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The Quant Delusion
In the year 1900 a little known French mathematician Louis Bachelier put forth the effort to eradicate risk involved with investing in financial markets. While his work was lost for 60 years, his original contribution to pricing options (more importantly, pricing volatility of a given asset) will become the cornerstone in what is today most widely used formula in finance; Black-Scholes-Merton formula for pricing options.
Until Bachelier, little effort was given to correctly price the assets which traded on exchanges. Bachelier, building on the efforts of physicists, decided to use arithmetic Brownian Motion to describe price movements in any given asset. Without questioning this, one of main contributors to BS option pricing model, Robert Merton assumed (taking a page directly from Bachelier's book) that price movements could be correctly described by using BM.
But there is a problem with using BM. In a recent paper, Oliveira and Mendes described the shortcomings of GB as following:
"Geometric Brownian motion (GBM) models the absence of linear correlations, but otherwise has some serious shortcomings. It does not reproduce the empirical leptokurtosis nor does it explain why nonlinear functions of the returns exhibit signi?cant positive autocorrelation.
For example, there is volatility clustering, with large returns expected to be followed by large returns and small returns by small returns (of either sign). This, together with the fact that autocorrelations of volatility measures decline very slowly [1], [2], [3] has the clear implication that long memory e?ects should somehow be represented in the process and this is not included in the geometric Brownian motion hypothesis. The existence of an essential memory component is also clear from the failure of reconstruction of a Gibbs measure and the need to use chains with complete connections in the phenomenological reconstruction of the market process [4].
As pointed out by Engle [5], when the future is uncertain investors are lesslikely to invest. Therefore uncertainty (volatility) would have to be changing over time. The conclusion is that a dynamical model for volatility is needed and σ in Eq.(1), rather than being a constant, becomes itself a process. This idea led to many deterministic and stochastic models for the volatility ([6],[7] and references therein).
The stochastic volatility models that were proposed described some partial features of the market data. For example leptokurtosis is easy to ?t but the long memory e?ects are much harder. On the other hand, and in contrast with GBM, some of the phenomenological ?ttings of historical volatility lack the kind of nice mathematical properties needed to develop the tools of mathematical ?nance. In an attempt to obtain a model that is both consistent with the data and mathematically sound, a new approach was developed in [8].
Starting only with some criteria of mathematical simplicity, the basic idea was to let the data itself tell us what the processes should be." [Oliveria, Mendes; 2010]
In the process of building the final formula, Merton had to build on some [untested] assumptions, which will later be proved, via ultra-volatile short-term price movements (October 1987, Fall 1998, May 6 2010, to name a few) to be wrong.
First assumption Merton made was that of a log-normal distribution, which was soon proven wrong by Fama who analyzed price distributions for all DJIA constituents. Fama's empirical analysis showed that prices are far from being log-normally distributed. Fama's findings are today popularly called "fat tails" and numerous techniques were developed in order to hedge fat tail risk (Good paper against using BS option pricing model "Why we have never used Black-Scholes-Merton option pricing formula" [Taleb, Haug])
It is needles to say, Black-Scholes-Merton formula never took into consideration Fama's findings and continued to use log-normal distribution as mathematical description. That proved fatal in 1987 when newly adopted portfolio insurance (built directly upon mathematics used in Black-Scholes-Merton formula ) caused the Dow Jones Industrial Average Index to have it's largest 1-day decline in history (-508 points).
Without getting into technicalities of BSM formula; best way to describe it's inadequacy is to read the following paragraph from above-linked Taleb and Haug paper:
"Such argument requires strange far-fetched assumptions: some liquidity at the level of transactions, knowledge of the probabilities of future events (in a neoclassical Arrow-Debreu style)4, and, more critically, a certain mathematical structure that requires “thintails”, or mild randomness, on which, later. The entire argument is indeed, quite strange and rather inapplicable for someone clinically and observation drivenstanding outside conventional neoclassical economics.
Simply, the dynamic hedging argument is dangerous in practice as it subjects you to blowups; it makes no sense unless you are concerned with neoclassical economic theory. The Black-Scholes-Merton argument and equation flow a top-down general equilibrium theory, built upon the assumptions of operators working in full knowledge of the probability distribution of future outcomes –in addition to a collection of assumptions that, we will see, are highly invalid mathematically, the main one being the ability to cut the risks using continuous trading which only works in the very narrowly special case of thin-tailed distributions.
But it is not just these flaws that make it inapplicable: option traders do not “buy theories”, particularly speculative general equilibrium ones, which they find too risky for them and extremely lacking in standards of reliability. A normative theory is, simply,not good for decision-making under uncertainty (particularly if it is in chronic disagreement with empirical evidence). People may take decisions based on speculative theories, but avoid the fragility of theories in running their risks.
Yet professional traders, including the authors (and, alas, the Swedish Academy of Science) have operated under the illusion that it was the Black-Scholes-Merton“formula” they actually used –we were told so. This myth has been progressively reinforced in the literature and in business schools, as the original sources have been lost or frowned upon as “anecdotal”" [Taleb, Haug].
It is easy to deduce, from the above paragraph what is exactly wrong behind arguments of BSM. First; BSM creators assumed that the market will always be liquid enough and gravitate towards equilibrium. Second; that the market participants are fully rational and their decisions are based solely on prices. Meaning that for every seller, there will be a buyer, and vice versa, and that the state of market symmetry will push assets prices to their equilibrium. Third; that asset prices experience absolutely no "jumps" [proven wrong by later research, as well as numerous new models which pay much attention to "jumps"].
Hedge Fund LTCM was built around these assumptions, re-creating the bond-arbitrage strategy that netted Solomon Brothers billions while its desk was the only one using this strategy. Basic assumption behind bond-arbitrage strategy was that of-the-run Treasuries [of same tenor, yield and coupon] were unnecessarily lower in price than their on-the-run equivalents.
Market argued that off-the-run securities had lower prices since the market for off-the-run securities was less liquid than the market for on-the-run securities. Solomon's arbitrage desk, building upon the assumptions of BSM model, correctly perceived that to be irrational. While that strategy [of-the-run / on-the-run convergence trade] worked well for some time, ultimately the market became efficient enough to arbitrage any spreads between two, or more, bonds that had the same yield, coupon and tenor.
But that didn't stop LTCM to further pursue the convergence strategy, but in slightly different form. Since bond prices are not as volatile as equities, and price movements are usually just a few cents, LTCM levered it's balance sheet to astronomical levels. This approach guaranteed it above-average return on equity, but in it's best year LTCM's return on assets was only 2.45%.
Venturing into European equities, event-driven arbitrage, European bond arbitrage (similar to convergence trade, but with more macro-economic uncertainty) risk profile of LTCM's balance sheet changed drastically, but it's VaR remained the same as it did when LTCM was involved only in convergence trade. They have blindly followed their models, without questioning the assumption behind those models. Something that would be repeated in the current crisis (in a slightly different form of pricing structured products and arguments behind high ratings given to those structured products).
Soon LTCM's positions grew so large that the markets wouldn't have enough liquidity if LTCM had to liquidate them. But the models showed large dis-equilibrium and LTCM' traders added more to their positions believing that no matter how large their position, market would accommodate potential unwind with necessary liquidity. Shorting macro-volatility across assets, LTCM's risk profile grew by the day, and as more markets became over-crowded, LTCM applied it's models to such exotics as Russian short-term bonds.
Then Russia defaulted and volatility shot up. Most of LTCM' positions were illiquid, and LTCM soon lost all of it's equity.
This is just one of the examples where financial modeling went wrong (there are more recent cases such as: AIG swap portfolio valuation, valuation of structured products, quant wipeout in 2007 which was very similar to LTCM fiasco etc etc).
In 2008 Emanuel Derman and Paul Wilmott (two most famous names among quants) wrote the following in the article published in Business Week:
"Financial markets are alive. A model, however beautiful, is an artifice. To confuse the model with the world is to embrace a future disaster in the belief that humans obey mathematical principles.
How can we get our fellow modelers to give up their fantasy of perfection? We propose, not entirely in jest, a model makers' Hippocratic Oath:
• I will remember that I didn't make the world and that it doesn't satisfy my equations.
• Though I will use models boldly to estimate value, I will not be overly impressed by mathematics.
• I will never sacrifice reality for elegance without explaining why I have done so. Nor will I give the people who use my model false comfort about its accuracy. Instead, I will make explicit its assumptions and oversights.
• I understand that my work may have enormous effects on society and the economy, many of them beyond my comprehension. "
Conclusion
The general consensus, with which I agree, is that the introduction of mathematical knowledge had vastly improved financial markets. That improvement translated into less risk for all market participants and into multi-year growth. But over-reliance on models, and models alone, no matter what the assumptions underlying the mathematics of those models may be, caused greater and greater systemic shocks.
What we must remember is; models are only representations of beliefs, not definitive statements about how the World operates. Risk modeling, and modeling in general was meant to be perceived as a set of tools, of guidelines to help market participants reduce their risk, not to eliminate risk in its totality.
When models went from being perceived as representations of belief, to statements about how the World operates, when "Human factor" was reduced to the minimum, finance stepped over the boundary of "scientific" into the area of dogmatic.
There are no fundamental laws of finance, there are no axioms of finance, only conjectures and beliefs of finance. And in that difference lies the problem. A system which is only based on probabilities (of any kind) is unable to produce true statements about itself, only valid statements, which validity needs always to be tested and questioned by observing empirical phenomena that underlay it's most basic assumptions.
We can not blindly rely on mathematical models to measure risk in financial world. There is no proof theory devoted to finance, there is no logic devoted to finance, only computations.
In conclusion. The state of financial markets is in no better shape today, than it was before the emergence of this crisis. Most of the basic assumptions are still considered true, most of basic modeling techniques are still used same as before.
Until that is changed, we continue to dance on the verge of a cliff with no safety net protecting us from the consequences if we fall.
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OR...
REALITY VS. NERDS http://www.youtube.com/watch?v=C3njjD41f48
I gave 5 stars for this posting even though I think the Chicago School has nailed economic theory.
File that under: Looks Good on Paper.
I kind of thought that, but didn't use those specific terms: The Greatest Possibilities are The Greatest IMpossibilities. I explain- a near-term risk is hedged against. Every risk is priced, as you say, by some mathematical formula, except The Greatest Risk. This is seen as not happening, having such a low probablilty that no hedges are placed, no protection taken. But when it happens, its a BIG problem because nobody's protected, and it 5 times as big as the things they ARE protected against.
This rare bird event should be wildy profitable to those on the right side of it, and absolutely devastating to the 99.99% who blindly dismissed the event as "never happening". For those caught on the wrong side, thank goodness your Governments intervene and cover your losses, be thankful because this will not always be the case. Stupidity Swaps have a short half-life.
This article should be subtitled: You're So Smart, You're Stupid- You've failed to cover that 0.01% risk probability, otherwise known as The Longshot. Long live The Longshot!
Taking that trade will bleed 99.99% dry as bone. Profit is trade AND timing = being a lucky bastard.
Precisely when somebody, or something, swoops in to save the defeat from the jaws of victory, because so many are losers. Hopefully The Fed will be broke by then.
Preach it, bro.
Hopefully the Fed will be broke by then... poetry to the ear.
I'm not sure why you are all begging Cheeky to come back. Unlike alot of ZHers that actually care about what happens to everyone else in the world or speaking truth to power, Cheeky only cares about making money off of his derivatives - although he does have good taste in music. And yes Cheeky, we all know that the mathematical formulas failed us and will fail us again.
I junked you Mr Know it all.
Perhaps CB is profiting as you suggest, but he's also provided valuable insight to many for a long time. It's still legal to make money in the pseudo-capitalist system, if you can manage to do so, right?
The math didn't fail. Rather, the system was never intended to serve you or I, prole: http://csper.org
I'll take back my junk if you will contribute something.
This was originally a contrarian investor site with a little bit of snarkiness thrown in. At least that was how I saw it when many people had names of investment themes such as force majeur and random walk and other snarky stuff, at least the ones that registered to comment. Personally I am not so thrilled that all of the people who have left life after the oil crash have settled here. apparently the blogger of life after the oil crash decided to leave the doomer world and get totally into analyzing the zodiac with his new website. I don't have anything against doomers and populists. we have some things in common, but I am mostly here for the snark and the egghead articles about governance, quantitative theory, etc. I hope it continues to be useful for speculators. for investors you don't need anything but a well constructed portfolio along the efficient frontier at whatever risk level you can tolerate, then dollar cost average into it, so this isn't a site for investors, but has been welcoming for maverick speculators and traders. the most trollish comments seem not to come from the traders and speculators on the site, but from the populists and doomers who have left life after the oil crash and have gotten bored with james kunstler and dmitry orlov who are now one trick ponies writing the same thing every time, except now dmitry orlov has gotten into dissing america a lot more, the place where he became a millionaire after he left russia. the arch druid is interesting for the meeker of the doomer types who are looking for something positive. the angry who blame others for their station in life rather than do something productive about it tend to annoy me to some degree, but why can't we all just get along? thank god Ilene finally posted something that pissed off the primitive populists or as major dickus said the rantier class. Hopefully this place won't be all about "speaking truth to power" or it will eventually die. A rather sophisticated snarky contrarian home for speculators is always needed.
Sheesh..... Perhaps it's not YOUR primary motivation to visit, but the whole point of ZH is about "speaking truth to power"... and in the process challenging the rigged game...........
Hence the Fight Club theme...
As a lower strata prole, I lurk here to try to gain an understanding of some of the myriad of processes by which I'm getting bent over.
I liked Fight Club, but don't remember it having a message of "speaking truth to power".
Personally I like ZH both for being the primary site for helping me see the big picture, but also for occasionally helping small fry like me make a quick buck. Thanks to ZH (and Mish) I went long long US treasuries late last spring and made a nice little profit when I cashed out late last summer. Would have gone long a month or two earlier, but Taleb scared me off for a while ("every human being on the planet should be short USTs", yeah right).
Stuffing twinkies in mylar bags and sucking my gut in while posing in my Mad Max outfit and giddily waiting for EOTWAWKI (or whatever the doomers call it) just isn't my cup of tea. To each his own.
I'm curious what message you gleened from Fight Club (the movie). Or The Matrix for that matter... I'm quite certain it absolutely was not intended to be about how to make a few bucks trading...
Twinkies probably would store well, but the nutritional content just isn't there. For your edification...
http://www.amazon.com/gp/product/0452295831?ie=UTF8&tag=whiskegunpow-20&...
Best of luck
I would also still be anonymous and unregistered if it were allowed. However it probably was a good thing to change it, but we somewhat maverick traders and contrarian speculators need a home too. I may tire of being a top calling troll and become a bottom calling troll at some point if we are at an inflection point. I got out of gold and silver too soon unless we really do have a retest of the 200dma. I think I have been banging the oil bitch about as long as I can and she is worn out now. This place has been good for me and given me a few nice pops. But now everything is unclear, so I seek guidance new guidance. Is it time for long dated treasures to shine for a while during the coming correction?
>Is it time for long dated treasuries to shine for a while during the coming correction?
I have been considering that possibility for the past few weeks.
But seeing TBT rise on Friday, which was supposed to be an risk off day, failed to make me bullish on treasuries and left me wandering across some charts and blogs looking for some clarity.
After a while, I felt pretty stupid when I noticed that there is clearly blood on the streets of Egypt.
http://www.google.com/finance?q=NYSE:EGPT
Who would have thought that having the police in Tunisia dump a poor man's vegetable cart would have led to uprisings all across the arab world. I hope that guy is Sainted and his family taken care of. Anybody know his name? This is a classic example of complex systems and emergent properties being sensitive to initial conditions. When that dumbass policeman dumped that poor guy's vegetable cart, he ignited the Arab world.
A Muslim being sainted- now there's a thought to match our turbulent times!
His name was Mohammed Bouazizi and it was a female government official who slapped him in the face.
thanks. It's amazing how easy it is to find and contact people if they are not hiding.
I'm going to be snarky here, but it is deserved. Hopefully yall can prove me wrong here, but most of the article and comments seem like tired regurgitation of some quotes backed up by no fucking understanding whatsoever. Discussing critically quant issues is desirable, but when there is no real understanding of the current landscape it has circle-jerk written all over it.
That is to say: everybody knows this shit already. The idea that there are no alternatives to normality is ridiculous. The idea that quants have no understanding of Gaussian limitations is asinine. The idea that quants are trying to reduce markets to equations is just numb-nut stupid.
So you think Black-Scholes is wrong. Great. Use Ornstein-Uhlenbeck, already done just waiting for you.
Don't like that? There's OTM.
Agree, saw a light of erudite sounding jargon being tossed around, but that's all. Seems rather late in the game to be dissing BSM--over 20 years late. However BS was a very elegant formula and it's always a pleasure to see a new PDE in the neighborhood. Not that I'm all that literate in quantitative finance, but I'd like to know what some of you quants think about the work of John Ehlers. He uses signal processing from electrical engineering. He uses the Fisher transform to deal with the non-normal distribution of prices. It would seem that you could Fisher transform the prices, which turns a non-normal distribution into a normal distribution with fatter tails and then use the transformed distribution to develop your option pricing formula in "Fisher Space" and then use the inverse of that to get back to the real world. In his MESA program he uses the Burg algorithm which was originally used in the oil industry to find deposits. At the very least he is applying concepts which do have a solid basis in modeling physical phenomena in an attempt to come to terms with the vagaries of the market.
Then there are people like Mark Jurik with his JMA. Though a black box, the idea of a moving average that eliminates the lag at the same time that it smooths the data seems to be attainable with applied mathematics. You can get some idea of how this works by reading Ehlers papers at his MESA website. These tools allow you to smooth indicators and get vastly better results from TA. With his knowledge of signal processing, for instance, John Ehlers is able to create a trend by subtracting away the oscillating components using bandpass filters. Kind of the reverse of using an MA to get the trend and then using that to find the oscillating components using Fourier techniques or other sine wave extraction methods.
Another mathematical application to finance that attempts to predict long term crashes or blowoffs is the work of Didier Sornette with his logperiodic series. He developed this by analyzing herding behavior. I would like to hear what he would have to say about gold and silver right now.
jm, could you point me in the direction of using Ohrnstein-Uhlenbeck in finance as a replacement for BS?
"Though a black box, the idea of a moving average that eliminates the lag at the same time that it smooths the data seems to be attainable with applied mathematics."
it is like taking candy from a baby... there is no defeating lag. no matter how many variables you plug in, you will be front run in every trade, fact.
There's tons of stuff on google, but you have to call it an "O-U process".
What you say looks like good stuff. I'll chew on it tomorrow.
Thanks mucho, I'll check back on this article even when it goes off the main page.
+3sigma
How quickly all these smart people forget goedel. The market is a complex system which has emergent non linear properties so of course any linear modeling will prove inaccurate at somepoint. For a.good read on the exviting history of statistics and insurance read Against the Gods. Even nonquants can understand it and if you will yrudge through the one semi hard.chapter you will understand how pascal developed statistics. There is no math involved. Its not nevessary to understand basic statistics, but you have to follow.closely in that one.chapter. a wonderful read.and no math.skills nevessary
Thank you for that article. I imagine it took you awhile.
I have always been suspicious of the BS model (and not just because of that abbreviation). The "as a given" adherence I perceived whenever it was presented set off all kinds of alarms. Men who are not testing their tools may not be wrong at the moment, but they'll get there.
Another well nigh incomprehensible dribbling on the matching of data sets to various mathematical models. Bachelier's option pricing formula is almost exactly the same as BS except that he couldn't get rid of the expected value (drift relative to time) of the pricing question. BS rejigger using heat transfer functions to drop expected value right out of the equation and there we have a solution to pricing based on volatility alone. Then the crowd wheedles away at fat tail actualities and slide into randomly varying sigmas to explain tails. The random varying sigmas seem to follow some arima process and things get confusing again.
What we really need are true delta shifts in the actual options chains to rebuild from the bottom up to an ascribed function but there the data is very sparse in real time. Maybe markov shifts in arbitrary distribution regimes with the prices reflecting assumptions of possible random regime states governing the process over the life of the contract. Indeed the stochastic regimes may have randomly varying parameters also.
Who gives a fuck when you know what the fed is buying tomorrow.
Liked what you had to say MOFO until "Maybe markov shifts in arbitrary distribution regimes with the prices reflecting assumptions of possible random regime states governing the process over the life of the contract" that part.
But like you said, who gives a fuck? HOMO the POMO
Sorry bout that, i skipped some bits. The general idea is this: The process generating the price changes can be thought of as a stochastic regime: a distribution and some parameters. ex lognormal, pareto etc.
The governing regime may switch at any time to another completely different regime, different distribution, different parameters. Say we had five processes, each of a different character, and sometimes the price changes are determined by one process and sometimes by another. Fuck it, while we are here, lets just embedd these five states in state shifting markov chain that governs the transition probablities from one regime to another.
Solving for options prices over the life of a contract would have to include both the likely periods, transition sequences, and parameters of the five states. The analytic solutions become quite involved, so we retreat into monte carlo and close enough solutions. All we really need are real deltas anyway because everybody knows the 30 delta strike is always way overpriced and going short those are the beginning move in every game...
Forgive me intruding here, but those regime shifts have to be fitted after the fact, correct?
No actually, we aren't looking to fit a dataset, we are looking for perturbations in the option smile. Fixing vol, we see all sorts of wierd little effects in tilt and tail. Our argument might be that the market is anticipating different transition probabilities in the markov. If atm vol isnt changing, can we come up with some explanation for shifting densities over the curve without casting into doubt our basic model?
Although I get confused here, maybe I should have finished High School...
Actually, I got what you're saying, and you sort of pre-empted what I was going to say, with this response, by saying "we aren't trying to fit a dataset." That would be a core disagreement in how I evaluate what the model is attempting to do. The only interest, in all these approaches, is the preservation of the model. This is a logical fallacy and not a scientific process.
I *DO* understand my friend, I do. That the idea is to find, where & how our model works, so that we can use it. To find it's useable lifespan/window. But the point of this post, imHo, is that ALL these models work--until they fail CATASTROPHICALLY. I wrote a lengthier response, further up, if you care, expanding on why--though I don't go into the math, because that's not the most important place where I feel the most critical errors are being made.
Though, I admit too, I get confused alot, maybe I should've finished grammar school ;P~
I totally get what you are saying now. Thx.
The tails get thicker and thinner as info gets processed by the market (even the center mass can shift around). This is spot-on IMHO.
and charlie need more hookers less drugs
the cboe reality of the moment and the futre is ignorant of those winded formulas and therefor the formulas are weak
fail. bs is right. I told everyone bs would break on tbt this week and did thurs and fri.
thurs was 15%+ on and fri 30%+ on tbt puts buy at the open sell before the close
ok..i confess to only a cursory knowledge of the detail of option pricing and mathematics.
doen't BSM model one standard deviation so not tails (bid.offer spreads.skew for bias in the market take care of tails anyways) and only 2/3 of probability around a forward price?
don't option models that are sufficiently close to the money just get outturns wrong by the height of a modelled bell curve, against an bell curve outturn which nobody knows?
so, are we talking more about the tails than the centres?
if there is a flawed option pricing model, shouldnt we keep quiet until we use it to correct pension fund deficits using the mis-pricing? sort of like a free bail-out for pension shortfalls?
Anyway, don't all models, only seek to capture the middle ground assuming choice prices at all levels of liquidity and no regulatory or compliance constraints for insitutional investors?
do these guys improvements actually price options (better vol estimates) better or do they just disprove the behaviour captured by a distribution model?
Anyways, thanks for the insights and for making me think above my iq heh
Got reaaaal good at the end. Also, let me clarify right away, I’m not MathBoy around here, and any one of you could take me, one on one, let alone if you gang up on me. But… I have a different view of these issues:
………
First, I readily confess a level of detestation at *purely* mathematically driven investing. It's the search for the golden wad, Capitalism's version of Numerology.
I only have one thing to add to the conclusions, though I do feel it’s a principal point. The critical error Quanties/Mathies/Algies etc make is not realizing that the *primary*role* of mathematical models in finance & economics is to serve an AUXILIARY and AUGMENTARY function. It’s the [hence poisonous] fruit of this Tree of Knowledge that leads to all sins [blow-ups]. More specifically, for ex, take a hedge, which is intended as a defensive strategy to protect a PRE-existing position and then you TAKE a position in ORDER TO put that on, you’ve prostituted the concept. Only in this context can you make such critical errors as not understanding what makes a market, getting caught in liquidity traps, etc.
The error is taking strategies that WORK and CONTINUE to work when used in PROPER context, ie, as they were intended [defensively, in conjunction with, augmenting other PRE-existing and SELF-justifying positions], and using them, as “offensive” strategies. By definition, your mathematical model is FLAWED when you’re trying to arb swaps, when in ORDER TO PUT THAT TRADE ON, YOU THEN START TAKING TSY/BOND/IR POSITIONS, IN **ORDER**TO**CREATE**THAT ARB. WHERE in that math model are you **accurately** pricing the risk of **assuming** that position **just** to do that arb? NOWHERE. Stat arb, the same. Dynamic hedges, the same. 99% of Options Strategies, the same thing.
Of course, there is the greed element, I mean, it doesn’t matter if you have a market background, a math background is enough to know that if you account for 65% of a market, it’s gonna get funky on you.
Simple example of course, of how you use Options as an *offensive* tactic has been made, and very well, by N.Taleb on how to use way-out-of-the-money Options.
More specifically Mathematically, I’ll say this [and I know this is a unique, different viewpoint]: Most of the math on these strategies is in itself wrong. Why? Because in continuously subdividing the field, you’ve forgotten what it is. And what it is, is NEITHER applied mathematics, nor is it finance. It’s mechanics. It’s Quantum Mechanics. IT. IS. PHYSICS. It’s PHYSICS!!! And what you’re not accounting for is dynamic and continuous input of parameters, and much more. The whole fucking way people are approaching this, is wrong. Most people also don’t realize that Schrödinger’s equation effectively disproves Einstein’s Theory of Relativity [I mean people are winning Nobels on it], but that’s another matter.
What’s my point? You can’t account for dynamic asymmetric variable input, in flux, continuously revaluing. That’s Chaos Theory. That’s Artificial Intelligence. That’s Big Blue Computers the size of 10mill football fields. Or
The Human Mind
Ps: Some MathGeek said: “Ps about option pricing : binomial tree pricing & finite difference methods,both used today except BS&Monte;Carlo” but I have no fucking clue what that shit means
Ps2: Cognitive Dissonance I read your Post on ZH Veterans also, that was excellent :)
Ps3: Cheeky, music :P http://bit.ly/hglS0B
The problem with math is that it is just a very precise language. Well, that's really not math's problem. The problem is those skilled at speaking it forget that bit, and think they've found god, or a god, or a crystal ball, or some such impossiblility. Math talks very precisely about fantasies too. Assume a dragon has to beat its wing 47 times per minute to stay aloft over a flaming castle that is releasing 10,000BTU's....
How many BTUs did the dragon generate to flame that castle?
Is The Bernank watching?
Note to self: locate nearest Loadall for Ferrari acquisition....
Wouldn't it just be easier to break out the ignition lock?
What Quant out there believes future prices are normally distributed?
None.
The structural problems in the markets today are not the result of a Math Problem. They are the result of a Cultural Problem. More specifically, it's nothing but a simple Sales Problem.
The Quants who create the formulas are anything but dumb. They know there is an "over-reliance" on the formulas. Tempering the over-reliance is not their job. And the decision-making managers know they are, in fact, "over-relying" on the formulas.
It's into this gap between Quant and Manager that the problem lies:
"Just sell the goddam formula. When we make money-and we will most of the time--it'll be because of the formula. And when we lose...nobody will be able to blame us...because we were simply followsing the goddam formula.
"If we are 'wrong', while everyone else is also 'wrong', then we really won't be considered to have been wrong."
And therein lies the problem...Wrong is no longer wrong. It's relative.
We know the data is unreliable, but we need it for planning purposes.
So it's a religion, then.
Grandma use to use the term BM...I don't think she was talking about Brownian Motion though. ;)
You sure??
Brownian motion deals with the movement of solids from an area of high concentration to low concentration ... (Wikipedia)
This is correct but the most important idea behind BM as stated by CB is that the each step of the brownian walk is uncorrelated with the previous step. This is true for a molecule of say sucrose in water undergoing random hits by water molecules from all possible directions. The next impulse size and direction has no connection to the last one. But now create a temperature gradient. Now there is a favored direction for the hits-the one that moves the sucrose molecule from hot regions to cold ones. Same for capital markets-they were down on Friday for a non-random cause-unrest in the mideast. No one could possibly believe the action on Monday will be uncorrelated. Down motions beget more down motions in prices-they have finite, but unknown correlation time. But the idea of a Brownian walk with correlation is very hard to implement. So scientists do what they always do in this situation-what they can do-even if they know its assumptions are flawed. Thus, we get bad models for a complex non-linear system which we know are flawed. Yet, because of humans desire for certainty (the origin of all superstitions and their organized counterpart, religion), they are embraced.
Nice to see you back posting CB.
You can even go back to Bernoulli and explain it by positing a solid under high pressure and at a low velocity suddenly entering a low pressure, high velocity region and voila...you have the classic blow-it-out-your-ass scenario!
LOL, just fabulous.
Welcome back Cheeky.
" Black-Scholes" - pronounced "black-assaholes".