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"How do you fucking pussies do it?"

Jan 29, 2011 4:25 PM

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**,

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.

- Cheeky Bastard's blog
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- Jan 29, 2011 4:25 PM
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very erudite Mr. Bastard....

A few points:

LTCM was not a failure for those who were watching. LTCM proved that TBTF was a viable long term strategy. A way to exploit political fear and ignorance for one's own ends. The basis for massive leverage without consequence.

Next, introduce interdependent systemic risk through the use of unregulated derivatives. Tie the firms together, and do so in such a way that the real exposure is also a quess. Then cultivate the implicite government (taxpayer) backing of a large asset class (real estate) and shift deleveraging costs to the GSEs and FED. Unaccountable exposure, with no legal repercussions.

I must say the plan worked and is working.

----------

The activities of Quants as applied to financial systems, is just a way to describe the system in an effort to understand how it works. The same basic goal in trying to measure business intangibles through probability and statistical methods. Computational finance (quants) goals are geared towards ulitmately justifying price. However, as you have pointed out with the LTCM example (Russian Default), singularities can invalidate a preceived correlation.

Statistical methods do work if your system responds as a system. What we have today for financial measurement, on a macro level, is no system at all. The backdrop is one of untested reaction to crisis. To this we see historical reference to describe, while experiencing the unhistorical.

Perhaps quants are not really required when FED primary bank profit is a basic as making money on the spread. There is no real risk on investment. No need to haggle about price.

Mark Beck

I will not comment on Putins ad hoc VAT tax to arrest the observed result of LTCM. It was rather self explainable in itself on Western leverages. "The basis for massive leverage without consequence." Sometimes IVAN calls it as it is.... There are viable realities. At the moment I will focus on M&A activities. That process was impeded in 08 and 09 and Minsky does a paper to the M&A proclivities of that encyclical nature surfacing cluster groups. This stems from Cambridge Capital theory in the past.

http://www.justice.gov/tax/082704JBALongTermUS.pdf

http://www.washingtonpost.com/wp-srv/inatl/longterm/russiagov/stories/reform081898.htm

http://www.cato.org/pubs/briefs/bp52.pdf

The intervention also is having more serious long-term consequences: it encourages more calls for the regulation of hedge-fund activity, which may drive such activity further offshore; it implies a major open-ended extension of Federal Reserve responsibilities, without any congressional authorization;

Russian government devalued the ruble and declared a moratorium on future debt

repayments. Those events led to a major deterioration in the creditworthiness of many

emerging-market bonds and corresponding large increases in the spreads between the

prices of Western government and emerging market bonds.

Liberal credentialsBut despite his current image as a strong man, Mr Putin has been endorsed by some of Russia's best-known liberals and reformers. His predecessor as premier, Sergey Stepashin, described the 47-year-old as a "decent and honest man". After the collapse of communism in 1991 he worked with Mayor Anatoli Sobchak in Petersburg.And when Mr Sobchak lost power in 1996 it was another reformer, Vice-Premier Anatoli Chubais, who recommended him for a job in the presidential administration.In an essay posted on the internet at the end of December - seen by many as his manifesto for the presidency

Mr Putin said he favoured a market economy, but one that was adapted to Russian conditions.

http://news.bbc.co.uk/2/hi/europe/415124.stm

"We can count on a worthy future only if we manage to naturally combine the principles of a market economy and democracy with Russia's realities," he wrote.

Add into the mix that the ones who are calling red light green light on P/L are generally

salesmenwho run the large firms / shops, and it is the salesman that generally resides outside of quantitative methods, i.e., they are central to the fictional extrapolation ofhow to make mo money mo money mo money without using none of yo money-- known affectionately and thanks to Hyman Minsky as "Ponzi Finance", and well, there you have it.http://www.youtube.com/watch?v=7jukQX2pl2Q

I have tried to live my life according to Brownian Motion. The problem is that I keep getting nowhere ....

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/BrownianMotio...

Good Luck Little Brother. We are Fighting for our economic lives so you can record our travail.

They admitted there failures on options. They will not seek stability on M2M since they seek stability contrary to economic law. I will never give up helping others with products the World needs. I am tired, so very tired little brother.

http://generationaldynamics.com/forum/viewtopic.php?f=14&t=2&hilit=aeden...

Wonderful and informative post. This is why I read zh.

"one of main contributors to BS option pricing model... ....that price movements could be correctly described by using BM"

to describe BS by using BM. That is a model we can all agree on.

welcome back Cheeky! CD, very glad you shook loose such a nice prize (along with a few MIA quality commentors) with that Monday post!

Present.

Welcome back, Cheeky! Until I was half way through this post, I didn't realize how much I have missed your contributions.

barliman

nice article cb.

I do however hope that you do not assume that economics in its current form is in some way good for life.

Let me explain.

We have a strong belief that medical science has enabled us to prolong life. We have a strong belief that security systems ( electronic alarms, naked body scanners, pat downs, bodyguards) etc can protect us. We often use statistics to justify this. People on this site will know how statistics can lie. If one observes, how death arrives, it is plain obvious that it has nothing can be done to avoid it. Yet we go along life believing that we are somehow safer. we are not. death is right beside us all the time. We all know our grandparents who survived as much, if not longer with lesser technology than us.

I remember attending a training program for Structured Products in 2007. My own thoughts were that it was a perfect product. Frankly i could not find any fault with that. Which was the same assumption we made about life, using medical science (or security) as the base, which in hindsight was completely wrong. It was the assumption that risk could be reduced by complex gimmicks( which i think u are alluding to)

Anyways..my research is suggesting to me that most important thing to life or its wellbeing is a form of energy. Not the energy that we normally think of (oil, electricity, magnetism), but some energy that in the current time can only be described in metaphysical terms. It is however accessible to each and everyone of us and

NOTonly the scientists. Since, I am now treading so close to conspiracy theories and religion that I dont think all the logic loving folks would want to get into right now.In conclusion, i am saying that there maybe more to life than trade, be it gold , silver, paper, copper, derivatives...does not matter what models you use or dont use. I would want to use maths to tap into this energy or at least focus our attention there.

A generous masterpiece of knowledge shared.

OK, so I gave a fair amount of consideration to whether I'd even want to comment.

A previous poster summarized what I consider a very strong point in saying that "modeling" the behavior of markets is PHYSICS.

And yet there's something that nagged at me about this...

In the physics realm, we assume that electrons or gas molecules are not working calculus in order to plan their next step. In the finance world, we pretty much have to assume that the other "atoms" involved in the market ARE doing so.

So the prisoner's dilemma is a real concern. Someone on the "other side" of whatever trade you believed maximized return on minimized risk is already consciously invalidating your strategy seeking an easy return based on second-guessing your model.

Which leads back to the intuitive view:

Any mathematical model a trader used to predict market behavior MUST be assumed to be a component of the forces driving market behavior. This is NOT an independent system. If you thought of something, so did someone else, and someone else's speculation is as likely to be predicated on the model you think you invented as the cost of tea in China.

As soon as you put your money on the line, the distinction between description and prediction is pretty damn obvious, isn't it?

There is another reason why models have become so popular, especially in the OTC market. When an asset or a derivative is thinly traded, it is marked to market based on the marker's model. Management, or investors in the case of hedge funds, do not generally understand the models, so in the end take someone else's word for it. That someone else has a stake in the value the model churns out, as bonuses are for many people based on NPV calculations of long term assets or positions.

The end result is that over the last few years opposite sides of the same trade have both been able to book "profits", and thus get bonused based on the mercurial working of their in-house models.

At the peak of the crisis, some of the TBTF's abused their models in order to maintain their liquidity. They were in the position to be able to tell some customers what the supposed value of positions were, thus saving themselves collateral transfers. Individual traders on the desks also had an incentive to maintain the illusion of value until reporting dates, so that the most favorable (for bonus purposes) picture could be painted.

Values might be assumptive, but the bonuses are real money.

Chindit, this comment is like gold amid shit. Finally something sensible.

Desks tell their quants to price a complex product. They find something as close to it as possible and then apply risk premia t determine a model price. Then the trader applies a haircut based on his experience.

Then he hangs it out there on the line like an angler waiting for a bite. He adjusts it because he wants his bonus and because somebody needs protection or wants to sell credit because he thinks it is a good trade, priced rich or no.

By the time there is a taker the bid is nothing like the model. So let's be idiots and blame the quants.

Models are a starting point. They may be good or bad, but the market determines the deed.

We have already witnessed some possible pitfalls of the classical expected utility

maximization approach which governs the risk-return trade-off in some of the most

celebrated modern portfolio theory models (e.g. Markowitz, 1952; Sharpe, 1964; Ross,

1976 etc.). Also it may prove somewhat inadequate in measuring the utility emanating

from complex portfolio insurance structures involving several underlying assets because

the capital guarantee mechanism that could potentially be embedded in such structured

products (Braddock, 1997; Fabozzi, 1998) impart an additional dimension to investor

utility by eliminating downside risk.

Moreover, besides eliminating downside potential, financial structured products also

allow the investors a greater element of choice through the availability of a number of

different assets that can enter the structure. Some of the more traditional capital guarantee

mechanisms like using zero-coupon bonds for example, cannot provide this additional

utility of choice.

The standard ordinal utility formalisms are quite sufficient for assessing the utility of such simplistic capital

guarantee schemes. However, in order to completely explore the utility forms that may

evolve out of an endogenously capital guaranteed financial structured product one feels

the need to go beyond the traditional utility measures and use one which will

appropriately capture this dimension of choice utility.

Abbas’ works modifies earlier works on interpretation of normalized utility functions

as a probability distribution of some hypothetical game of chance that is independent of

the problem faced by the decision maker (Castagnoli and LiCalzi, 1996) and rescaling

probability distributions with the objective of obtaining convenient expressions for utility

functions (Berhold, 1973). According to Abbas’ formulation, when faced with the

problem of drawing inference on the basis of partial information, one should use that

utiltiy curve (or utility vector) whose utiltiy density function (or utility increment vector)

has maximum entropy subject to the limited known preference constraints.

There have also been theoretical advances in the esoteric area of econophysics

whereby mathematical analogs have been proposed and substantiated between utility

theory and classical thermodynamics in so far as that both neoclassical economics and

classical thermal physics seek to model natural systems in terms of solutions to

constrained optimization problems. Both economic and physical state variables come in

intensive/extensive variable pairs and the one such pair that is receiving much current

intellectual attention is that of temperature and entropy and its purported economical

analog – price and utility (Foley, 1994; Candeal et. al., 2001).

However it is the entropic formulation advanced by Abbas that serves as a major

theoretical cornerstone of our present work. What we have aimed to accomplish is to

devise an entropic measure of extrinsic utility of choice; as an additional dimension over

and above the intrinsic utility which may be measured by the known methods of von

Neumann-Morgenstern expected utility; to completely account for the utility derived by

an individual investor from an endogenously capital-guaranteed financial structured

product enveloping multiple assets.

The strength of our approach in breaking down total utility into intrinsic and extrinsic

components is that while one may choose whatever appropriate paradigm to model

intrinsic utility of a financial structured product, the additional dimension of choice utility

can always be adequately captured using the analytical framework we’ve proposed here.

Gee? You mean a system designed to parlay everyone's greed into more greed isn't sustainable?

And you think the solution is better equations?

And then you wonder why no one is in the streets protesting in the country which created this system?

Well done and welcome back, Cheeky. It's always nice to hear an intelligent and knowledgeable voice.

Trying to reform the model maker by insisting on a "Hippocratic oath" of sorts is probably NOT going to happen--and equally responsible use of models is also a pipedream--

and as an analogy, drinking and driving is not advised, using models without understanding and managing the risk isn't advised and what is worse, we have no DUI for the irresponsible model users, only bailouts if the fund is affiliated with the fed.

Hope all is well Cheeky!

Its all perfectly normal.

You can't expect precise results when the "units" your pricing model is based upon is nothing more than a nebulous concept. Sorry, but it's hard for me to be impressed with people who spend their lives crunching numbers, while ignoring fundamental truths. Am I supposed to think they're clever?

I have studied markets for years (disclaimer: have never invested in anything), and do not consider myself an expert at all. But I think markets are psychological....even when HFT computers are trading, since they are programmed based on human predilections for math models. I understand that models can mimic human tendencies based on historical trends and be successful, but none of the above is risk-averse enough for me to invest in it. And, I do not trust the information system nor the investing system. Even if I devised a surefire way to invest that could not lose based on theory, how could I prevent being ripped-off by the people who have access and market control.... that I do not have?

http://kavanna.blogspot.com/2008/04/chaos-and-markets-ii.html

One can extend this modeling phenomenon to that used in Climate Change models. Have read the Quants book, and what i take away is a certain amount of arrogance on the part of these financial modelers. They made beaucoup $$$ on skimming off the top of markets....and also got caught and we all paid dearly for their arrogance and play. From my perspective where are the handcuffs and jail time with fellow inmates like Bernie Madoff ....

"economists can indeed construct, coherent theories of agent choice and macrodynamics in a Keynesian world as long as they are willing to add new research methods to their analytical tool kit...[and]why decision making under uncertainty exhibits...“conditional stability,” a situation in which behavioral equations will be relatively stable under conditions that hold most of the time."

what quant model could've predicted Bouzid on fire and also predicted the ensuing events with any sort of credibility? None as dogmatically practiced. All to your point, well done.

all of you insects bow to Cheeky!

Cheeky, Luv Ya Bro!

Idiots:

Note the diabolical inversion of "speaking the truth to power" here. Worship some guy that clearly knows little about a subject and is most likely a liar about his CDS expertise.

Just a pathetic showing.

You said: "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."

I said: "I'm so sick of shallow quant analyses by pompous pretend and extend assholes who think they can come up with an equation to model and predict with any high degree of certainty human behavior."

You said: "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."

I said: "When you reduce humanity to utils, when you strip human behavior of its moral component and try to reduce all human action to "rational utility" you are essentially attempting in a hollow way to eliminate risk."

You said: "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"

I said: "A system that strips morality from the analysis is alienating its own humanity and misses a lot of the information willingly and arrogantly. By excluding, or attempting to exclude human morality, simply to make models work, such a structurally hollow system inevitably admits its own failure even prior to probability one!"

You said: "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."

I said: "We do not have the math to map out all the risks and possibilities, yet we pretend we do in our arrogance. I should not have to point out examples of neo-classical model and its incentive model failures...economic uncertainty, read inherently risky human behavior, carries with it uninsurable risks that cannot be statistically correlated to games of dice."

sympatico! ; )

This is a statement with zero understanding. Quant build models and comapre them to market quote. They take the over or the under based on model strength and accuracy of input.

'Util' is a ridiculous concept that economists use. No quant would ever think this shit is remotely useful.

So vacant that I have no words adequate for my derision.

Most of the people talking here don't even know what the assumptions are, nor understand the modelling techniques.

This article is like gramma playing linebacker in the NFL. It should be killed, but it is so pathetic that most who are playing just ignore it.

What is really sad and irritating is that the author perpetuates a stereptype for idiots to hang their insecurities and fears on, I'm assuming because he knows nothing himself.

CDS trader indeed.

The problem of utility is best illustrated by the problem of self-insurance. Individuals

faced with the risk of loss due to the occurrence (or non-occurrence) of a chance event

can either assume the risk themselves or pay an insurance company to assume the risk for

them. Then the pertinent question is when to assume the risk on one’s own and when to

purchase an insurance policy? By Bernoulli’s logarithmic measure of utility, the expected

payoff to the individual without insurance is given as follows:

E (X) = p (X) loge X + [1 – p (X)] loge [X – f (X)] … (1)

In the above equation, X is the total pay-off at stake, f (X) is a pre-determined loss

function and p (X) is the probability of receiving the total pay-off. If the individual

decides to purchase an insurance policy, the expected pay-off function will be as follows:

E (X) = loge (X – k) … (2)

In the above equation, k is the cost of insurance payable by the insured party to the

insurance provider. The insurance is cost-effective only if the following inequality holds:

loge (X – k) ≥ p (X) loge X + [1 – p (X)] loge [X – f (X)] … (3)

8

i. e. loge (X – k) ≥ loge [Xp (X) {X – f (X)}{1 – p (X)}] … (4)

i. e. k ≤ X [1 – X {p (X) – 1} {X – f (X)}{1 – p (X)}] … (5)

However, it can be intuitively reasoned out that a problem would surface if one is

dealing with a situation where one of the probable outcomes is a total loss i.e. bankruptcy

whereby f(X) ≥ X (Kahnemann and Tversky, 1979). The logarithm of zero is negative

infinity, so f(X) = X could still possibly be explained away as “infinite loss” but there is

no logically acceptable way to explain the log of a negative number if f(X) > X.

Speculative trading in derivative securities like stock index futures with a highly

leveraged position could indeed have unfortunate cases where f(X) > X indicating a finite

probability of complete financial ruin for the trader but

no meaningful mathematicalexpression can model this case under the assumption of logarithmic utility!

SUKANTO BHATTACHARYA

Utility, Rationality and Beyond –

From Behavioral Finance to Informational Finance Pp. 8-9.

No Way! Welcome back man.

Well Done. I knew you'd be back, you were sorely missed. Great to see you back strong. not that it matters but you make me proud.

"As Davidson has stressed, classical expectations formation theory is applicable

only to “ergodic” stochastic processes: 'an ergodic stochastic process simply means that

averages calculated from past observations can not be persistently different from the time

average of future outcomes'. In ergodic processes, 'economic relationships

among variables are timeless (ahistoric) and immutable'. (are there immeasurable behaviors?)

Davidson, P. (1987), “Sensible Expectations and the Long-Run Non-Neutrality of

Money,” Journal of Post Keynesian Economics, vol. 10, pp. 146-153.

Davidson, P. (1991), “Is Probability Theory Relevant for Uncertainty? A Post

Keynes- ian Perspective,” Journal of Economic Perspectives, vol. 5, pp. 129-144.

http://www.people.umass.edu/crotty/Keynes,%20Uncertanty%20and%20Macro-th...

Relevant work has been done with analysis of unit root processes in the context of purchasing power parody. Thanks for the article.

Its so good to see you my friend !! I hope your feeling well..

Cheeky, good to hear from you. See you're still having sleepless nights. Anyway glad your still around.

Thanks for sharing your thoughts with the common folk, Cheeky. A trusted voice is sorely missed upon it's absence. I hope you keep posting.

"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"Really??

Is there a way to figure (Delta S is greater than or equal to zero), into that equation/model?

How to allow for creeping entropy?

(I am a know-nothing, but moshitos comment that it is physics struck home, and maybe it's quantum when it approaches either end of the curve...?, or warp-collapse or something.)

Cheeky, I liked your post too. Welcome back! Hope you write long and prosper.

...

A question for anyone. Far as I know, the Normal Distribution was discredited (for modeling prices in the financial markets) almost immediately after the 1987 crash, almost 24 years ago. I have read Taleb, Mandelbrot as well as

Iceberg Risk(Kent Osband) and to one degree or another I have understood the math OK, but I cannot claim Braniac Status...So, my question is: have there been any newer probabilistic models that DO mimic what we have seen better than the older models, of say, 20 years ago?

So much progress has been made in math and technology that maybe (not in predictive power perhaps) there ARE models that would better simulate "real life". I DO understand that no one can predict the future, but are there BETTER MODELS out there that can give us shrimps better insights into risks? Models that DO show low probability events happening at about the rates they seem to?

Thanks SME and Cull!

Escapeclaws up-thread also posted some more new math ideas I have not run into.

I'll think about all of this. Really!

A couple of years ago I had read 10-20 papers from the 1980s about a clever algorithm that could have sped up some physics simulations I was working on by some really large factor. A guy from Los Alamos National Laboratory was first or co-author on half those papers. I cornered him at a conference we both attended to ask some questions. His response was: "Oh, that stuff. Well, it was good enough to publish, but not good enough to use". And these were all peer-reviewed papers published in very prestigious journals.

real time physics simulations, now thats a real working area of math! mixed with huge data sets and lots of events and responsechains I WILL BRING ANY CPU ON EARTH TO ITS KNEES. BOW DOWN TO ROCK AND ROLL

Attempts have certainly been made to come up with mathematical models better suited for describing living things. They often looked initially promising, but AFAIK has always failed to deliver any real breakthroughs.

An example is Levy flights, which does a much better job of describing for example the flight path of a bee looking for nectar than Brownian motion ever could. However, the fractional order differential equations one can derive from Levy flights, similarly to how Brownian motion leads to diffusion-type differential equations (like Black-Scholes), have had very limited applicability.

My humble opinion is that we will never be able to develop useful models for collective behavior as complex as that of investors interacting in a market. But it is kind of a Holy Grail, so people will certainly keep trying. I was very optimistic once about a simple algorithm that managed to model flocking (of starlings, say) remarkably well. But when people have tried to generalize it, the results were disappointing.

So much progress has been made in math and technology that maybe (not in predictive power perhaps) there ARE models that would better simulate "real life".Vince Lombardi:

"Perfection is impossible. But in the pursuit of perfection you find excellence."

You can always just Monte Carlo your way to anything using as many price change sequences from historical sets as you can get your hands on. Assuming time frame invariance and some independence assumptions you can even rescale and reorder tick data repeatedly from the same historical real-life sequences to build up path simulations. Elegant math is no defense against teraflop computing. Models are what we teach the kiddies...

Nicely done Cheeky. I am emailing it to my engineering student son. Hope it will hook him into ZH. Good to see you again.

Quants are no different to other money managers. You're better off with the Jim Simons of this world, than the Meriwethers, ie: some are good at it consistently, most are not, for the reasons outlined by Cheeky and many others. Choose your manager wisely, and remember that the majority of managers do not deserve the fees they are charging. Caveat emptor.

Thanks for the post.

I agree with wiliambanzai7's first comment. I have never met anyone who would use BS to make predictions. It is used for extracting information for relative valuation.

Sure, you can complain about its weaknesses for extracting market information, but how about another model that is equally bogus and is used even more extensively everyday without question: bond yields?

The "model" for computing bond yields is even more bogus than BS yet you don't hear Taleb, Derman and Wilmott go on diatribes about that.

Bond Yield Model:

For relative value purposes, implied volatility is not any worse than bond yield.

Nice article...