to the real that is not actual, a real, called the virtual, that should in no circumstances be confused with the possible (as per the traditional opposition between the possible and the actual).What definitely changes, after the book, is the schema of stable, delimited and identified states of the world (i.e. the basis of probabilistic thought, and perhaps also of objectivist thinking in general) which should be replaced, I speculate, by the medium of the market and prices as translators of contingent claims. Also, I was very serious about changing the meaning of the verb "to be" (which is the basis of the thought of states), and replacing it with the verb "can be" (which is the basis of the thought of contingency). If you read Deleuze, the whole logic and ontology of the world should change from an ontology of beings to an ontology of "becomings". This is what I meant when I said: "In a word (or rather, by changing a single word), my book changes the world."My book is a reflection on possibility, probability, state, time, etc. as metaphysical categories, and I propose replacing them with contingent claims, prices, money, market dynamics as metaphysical categories of their own. You can see how far I place myself from the sociologists, behaviourists, econometricians, etc., or indeed quants of any following. I just deal with thought as my primary matter.

Numbersix,Another (re)action to your thought provoking (re)action. We become slowly entangled more and more. Despite our deep philosophical differences, you and I do share much in common.I entirely agree about the siren-call of state-based thinking, especially with regard to future states. To think that we know what is possible (let alone probable) is hubris. The set of states that we mere humans enumerate as possible must be, on the one hand, bounded by our experience, theories, intelligence, and personal phobias while, on the other hand, being over-extended by our imaginations and hopes. That which is unthought or unthinkable will never enter our set of possible states. That which we wish desperately to be true may never occur.I wholeheartedly agree that sometimes we don't even know (or refuse to consider) all the possible states of the system. Moreover, imperfections in our sensing systems (both the imperfect coupling to the world and non-zero coupling to spurious phenomena) mean that perceived state != world state. Finally, and in the context of human systems, the future can impact the past such as when an exchange unilaterally rolls-back certain previous trades (e.g., see the Flashcrash) or a legal judgement forces a resettlement of what seemed like a fully executed contingent claim (e.g., see the Madoff fraud clawback on investors that left the fund before the fraud was detected). For that reason, I tend to have a loose definition of "state" that is less about a concrete values for concrete variables and more about a time-varying coupling between underlying and observer. Thus "state" can include both quantum and legal entanglements that make the world less black-and-white than a classical physicist or mathematician would like. (Perhaps I should use a word other than "state" but I don't know what would I would use)To me, contingency equals ignorance of the future and might arise from some combination of voluntary and involuntary factors such as lack of data, lack of theory, lack of foresight, lack of knowability, lack of time (to turn the crank on a complex model in a real-time trading environment), lack of control, etc. That is, contingency is a negative quantity in that contingency is an absence of knowledge. (Note: the fact that contingency equals ignorance and the fact that we begin our personal and evolutionary lives in ignorance means that contingency precedes being or at least our perception of being).The quest of a scientist (or an engineer) is to reduce (or control) contingency and to know that they have successfully reduced/controlled contingency. At this point we could go on a long tangent on why market participants have overestimated the reduction in contingency (including market maker's dangerous use of trees) but that might take us too far afield. Now I would never ever assert that contingency can be entirely eliminated. Some of the more fascinating results in epistemology in the last century have been in discovering the ultimate or unavoidable contingency found in phenomena such as chaotic divergence, formal Godelian undecidability, and spooky quantum mechanical phenomena. Although there may be unassailable logical or physical reasons for the lack of knowledge, contingency is still a lack of knowledge.Knowledge can be viewed as a coupling between the mental state of an observer and the physical state of the world (with "state" being loosely defined to encompass things like quantum wavefunctions and judicial capriciousness). Thus, contingency occurs when the agent's mind is not coupled to the physical world for some correctable or uncorrectable reason. The crucial point then how agents handle ignorance -- do they devote their energies to reducing ignorance or do they devote their energies to insulating themselves from the effects of ignorance. And if a person seeks insulation over knowledge, will they do a good job at price formation?QuoteOriginally posted by: numbersixBy contrast, you seem to want to understand "real" only in the sense of prices being the reflection of some underlying objective reality.Hmmm... I've failed somewhere -- probably an oversight on my part or a side effect of my desire to avoid discussing an even more complex metaphysics of markets and economies that will engender even more disagreements. I admit that I do suspect there is some untapped objectivity latent in the markets but it's not very large. The more important issue is the imposition of a subjective reality on the market -- that the beliefs of market participants affect the market outcomes and induce systemic mispricings. The issue then becomes whether the participants are aware of their impact on the market (i.e., the discrepancy between their model of prices versus the price action imposed by their use of their model). Some may be incidentally ignorant of their impact because they use math that cannot represent or denies the existence of such endogenous dynamics. Some may be willfully ignorant of their impact because they are hedged and thus uncoupled from the effects they create.***Sadly, I've run out of time for discussing some of the other points you raise (e.g.. I agree with most of views on probability, have some thoughts on the contingency of time based on time defined by change-of-state, and whether the inevitability of probability and stochastic calculus reflects human desires more so than physical reality). Please know that if I don't response to every one of your points or don't respond quickly it because your ideas are the most challenging ones on Wilmott and they take time (a slow read) and thought (a slow write) to consider properly.

Has anyone completed a powerpoint summary with the key messages of the book, in a format intelligible for the masses? I've seen this mentionned several times in this thread but found it nowhere. Aside from pricing derivatives, does this book have any implications/applications on asset allocation decisions? Tx in advance.

You might have seen this already?

Thanks, I have already seen the lecture. While I think I understand his explanation of why the current way of thinking is "wrong", I am still very unclear as to what one should "do" instead. I'm also curious if one can find any applications in the world of asset allocation.

QuoteOriginally posted by: alexwThanks, I have already seen the lecture. While I think I understand his explanation of why the current way of thinking is "wrong", I am still very unclear as to what one should "do" instead. I'm also curious if one can find any applications in the world of asset allocation.I have not read Mr. Ayache's book but what I understood the goal is to redefine and extend the foundations of literature by means of a specific domain of discourse. Commentators (for example, T4A) can shed more light on this. --------------------------------------------------------------------------------Philosophy and finance were only a façade. In reality, my true domain is literary theory. ----------------------------------------------------------------------------------------------------------------------------------------------------------------Literary theory in a strict sense is the systematic study of the nature of literature and of the methods for analyzing literature--------------------------------------------------------------------------------

Thank you both. There is also the hint that contingent claims are said to be written and that objectivist language is basically statist, just like probability. Hence the extension both of the logic of discourse, through the medium of contingent claims or the market, and of finance, through the absolutization of contingency. Now I am sure that the way I understand pricing, over and above probability, can be extended to other domains of application of probability, such as asset allocation. I am sure financial theory can be reformulated as derivative pricing theory. One then has to work out the details of my conversion from probabilities to prices and from possible states to written contingent claims.