Style Drift: Tenure as an Infinite Lockup

This is a sample from a recent newsletter of a listing of bunch of papers in behavioral finance:

Conditional Cooperation: Evidence for the Role of Self-Control

Peter Martinsson, University of Gothenburg - Department of Economics Kristian Ove R. Myrseth, ESMT European School of Management and Technology Conny E. Wollbrant, Göteborg University - School of Business, Economics and Law

Willpower and the Optimal Control of Visceral Urges

Emre Ozdenoren, London Business School, University of Michigan at Ann Arbor - Department of Economics, Centre for Economic Policy Research (CEPR) Stephen W. Salant, University of Michigan, Resources for the Future Dan Silverman, University of Michigan at Ann Arbor - Economics Department, National Bureau of Economic Research (NBER)

How Much can Taxation Alleviate Temptation and Self-Control Problems?

Per L. Krusell, Princeton University - Department of Economics, Stockholm University - Institute for International Economic Studies (IIES), Centre for Economic Policy Research (CEPR) Burhanettin Kuruscu, University of Toronto - Department of Economics Anthony A. Smith, Yale University - Cowles Foundation

Demand for Self Control: A Model of Consumer Response to Programs and Products that Moderate Consumption

Nathan Berg, University of Texas at Dallas - School of Economic, Political and Policy Sciences Jeong-Yoo Kim, Kyung Hee University - Department of Economics

Risk, Delay, and Convex Self-Control Costs

Drew Fudenberg, Harvard University - Department of Economics David K. Levine, Washington University in St. Louis

Consumer Spending Self-Control Effectiveness and Outcome Elaboration Prompts

Kelly Haws, Texas A&M University William O. Bearden, affiliation not provided to SSRN Gergana Y. Nenkov, Boston College - Carroll School of Management

Grapes of Wrath: The Angry Effects of Self Control

David Gal, Northwestern University - Kellogg School of Management Wendy Liu, UCSD Rady School of Management

Self-Regulation Through Goal Setting

Alexander K. Koch, University of Aarhus - School of Economics and Management, Institute for the Study of Labor (IZA) Julia Nafziger, affiliation not provided to SSRN

Endogenous Preferences, Self-Control, and Dynamic Contract Design

Wei Zhang, Northern Illinois University

It's amazing where business schools have gone with behavioral "finance". Is this stuff seriously related to business, and is it useful?

If the business school were a hedge fund you hired to manage your money, and they did something analogous, I think this would count as style drift, and you would redeem your investment.

Can hedge funds get tenure? It's kind of an infinite lockup, or the ability to gate forever.

Models.Behaving.Badly

Free Press finally has some version of my forthcoming (Oct 25) book listed on Amazon here, sans cover for now, which they haven't done yet. If anyone has any ideas for a cover, they and I would appreciate it.

The description isn't 100% accurate, but it's getting there.

I am told by them to get on Twitter and Facebook too, something I've avoided, but I am being persuaded.

Biology is Destiny?

I haven't read The Social Animal by David Brooks, which I gather is about the ways in which a couple's life illustrates the insights of behavioral psychology and the idea of emotional intelligence.

But I have seen the new Kiorastami movie, Certified Copy with Juliet Binoche, which is an interesting and probably more imaginative take on similar territory: male and female stereotypes and models. It begins with two slightly unconventional and attractively independent characters who engage with each other and seem to avoid the stereotypes of masculine and feminine behavior; then they slide, very realistically, into behaving true to form/stereotype/archetype, wanting the things men and women supposedly and traditionally want. Biology turns out to be destiny. It gets a little corny towards the end, because stereotype is corny, but it has a terrific first half.

Along similar lines, I recently saw the old Truffaut movie Soft Skin which you cannot get on DVD. In the end it is also about male and female stereotypes, very well done with a fatalistic sense of doom hanging over it. It gets a little melodramatic in principle, but in practice it hangs together perfectly, organically whole and realistic.

Black-Scholes Or Bust

Black-Scholes or Bust

There are two ways to look at the derivation of Black-Scholes:

(i) the way Black and Scholes derived it originally, which was based on the hope that the market for a stock and its options would be in equilibrium when their Sharpe ratios were equal; and

(ii) via dynamic riskless replication of a portfolio that has the same payoff of the option.

Everyone nowadays learns the second method, Merton's elegant discovery.

The two methods are equivalent as long as you assume geometric Brownian motion (GBM) for the stock, and lead to the same PDE.

But over the years, after I learned method (i) rather than method (ii), I've come to see it as more realistic and capable of extension, in other words, robust.

For GBM, the Sharpe ratio or risk premium is the excess return per unit of risk, and method (i) says that the stock and option will have the same price when they provide the same risk bang for the buck. But even when you don't have GBM, the idea that the prices will equilibrate when both securities provide the same excess return per unit of risk is a good idea and seems like a more general truth.

Irrespective of subtleties, the risk of the stock and the risk of the option, whatever nature they take, are clearly related, so that equating their risk premiums gives a sensible constraint on their relative prices. That makes the Black-Scholes model robust and a rarity among financial models. In contrast, CAPM, from which it stems, is also based on GBM, but it works much less well for stock valuation, because stock prices suffer risks more diverse and wild than those associated with diffusion. There are many other huge risks – that prices can jump, that volatility can spike, that liquidity can dry up, that counterparties can all fail together in a crisis – that GBM ignores and that can therefore invalidate many of its results. But the idea behind BS can survive the invalidity of GBM

How Do Options Prices Get Determined?

When there is some news, do traders in the pits (when there were pits) think about the right vol and then set the option price?

Or does the news make them respond with a price move and then see what vol it corresponds to?

The answer may be different depending on whether the news moves the equity market or the vol market, though even that separation isn't really clear.

What is the actual interaction between models and prices at the front line? Anyone know the answer from experience?

Metaphors Models Theories

A version of a talk I gave now on: ssrn

Calibration

At work this morning I found myself thinking about calibration. Lately, some people have tried to debunk the idea of calibrating financial models, but I still feel that calibration is one of the key ideas of financial modeling.

Financial models are models of relative value; in essence they tell you how to value something when you know the price of something else. Calibration is about satisfying that constraint: building a model to value one thing and making sure that it values known things correctly.

Of course, you can take anything too far, and the people who prefer mathematical style over content will do that. You can calibrate any old model, and that doesn't make it right. Calibration alone isn't enough. A model has to have appropriate dynamics. But once you've built in realistic dynamics, you need some kind of calibration to determine the parameters.

If the dynamics is badly wrong, calibration is of dubious help. You can't make a silk purse etc. But if the dynamics is not too far off, then calibration is critical. You can't make any purse at all without some stitching.

Finance For The Ages

Almost four years ago I had a competition in which I asked people to enter one sentence that would pass on the essence quantitative finance to our descendants, assuming all knowledge had been destroyed.

One of the entries that summed it up was:

Time and the right to choose have value.

by Marcos Carreira.

I want to modify it with an asterisk:

Time and the right to choose have value*.

* And when you're dealing with an uncertain future**, the average value across possible futures is a better estimate than the value at the average future.

** And aren't they all?

What Humans Can Do

An interesting remark, but I think a fallacious one, by Richard Dawkins in a recent conversation with David Attenborough:

RD: There does seem to be a sense in which physics has gone beyond what human intuition can understand. We shouldn't be too surprised about that because we're evolved to understand things that move at a medium pace at a medium scale. We can't cope with the very tiny scale of quantum physics or the very large scale of relativity.

Actually, we cope exceptionally well because in the end everything comes to us through detectors whose pointers are of human scale. So, despite what we've evolved to react to (I think that's a better word for this than understanding) humans can truly understand electrons and electromagnetic fields, with amazing intuition, at distances smaller than 10-12 cm and close to the speed of light, better than anyone understands anything else in the whole wide world. Hence lasers, PET scans , electron microscopes, carbon dating, the Bohm Aharanov effect, quantum computers …

Courtesy?? Professionalism!! #$%!@ Respek!!!

Courtesy??

Google has released a new upgrade to their operating system for Android mobile phones, and it is a bit of an improvement, so good for them. It is nevertheless endlessly astonishing to me how people can sell you stuff that doesn't work. In the days when you bought a phone from Western Electric, if it was flawed you returned it and got a replacement or a refund. Google sells consumer devices with buggy software and has absolutely no customer support. Zero. I can understand no customer support for searching the internet or twittering, since you're not paying for it and it's funded by other people's money, but I'm paying for my phone.

Professionalism

For reasons too complex to go into (well maybe not: actually, the logic board seems to have a flaw in it), Apple has kindly replaced my two-year-old 24" iMac with a new 27" iMac. I connected the new machine they shipped me overnite to the old one with a FireWire cable; on switching it on it asked me whether I wanted to transfer Applications as well as Internet settings and Documents. I said yes. Two hours later my new machine looked exactly like my old one (except that behind the scenes it was running Snow Leopard rather than Tiger and it was 3" bigger); the dock still contained every application I have ever used; I didn't have to reinstall any software again, not Word, not Illustrator, not Mathgematica, not Matlab which requires Xwindows from Unix, not even Parallel Systems and Microsoft Windows XP which runs under it, and the Windows programs I use ran as before and remembered the last file they opened. There is a number to call for help. But I didn't need it.

#$%!@ Respek!!!

I'm always interested in how people get to make discoveries, and Jeremy Bernstein pointed me at Arthur Koestler's book The Sleepwalkers, a history of man's view of the cosmos. I've read only part of it. It has a wonderful account of Kepler's discovery of his three laws of planetary motion. Koestler stresses several things that strike me:

First of all, Kepler's unique contribution. Many discoveries are part of the zeitgeist; if not for Heisenberg then Schrodinger, if not for Apple then Microsoft, but if not for Kepler, then nothing. No one else came close. And without Kepler, no Newton.

Second, until Kepler, astronomy was about explaining the shape of the orbits. Kepler brought physics into astronomy by focusing not just on their shape, but also on their motion, the speed with which planets moved, the ratio of orbital times to orbital distances. His law that"planets sweep out equal areas in equal times" is the law of conservation of angular momentum. And Kepler came close to understanding gravity. He understood that elliptical orbits are the result of a force from the sun and a force from the planet, i.e. the tension between gravitation and inertia.

Kepler couldn't have done any of this without Tycho Brahe's data. And he took data seriously -- 8 minutes of an arc was enough for him to invalidate one of his own wrong theories; before him 8 minutes of an arc was ignorable for the sake of complying with Aristotelian principles.

But Kepler didn't slavishly follow data. He played leapfrog with theory, intuition, guesswork and data, somehow knowing when to pay attention to one rather than another, trampolining from method to method at the right time until he finally, after years, got everything right. And here we are.

Artificial Intelligence and Natural Stupidity

Finally, a sensible Op-Ed about AI and the premature and naive attribution of human qualities to human artefacts:

Jaron Lanier in the NY Times

"Nothing creates more misunderstanding of the results of scientific research …

… than scientists’ use of metaphors"

That is the opening line of an article ( Not so Natural Selection ) in the latest NYR of Books by Richard Lewontin, an evolutionary geneticist who has been a critic of sociobiology and evolutionary psychology,

He concludes:

The other source of anxiety and anger (in the community of evolutionary biologists) is that the argument made by Fodor and Piattelli-Palmarini strikes at the way in which evolutionary biologists provide adaptive natural historical explanations for a vast array of phenomena, as well as the use by a wider scholarly community of the metaphor of natural selection to provide theories of history, social structure, human psychological phenomena, and culture. If you make a living by inventing scenarios of how natural selection produced, say, xenophobia and racism or the love of music, you will not take kindly to the book. Even biologists who have made fundamental contributions to our understanding of what the actual genetic changes are in the evolution of species cannot resist the temptation to defend evolution against its know-nothing enemies by appealing to the fact that biologists are always able to provide plausible scenarios for evolution by natural selection. But plausibility is not science. True and sufficient explanations of particular examples of evolution are extremely hard to arrive at because we do not have world enough and time. The cytogeneticist Jakov Krivshenko used to dismiss merely plausible explanations, in a strong Russian accent that lent it greater derisive force, as “idel specoolations.”

Even at the expense of having to say “I don’t know how it evolved” most of the time, biologists should not engage in idle speculations.

Disclaimers

Wall Street emails end with a disclaimer saying "Nothing in this email should be construed as a solicitation." This is for legal protection.

Environmentalists inform you to ponder the environment before printing their email. This is to show that the emailer is a good guy.

Today's NY Times has an article about how a scientist rediscovered that psilocybin induces religious states that change people's lives:

Hallucinogens Have Doctors Tuning In Again

But, lest other scientists think there is something fuzzy about his thinking, he feels obliged to add a disclaimer:

"The subjects’ reports mirrored so closely the accounts of religious mystical experiences, Dr. Griffiths said, that it seems likely the human brain is wired to undergo these “unitive” experiences, perhaps because of some evolutionary advantage.

“This feeling that we’re all in it together may have benefited communities by encouraging reciprocal generosity,” Dr. Griffiths said."

Modern Portfolio Theory And Its Effect on What You Cannot Buy

The other day I wanted to look up some statistics on certain stocks -- volatility, correlation with the S&P, etc. I went to yahoo/finance and google/finance, and eventually to a Bloomberg. To my great surprise, all I could easily find was beta. None of these sites or machines told you the volatility of the stock itself, or its correlation, in any direct way, though you could eventually back it out.

Beta, though it is indeed a statistic, the covariance with the market divided by the variance of the market, is of interest because of its role in the capital asset pricing mode. I was quite surprised that it had infiltrated the commercial world to such an extent that they gave you that information without bothering to give you variance or correlation, which are less theoretical in nature and likely at least as useful. This is an indication of how successfully modern portfolio theory, right or wrong, has influenced what you can buy in the way of information.

Interestingly, if you go www.wolframalpha.com and simply enter the stock symbol, you will find a useful set of information and graphics that is much less theoretically prejudiced and very useful, all obtained by typing one symbol.

"A thought from a former student" on quantitative finance

A real letter I received a few days ago.

____________

Dear Professor Derman,

I graduated from Columbia last May. I took your seminar on FE important papers during my senior year and enjoyed it very much. I went to work at ***** doing things that have pretty much no relation to the things I learned in school. I am however still very interested in quantitative finance and it is something I like to read about and think about fairly often.

I am also very interested in economics in a more general sense. I am one of those people that still thinks people are rational and markets work. I know these are ideas that have fallen severely out of fashion, but it is the only thing that ever made any sense to me from a theoretical/analytical point of view. I don't mean to say that I don't believe in the experiments carried out by the behavioral economists, but I am yet to be convinced that these things can have any real effects in the aggregate. Having worked in at least one part of the financial industry for a little while, I can say that the approach to valuation and overall decision making seems pretty rational over here. I really don't think that we give higher valuations to a company on a given day simply because we just paid a high price for our lunch (That one was called anchoring, right?).

Lately I have been having certain doubts about some of the first principles on which so much of what I studied in school is built and I thought perhaps I would share them with you and you would have some interesting insight or comment.

Basically it boils down to the following: in most areas of economics, when I think of the first principles, it is a collection of assumptions that all make logical sense. Many of the variables are not directly observable, but we know the general form and it is something one would have a hard time refuting. For example, while I can't easily observe the demand curve for apples, i can safely say that it has to be "downward sloping"--If apples are more expensive I will buy less apples. That is simple and about as true as we can expect anything in the realm of human behavior to be.

My issue comes when I try to think of first principles, or just the "form of first principles" in the area of quantitative finance. We have the law of no arbitrage and the efficient market hypothesis (both of which I think make a lot of logical sense, which I like), but those two alone don't really get you anywhere. We need some assumption for how asset prices evolve. And that is where I think things get murky. There is no logical explanation that gets us to Brownian motion or anything of the like. I can see an explanation for assuming some sort of evolution that is a "martingale", which can logically follow from the efficient market hypothesis (in fact, its almost like saying the same thing), but any assumption we make as far as the form of the distribution seems to come out of thin air. Sure, we can inform the guess with past data, but that does not seem theoretically rigorous. So I look at the entire paradigm of the mean-variance (or risk-return) approach to investing and I am left thinking: risk is not even well defined. Markowitz (or Bachelier) woke up one morning and said "these returns look normally distributed" and we started defining risk in terms of standard deviations, but that's just one random (pun not intended) guess!

And it feels like from then on it just gets worse. Will Sharpe came up with his Capital Asset Pricing Model (which we use at **** all the time, in its most simplistic form) and now it is part of the dogma that asset returns are linearly related to market returns. What is the logical basis to assume a linear relationship here? He could have just as easily assumed a cubic relationship (which will almost by definition fit past data better) and done the same work. His math would have probably gotten messier, but it is hard to find any merits to the linear assumption other than the fact that it is simple. I am all for simplicity, and perhaps if I asked Sharpe he'd tell me that was just a reasonable first approximation, but that is certainly not the way in which people use it now (maybe they are not so rational after all?).

Well, I think this e-mail is well past the point of "long enough". Maybe this is just me longing for the more intellectually challenging days of school, but as I said earlier, I have been struggling with these questions. I would greatly appreciate a response.

Best,

....

Eating Your Dog

Premises Premises

Walking to work this morning I passed a Citibank branch which prominently displayed their promises to New York.

The first was:

We Promise
to be there when you need us.

That's a promise only the government can make for them.

This is pure noise, expanded on by the aptly-named Brad Dinsmore, formerly of BoA, now Head of Retail Banking, North America Consumer Banking, who said: "We are thrilled to share the power and promise of Citi with one of the greatest cities in the world, New York …"

It's a scary phrase, Consumer Banking. I never looked at it before.

They also promise "to protect your identity as if it were our own," which I take as more of a threat than a promise.

_____

My instinct much of the time these days is that the cure the government has chosen for the excesses of the past decades is the same sickness that caused it. Each successively larger mini-crisis since the mid-90s was met by an attempt to restore the status ante quo which temporarily postponed a still larger crisis that then led to a still larger intervention which led to … …

I don't totally believe the world would have ended if various firms had fallen into the hands of bondholders, and I like to think that if it had, then we've only postponed it.

________

In this regard, I am working on a book about the way we use theories & models to handle the world and life in general, and how these theories and models work and don't work. One of the things I've been writing about, on a tangent that is getting longer and longer, is the miraculous history of the theory of electromagnetism from Coulomb to Feynman. I want to try to explain the Wonder (in the Spinozan sense, capital intended) of being able to discover/create an understanding like this. It's taking all of my available time so I don't do much else.

_________

What makes me much happier today is the announcement that Verizon Wireless, my carrier of choice, who have the best service in New York but the worst phones in the world, are finally going to get an Android phone. I am subsisting on a Palm Treo that won't sync with my Mac properly anymore unless I spend hours trying to transfer data using any software I can find, which I do, and I am waiting for a Mac-compatible Verizon phone to arrive before I spend all my days as well as nights on this. As an early Newton owner (the first smartphone though it didn't have a phone) through the 90s and proud of it, I have suffered long enough.

What also makes me happy is that Apple has rehired the guy that was the marketing manager for the Newton of long ago, and so it seems they are coming out with a tablet version of the iPod Touch that will let you read books on it in color looking like the real thing. I suspect it'll be much better than the Kindle, which sounds slapped together. Newton is a good name. In Vienna they have a street named (and not just fake-alternately named like in New York) after Boltzman.

Encoding

I gave a talk recently in which I remarked that what distinguished theories from models iis that theories aspire to some sort of absolute truth whereas models simply aspire to a limited description. A physicist in the audience objected to this talk of truth, telling me that all of these theories (e.g. Newton, Einstein, Dirac) were simply "encodings", some better, some worse.

I find I cannot believe that theories like QED are simply encodings, which I assume means convenient but not necessarily correct ways of looking at things. Yes, I understand that Newtonian mechanics and General Relativity are two different ways of looking at the same thing, but there is something truthful about both of them.

I am obliged to think, I guess, about how to define what I mean by that last sentence more precisely.

When someone disagrees with your views, you might as well say that calling their disagreement a disagreement is simply a convenient encoding of their behavior too.

Avoiding Economic Crises via the Stochastic Money Supply

I received an interesting-looking paper which I converted to PDF and posted at http://www.ederman.com/new/docs/economia-lor.pdf

Avoiding Economic Crises via the Stochastic Money Supply

Falip. O. Lor Ph.D1,2

[version: 1.4.09]

Abstract

We generalise the arguments of Minsky to propose a stochastic differentialequation (SDE) using GBM for modelling the domestic money supply and its effect on GDP via the velocity of money v. Using Prospect Theory’s positive convexity of investors’ risk preferences under framing losses, and assuming the scaling behavior of the black tails of asset returns, we can show that positive feedback loop leading to bubbles in the economies can be dampable if central banks will take action to limit the volatility of volatility of v.

We solve our equation in discreet time via simulation involving cellular automata. Extending the stochastic behavior of money supply to allow for Levi-Khinchine processes, we have used Malliavin calculus to demonstrate that our results still hold true in aggregate.

Finally, we propose a new risk measure, CVaR-V, measuring the bubble risk in a domestic economy. Assuming the validity of the Black-Litterman model, we extend our results to economies of several coupled countries for all logarithmic utility functions.

_______________

1. Current affiliation: Lecturer, Dept of Economics, Universidad Sao Seriffe. Also Adjunct Lecturer in Physics, SS Istituta di Tecnologia.

2. Supported in part by grant from Departamento di Energia & Sanidad, SS.

Giving Credit where Credit is Due

I get a fair number of calls or emails from reporters who want to know if there really is a formula that destroyed the world.

Something that seems significant in this regard was pointed out to me the other day.

° Fund managers whose careers were ruined by Madoff's alleged Ponzi scheme are quite open in taking the easy route of blaming Madoff for having so cleverly misled them.

° Investment bankers whose careers and fortunes too were destroyed by the subprime market collapse (Stan O'Neal, Dick Fuld, Jimmy Cayne, …) don't seem to have taken the easy route to citing subtle financial models as the cause of their downfall.

The Financial Modelers' Manifesto

The Financial Modelers' Manifesto

Preface

A spectre is haunting Markets – the spectre of illiquidity, frozen credit, and the failure of financial models.

Beginning with the 2007 collapse in subprime mortgages, financial markets have shifted to new regimes characterized by violent movements, epidemics of contagion from market to market, and almost unimaginable anomalies (who would have ever thought that swap spreads to Treasuries could go negative?). Familiar valuation models have become increasingly unreliable. Where is the risk manager that has not ascribed his losses to a once-in-a-century tsunami?

To this end, we have assembled in New York City and written the following manifesto.

Manifesto

In finance we study how to manage funds – from simple securities like dollars and yen, stocks and bonds to complex ones like futures and options, subprime CDOs and credit default swaps. We build financial models to estimate the fair value of securities, to estimate their risks and to show how those risks can be controlled. How can a model tell you the value of a security? And how did these models fail so badly in the case of the subprime CDO market?

Physics, because of its astonishing success at predicting the future behavior of material objects from their present state, has inspired most financial modeling. Physicists study the world by repeating the same experiments over and over again to discover forces and their almost magical mathematical laws. Galileo dropped balls off the leaning tower, giant teams in Geneva collide protons on protons, over and over again. If a law is proposed and its predictions contradict experiments, it's back to the drawing board. The method works. The laws of atomic physics are accurate to more than ten decimal places.

It's a different story with finance and economics, which are concerned with the mental world of monetary value. Financial theory has tried hard to emulate the style and elegance of physics in order to discover its own laws. But markets are made of people, who are influenced by events, by their ephemeral feelings about events and by their expectations of other people's feelings. The truth is that there are no fundamental laws in finance. And even if there were, there is no way to run repeatable experiments to verify them.

You can hardly find a better example of confusedly elegant modeling than models of CDOs. The CDO research papers apply abstract probability theory to the price co-movements of thousands of mortgages. The relationships between so many mortgages can be vastly complex. The modelers, having built up their fantastical theory, need to make it useable; they resort to sweeping under the model's rug all unknown dynamics; with the dirt ignored, all that's left is a single number, called the default correlation. From the sublime to the elegantly ridiculous: all uncertainty is reduced to a single parameter that, when entered into the model by a trader, produces a CDO value. This over-reliance on probability and statistics is a severe limitation. Statistics is shallow description, quite unlike the deeper cause and effect of physics, and can’t easily capture the complex dynamics of default.

Models are at bottom tools for approximate thinking; they serve to transform your intuition about the future into a price for a security today. It’s easier to think intuitively about future housing prices, default rates and default correlations than it is about CDO prices. CDO models turn your guess about future housing prices, mortgage default rates and a simplistic default correlation into the model’s output: a current CDO price.

Our experience in the financial arena has taught us to be very humble in applying mathematics to markets, and to be extremely wary of ambitious theories, which are in the end trying to model human behavior. We like simplicity, but we like to remember that it is our models that are simple, not the world.

Unfortunately, the teachers of finance haven’t learned these lessons. You have only to glance at business school textbooks on finance to discover stilts of mathematical axioms supporting a house of numbered theorems, lemmas and results. Who would think that the textbook is at bottom dealing with people and money? It should be obvious to anyone with common sense that every financial axiom is wrong, and that finance can never in its wildest dreams be Euclid. Different endeavors, as Aristotle wrote, require different degrees of precision. Finance is not one of the natural sciences, and its invisible worm is its dark secret love of mathematical elegance and too much exactitude.

We do need models and mathematics – you cannot think about finance and economics without them – but one must never forget that models are not the world. Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister’s foot into Cinderella’s pretty glass slipper. It doesn't fit without cutting off some essential parts. And in cutting off parts for the sake of beauty and precision, models inevitably mask the true risk rather than exposing it. The most important question about any financial model is how wrong it is likely to be, and how useful it is despite its assumptions. You must start with models and then overlay them with common sense and experience.

Many academics imagine that one beautiful day we will find the ‘right’ model. But there is no right model, because the world changes in response to the ones we use. Progress in financial modeling is fleeting and temporary. Markets change and newer models become necessary. Simple clear models with explicit assumptions about small numbers of variables are therefore the best way to leverage your intuition without deluding yourself.

All models sweep dirt under the rug. A good model makes the absence of the dirt visible. In this regard, we believe that the Black-Scholes model of options valuation, now often unjustly maligned, is a model for models; it is clear and robust. Clear, because it is based on true engineering; it tells you how to manufacture an option out of stocks and bonds and what that will cost you, under ideal dirt-free circumstances that it defines. Its method of valuation is analogous to figuring out the price of a can of fruit salad from the cost of fruit, sugar, labor and transportation. The world of markets doesn’t exactly match the ideal circumstances Black-Scholes requires, but the model is robust because it allows an intelligent trader to qualitatively adjust for those mismatches. You know what you are assuming when you use the model, and you know exactly what has been swept out of view.

Building financial models is challenging and worthwhile: you need to combine the qualitative and the quantitative, imagination and observation, art and science, all in the service of finding approximate patterns in the behavior of markets and securities. The greatest danger is the age-old sin of idolatry. Financial markets are alive but a model, however beautiful, is an artifice. No matter how hard you try, you will not be able to breathe life into it. To confuse the model with the world is to embrace a future disaster driven by the belief that humans obey mathematical rules.

MODELERS OF ALL MARKETS, UNITE! You have nothing to lose but your illusions.

The Modelers' Hippocratic Oath

~ I will remember that I didn't make the world, and 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.

Emanuel Derman and Paul Wilmott January 7 2009

More Like a Bow and Arrow Than Like a Transistor

www.edge.org has a proposal

Can Science Help Solve The Economic Crisis?

http://www.edge.org/3rd_culture/brown08/brown08_index.html

for a group of scientists and economists to collaborate in solving the economic crisis.

I have a comment in the debate there:

http://www.edge.org/3rd_culture/brown08/brown08_index.html#derman

which contains this:

----------------------------

This is a noble proposal, but I remain a bit of a skeptic with respect to the ability of a cohort of scientists and economists to find a scientific solution to the problems of our economy. Economies are living organisms, about as old as the oldest profession, and rebuilding the economic system from scratch is a problem in engineering and social engineering, not in science. Humans and scientists don't have a good history as regards social engineering.

Science is reductive, and seeks to establish the laws which govern physical systems. To do so, scientists carry out repeatable experiments. For an experiment to be approximately repeatable, history has to be unimportant, and so the system has to couple very weakly to the rest of the universe. You can figure out the statistics of a coin flip because initial conditions of the coin are more or less irrelevant. The hand of the coin flipper, the temperature of the room, the location on earth, don't matter too much because the coin is coupled weakly to the rest of the world, and hence to history.

Engineering is constructive, and tries to build little almost-isolated universes (usually called machines) which obey the laws of physics and chemistry and more or less do what we want them to do, in certain regimes. You can do engineering without knowing too much science but by having a good empirical understanding of how matter behaves (building a hammer or chisel or lever or bow and arrow), or you can engineer it using scientific laws (using quantum electrodynamics and solid state physics to build transistor radios).

Now let's think about economics and the behavior of markets and the people who comprise them. First of all, we don't have the scientific basis for engineering economics. Second, it will be very difficult to find the scientific laws governing the behavior of economies, because there are very few isolated economic machines. There is one large economy, more or less. Since economies aren't isolated, you can't carry out the repeated experiments that science requires. History is important in economics, and in human behavior in general. You cannot replicate the initial conditions over and over again, as you can with a coin flip. Credit markets tomorrow won't behave like credit markets last year because we have learned what happened last year, and you cannot get back to the initial conditions of a year ago. Human beings and societies learn; physical systems by and large don't.

Though I came to finance as a scientist, my experience working in the financial arena has taught me to be very humble of scientific claims and of big universal ambitions. Whenever we make a model of something involving human beings, we are trying to force the ugly stepsister's foot into Cinderella's pretty glass slipper. It doesn't fit without cutting off some of the essential parts. You have to understand that you do need models—you can't think about finance and economics without math and models but you have to understand too that models are not the world, at least not in the social sciences, and so the models have to be simple, shallow even.

I would add that the economy we have been part of has not been treated as an efficient market, even by the economists who claim that it is. Every time the economy has suffered a threat, the Fed has eased credit to reignite it, but whenever it has boomed they have never tried to quench it very hard. It is an oddity that the only solution people can think of now to the credit crisis, which was in large part caused by too much easy credit rather than by scientism or mathematics, is to ease credit again and have the government spend money on infrastructure and public works. This is probably the right thing to do, but it shows you how counterintuitive and complex the system is, and how important history in fact is: first time around easy credit is the problem, second time around it's the hoped-for solution.

So, let's try to figure out how to do things better, with words and thoughts and with math too. More uniform regulation, more transparency, less leverage are going to be critical. I'd guess that in the short run the robust solution will lie in a proposal written with words rather than with equations, and be more like a bow and arrow than like a transistor.

A Model is Only a Model …

but a good cigar is a smoke.

Rudyard Kipling understood this. Why does no one else?

Paying in Kind

Part of the trouble with the economic crisis is that people and firms have an incentive to borrow short term to invest in long-term illiquid securities that are chancy and hard to value. If they can get them off their books and make a profit, the risk is no longer theirs.

I have a solution: Oblige anyone who creates long-term illiquid securities to get paid for their services in kind, so that a large fraction of their pay has to be in the stuff they traffic in. This would make them think twice or thrice about the honest risks of the product

Come to think of it, this is what happened to Merrill -- they held on to big chunks of the stuff they sold, and suffered the fate of their clients. Maybe that's the way it should work.

Marking Illiquid Securities

The last two years I spent at Goldman in risk management I was involved in developing methodologies to mark illiquid derivatives held by a variety of trading desks. The approach we took for illiquids was to simulate, under a broad variety of scenarios, both underlier behaviour and a trader’s hedging strategy, even if it isn't optimal, and then to create distributions of the resultant profit or loss of the entire portfolio. These distributions and their standard deviation or tail loss were then used to determine a realistic adjustment to the trading desk’s conventional marks that could be withheld until the trade was unwound and their realised profit or loss determined.

Here's a link to the Risk paper that described it. Maybe it's a complicated but reasonable way to estimate prices and their uncertainty when markets disappear.

http://www.ederman.com/new/docs/risk-markets_and_models.pdf

If you want things to stay the same …

I spent most of my time in firmwide risk management at Goldman trying to get traders to mark their exotic products to market, or else find a good proxy for it. Mark to market was the unquestioned gospel. Now it's totally astonishing to see the beginning of a backlash against mark to market. Some people are even suggesting moving averages of prices, which would once have been regarded as near to criminal mismarking and managing of volatility, to be watched for and prosecuted.

__________

It reminds me of a line from "The Leopard" by Giuseppe di Lampedusa: If you want things to stay the same, then things will have to change.

__________

There are reversals of what passed for common wisdom everywhere. I suppose this is one of the characteristics of the social sciences and the so-called sciences of nutrition, sociology, etc. when compared with the natural sciences, the total turnabouts from butter to margarine to butter.

___________

I never fully realized just how much the banking system is the lifeblood of the capitalist economy -- well, perhaps money is the lifeblood and banking is the lungs and heart, effecting a swap between unoxygenated and oxygenated blood. As someone pointed out on yahoo today, when pets.com dies it doesn't affect the financial sector, but when the financial sector dies it affects pets.com, hence the bailout of banks rather than internet companies.

____________

It depends upon what the meaning of the word 'is' is.

I saw this conclusion on a website about the sociology of finance:

"Are the purveyors of models selling us lemons? At the core of the controversy, I believe, is a fundamental question that orthodox finance has not, to my knowledge, yet addressed: what is the practical accuracy of a theoretically correct model?"

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If you tell me what you mean by 'correct model', I'll tell you what the practical accuracy is.

Meanwhile, I have something I once wrote along these lines:

http://www.ederman.com/new/docs/metaphors.pdf

On Models

Written for the Encyclopedia of Quantitative Finance

http://www.ederman.com/new/docs/models-web.pdf

Artificial Intelligence/ Natural Stupidity

Today's News Of The Week in Review has an article about the precipitous temporary decline in UAL stock when an old news story about their 2002 bankruptcy filing mistakenly appeared on the internet and was picked up by Google as current news. The Times reporter claims that automated AI computer news scanners picked up the news, shorted United, and, following that, algorithmic trading programs detected momentum and kicked in to do the same.

I'm a little skeptical about the first part of this argument. I know there are people stupid-smart enough to use algorithms to trade first without removing stocks (like Lehman) which are going down for a good reason. But are there really people willing to take a chance on a machine detecting news and trading without a quick look at the story itself? I'm inclined to think this started with simple human hot-to-trotness before the machines kicked in.

Things like this have happened before the widespread advent of algorithmic trading, which I first heard about in a talk by Steve Ross: "An amusing example is the case of the stock MCI (see Rashes [2001]). There is another company that is traded on the NASDAQ with no affiliation whatsoever to MCI, call it MCI2, and it is well documented that its price is highly correlated with that of MCI. Important news about MCI moves the price of MCI2. It is no mystery what is happening; some investors are confused. But investor confusion and silliness is not grounds for dismissing efficient market theory. MCI has a market capitalization of $100 billion and MCI2 has a capitalization of $300 million and a small float."

Skewed

1. When did people first start to begin their emails with "Good morning" or "Good afternoon"? It suggests that you're going to pay attention to the missive as soon as it arrives, another step in the morphing of email from letter to phone call.

2. I was at the Global Derivatives conference in Paris, and thinking about stochastic volatility, motivated in part by an old talk by Peter Jaeckel that someone emailed me. There's no doubt that volatility IS stochastic, and that the models are elegant, but … does it explain the smile, in particular the equity index smile?

Jaeckel points out how many of the economic causes of the smile in FX, equity and interest rates in particular, are related to what I think of as violations of scale invariance rather than the correlation between an asset price and its volatility. There is a more or less absolute meaning to 'low' and' high' for interest rates, as intuited by both crowds and the Fed. And for FX and equities, though they may be scale invariant in the long run, during each short-term period 'low' and 'high' have meaning too, a meaning imparted by investors, central banks and governments. There is something vaguely local about all of this.

Bubbles

There's an article in the Sunday NY Times Business Section and one in the Economist. I have to say I've never seen anything really comforting from a theoretical point of view on this topic, and I once wrote a paper on this too. The Economist does refer to a sort of probabilistic model from which one might perhaps back out some implied probabilities of bubbles.

It seems to me:

1. No one knows what fair value of anything is, though one can begin to tell when it gets to be unfair. Fischer Black wrote somewhere that a price anywhere between half and twice is fair value is fair value. If you run this recursively, you get a range from zero to infinity.

2. People are strongly influenced by other people's opinions.

3. People try to figure out what other people will do.

4. People have a tendency to get on moving trains.

Is there a way to turn all this into a convincing model?

Painted Black

This is an unconsidered piece.

I'm a little tired of reading about what a travesty Black-Scholes is. First of all, the real trouble isn't Black-Scholes, it's geometric Brownian motion. That's the underlying error.

Black-Scholes is an engineering construction that would work if stocks really did evolve under GBM. They don't. So, using Black-Scholes has plenty of problems. Stocks can jump, volatility isn't constant, you can't always short, there are transactions costs, and so on.

So, what can you do? Black-Scholes is a zeroth order approximation with (perhaps) a series of first- and second- and higher-order corrections. I say "perhaps" because claiming there are higher order corrections implies that someone knows the correct answer, and that's not true. You have to think of Black-Scholes as being the right answer is a Platonic world that doesn't match the one we live in.

It's true that many devotees of Black-Scholes are naive. They assume that if you correct it to accommodate the things it neglects you can get there. Instead, if you're a trader or a quant, you ought to think of Black-Scholes as a way of thinking about things, an ideal formula that doesn't hold in the real world, and now it's up to you to decide how to correct for its omissions. Live with it -- you can't do much better, at least for options. Even static hedging of the weak form (when there is no exact payoff matching) requires a model to construct the static hedge.

As someone I know once said: You can't give someone a Black-Scholes calculator and turn him into a trader.

People put too much faith in the model in the past. Now there's an over-reaction to its difficulties. What you have to do is look at the problems and then decide how to work your way around them, with a few calculations and a big dose of common sense.

The enthusiastic use of replication a la Black-Scholes is no doubt responsible for many disasters and market bubbles. But so is the naive reliance on anything: low future default rates, low P/E, The Nifty Fifty, you name it. Part of the trouble is the model itself -- P/E is a model of sorts. But another part of the trouble, perhaps an equal or greater part, is human enthusiasm, in particular desperate enthusiasm for some metric. Metrics in the social sciences (someone I know told me his father said that any field that has the word 'science' in its name isn't science) are always approximations.

If you get rid of Black-Scholes there will still be bubbles. Nevertheless, it's compulsory to understand its limiations. Wild horses couldn't drag me away??

Don't Look Back; I'm Not There; And I'm not a martingale either.

I went to see "I'm Not There", a movie about Bob Dylan's double. It's a bit long, but what's impressive in the movie, besides his music and the covers of it (and perhaps in real life according to "Don't Look Back" as well as various biographies) is his refusal to be typecast, to be or do what his fans expect him to be. He accentuates that in his Chronicles - Volume One, which has an interesting first part but then gets too much (for me) into describing all his recording sessions.

There's a review of the movie in The New Republic which I skimmed though and it makes the point that the movie doesn't show the consequent sacrifices of this kind of position. It's a risky sacrificial position to take in real life, talented or not. I know few people capable of it. He's not a fat tail or an outlier; he's simply not part of the distribution, and hence his present is not the expected value of his future. He's not a martingale.

I suppose there are people like that in all fields, but I'm trying to think who. In finance Fischer Black was a little that way. In the fiction world the review mentions Pynchon, who refuses to enter the fan game at all, and wants no persona, just his books, to exist. In theater or movies, I don't know -- maybe Greta Garbo. There must be other and better examples.

---------------------------------

On the martingale/numeraire front, I've been reading bits and pieces and I still feel uncomfortable with any of the expositions I've seen. The binomially based ones are like scratching your left ear with your right hand by by putting your arm behind your neck. The binomial proof of option valuation is economically based, with clear intuition and a straightforward proof of risk neutrality. The binomially based proofs of the martingale theorems are irritating; they try to rephrase the simple results of the binomial risk-neutral model in terms of the theorems of martingale theory, and they're awkward and provide a very unnatural extension. But the continuous time proofs get buried in technicalities and intuition is very hard to extract.

I notice that Wilmott's book, or at least the previous one that I have with me right now, doesn't even attempt to cover this approach. That says something.

Martingales and Numeraires

Kerry Back's excellent Springer book entitled "A Course in Derivative Securities" makes a remark about the numeraire/martingale way of looking at options pricing:

"It seems worthwhile here to step back a bit from the calculations and try to offer some perspectives on the methods developed in this chapter. The change of numeraire technique probably seems mysterious. Even though one may agree that it works after following the steps in the chapter, there is probably a lingering question about why it works. The author's opinion is that it may be best simply to regard it as a 'computational trick'. Fundamentally it works because valuation is linear. … The linearity is manifested in the statement that the value of a cash flow is the sum across states of the world of the state prices multiplied by the size of the cash flow in each state. The change of numeraire technique exploits the linearity to further simplify the valuation exercise … After enough practice with it, it will seem as natural as other computational tricks on might have learned."

Thinking of it as a computational trick indicates how unintuitive the result is. Anyone have a better introductory proof?

?Hedge Fund Replication?

GAIM recently had an all-day conference in New York City on hedge fund replication. There are three approaches, and I'm a little sceptical/skeptical about them all.

Hedge fund returns display all sorts of nonlinearities -- some because the underlying instruments are noninear, others because they modify their exposure to linear securities as markets move, inducing a nonlinearity.

The first method is linear factor replication -- a sort of least squares regression of observed hf returns to market factors, an APT model.

The second is nonlinear factor replication -- a similar statistical analysis using nonlinear factors or nonlinear trading strategies.

The third is distribution replication -- an attempt to build a payoff distribution, out of any underlying security (copper, electricity, the S&P, the price of sugar -- pick one) that will have the same shape as the hedge fund returns your trying to replicate. Value the distribution as an option, compare its value to the value of the actual hedge fund you're interested in, and then, if it looks cheaper, replicate it by dynamic delta hedging. The idea is that since you have the same distribution of returns, you should earn the same expected return. Same (expected) risk, same (expected) return.

There's a funny cartoon in Grant's Interest Rate Observer that has a picture of a road sign saying "Entering Greenwich CT: 2 and 20." Getting hedge fund returns on the cheap is what this activity of replication is all about.

Does it work well enough to use reliably? I'm a little scepticalskeptical.

The main problem is that you don't really know the payoff function for hedge funds, whereas you do for options. Probably this stuff is more useful for creating synthetic beta-driven hedge funds, with betas to anything you like, that can run algorithmically for cheap and may expose you to synthetic merger arb funds or vol trading funds.

The distribution approach is in the true spirit of finance, driven by the idea of equal risk equal return even when lognormality doesn't hold. But it requires so much statistics on such poor data that it's hard to swallow. And furthermore, since you replicate the eventual return distribution (if there is a stable one and if the method works) but not the month by month exposure, you don't know how long it'll take to generate the same return you expect from the hedge fund.

Necessity is the mother of invention. Invention often requires desperate measures.

Stochastic calculus for interviewees

An amalgam of the answers I liked best came from Umut Gokcen and Mario G. It went something like this, modified a little by me.

In physics a law of motion tell you exactly where a particle whose position you know right now will be at a very small instant of time later. Used again, the same law of motion then tells you where it will move to another instant later.

Calculus is the branch of mathematics that tells you how to add up all the small future exact position changes over instants of time to determine exactly where the particle will be in the future.

But not everything obeys such exact laws of motion. A stock price which you know today will not take some definite value an instant later, but rather will have a probability of being in some range of values. This price motion is called random or 'stochastic.'

Stochastic calculus is an extension of calculus that tells you how to add up all the small future ranges of movements over each instant of time to determine the final range of values and probabilities the stock price can take at some future time.

Poor Man's Stochastic Calculus

A student today asked me how one would explain stochastic calculus to someone who knew no math.

I think it's a tough question and a clever one. I'd be curious to hear short answers –  paragraphs, not essays. You don't have to spell out everything, just a line of approach. If you have a good idea, send it to me at eman.derman.blog@mac.com.

The Problems in Modeling Nature

is the title of an article today in the Science section of the NY Times. It's a report of a b ook called "Why Environmental Scientists Can't Predict the Future."

Here are a few excerpts:

"They also discuss concepts like model sensitivity — the analysis of parameters included in a model to see which ones, if changed, are most likely to change model results.

But, the authors say it is important to remember that model sensitivity assesses the parameter’s importance in the model, not necessarily in nature. If a model itself is “a poor representation of reality,” they write, “determining the sensitivity of an individual parameter in the model is a meaningless pursuit.” …

Besides, they acknowledge, people seem to have such a powerful desire to defend policies with formulas (or “fig leaves,” as the authors call them), that managers keep applying them, long after their utility has been called into question …

Models should be regarded as producing “ballpark figures,” they write, not accurate impact forecasts.

The Second-Most Important Equation

The key result of options pricing is that if you hedge at implied volatility, then over the next instant dt a long options position produces

dP&L = (1/2)Gamma*S^2(realized vol^2 - implied vol^2) dt

Of course this is in theory, assuming Wiener process for the innovations, etc.

I learned this years ago, but not right when I learned options theory. It was several years later. I think the equation is almost more general than Black-Scholes -- it tells you how to benefit from curvature. You can understand the equation even if you don't understand PDEs.

I've been doing a lot of teaching lately, both to practitioners and students, and many students and many many professors know all about Black-Scholes and how to derive it and how to solve it, but many many don't recognize this equation or the information embodied in it.

Paul and Reza Ahmed have a beautiful paper on this in Wilmott.

The Winner

I got a fair number of answers to the question of what single sentence would best pass on the essence of quantitative finance to the future, assuming all knowledge had been destroyed.

I have two winners in a tie:

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1." In quantitative finance there's arbitrage and diversification - the rest are details." by Athletico on the Wilmott forum;

(I suspect it should be "the rest IS details" but I'm not taking points off for grammar.)

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and

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2. "Time and the right to choose have value" by Marcos Carreira.

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Both of them are kind of crisp and accurate, though whether anyone could really recreate anything from one sentence is questionable, but that's my fault.

If Athletico and Carreira send me their physical addresses, I'll send them each a prize.

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Honors for originality goes to Zeta: "Money talks, and BS (prices options on random) walks."

Honors and thank to 'farmer' for putting an end to the future of quantitative finance:

"After correlation trading has smoothed the arrival of new information, residual uncertainty in the value of an asset can be summarized and communicated as a location on one or two axes which the majority of participants will have only slight disagreements about, and so a standard dollar value and other practices can be mapped to or associated with each location."

The rest are history.

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Model "Risk"

I was having a conversation about model risk the other day, and I think it's a misnomer.

Risk to me means the possibility that something bad (or maybe good) will happen tomorrow. It implies future uncertainty. If I'm standing on the corner, I know exactly where I am now, but I don't know what will happen when I start to cross against the light. If I own Google right now, I know what it's worth; risk involves what it will be worth later.

Model "risk" is different. It's not a future risk, it's a PRESENT uncertainty. You don't know what a hybrid product is worth now because there is no liquid market, and you don't know which model to use in order to tell you what someone will pay for it NOW. It's not model risk, it's model uncertainty.

(I just googled risk and came upon a reference to a book by Frank Knight called Risk, Uncertainty, and Profit written in 1921. I am obviously fairly ignorant because this is apparently a famous book. Anyhow, he seems to define In it "risk" as randomness with knowable probabilities and "uncertainty" as randomness with unknowable probabilities. I'm not sure I agree -- in economics all probabilities are pretty much unknowable, so there is only uncertainty in that case.+

What To Tell The Future

I was in Geneva at a Risk Conference earlier this week, and one of the talks I heard about behavioral finance posited that the most fundamental quantities in quantitative finance were SDFs, stochastic discount factors, analogous to DNA in molecular biology or atoms in physics.

I once read a remark by Feynman, who said that if all knowledge about physics was about to expire, and you were allowed to transmit only one sentence to the future to help them recreate what we know, then you would tell them "Everything is made of atoms."

Similarly, I suppose, that if you wanted to set up a one-sentence guidepost to biology for people in the future, you would tell them something about heredity being controlled by genes within cells and genes being made out of DNA with four bases. (I'm getting onto shaky ground here.)

And, if you wanted to do the same for medicine, you'd probably say "Diseases are (mostly) caused by tiny living germs."

Now for finance: what would you say in once sentence? I have some idea, but I suspect it doesn't involve stochastic discount factors.

Remembrance of Strings Past

In his review of the recent books by Smolin and Woit on the status of string theory, David Lindley writes: (see http://www.wilsoncenter.org/index.cfm?fuseaction=wq.essay&essay_id=204018):

"The problem with string mania, Smolin concludes, is that it suits the wrong kind of mentality. He makes a nice distinction between scientific seers— people such as Einstein and Niels Bohr, his heroes, who deeply pondered the working of nature and were by no means brilliant ­mathematicians— and craftspeople, who are enormously adept at intricate calculation but don’t seem to think much about the larger meaning of their ingenious manipulations. Seers are always in short supply, and the technical demands of mastering string theory are such that would-be researchers of a more philosophical stripe can rarely meet the price of entry."

I like to think that much the same thing applies to quantitative finance: we need more (flashes of) insight and less mathematical manipulation if we are to make major advances.

Thither Quantitative Finance?

I wrote a couple of days ago about how quantitative finance keeps working in the same paradigm -- pick a process, calibrate it to liquid securities, calculate the value of illiquid ones, and then asked 'Is that all there is?'

I received several emails in response, some agreeing with me, and one or two chiding me for being pessimistic, so I want to expand a little.

I'm not pessimistic. So many new markets (synthetic CDOs, etc) have exploded in part because of the applicability of some form of derivatives technology to hedging them. What I was saying was that I was a little bored at seeing derivatives technology applied over and over again. I do the same thing myself, because the theory is so clean and so tempting, so people in glass houses ... but nevertheless.

But there are interesting things that can be done and are being done in at least two other areas.

One is the behavior of underlyers rather than derivatives -- how do stocks, currencies, etc evolve beyond lognormality? Variance gamma, Mandelbrot, Stanley & co, etc? This is long overdue.

The second is valuation in incomplete markets. Since most things trade in incomplete markets, in the sense that you cannot replicate them with something more primitive, this is related to modeling underlyers.

Whither Quantitative Finance?

I heard some very good seminars in the last few days on credit modeling. But after my excitement at understanding something I didn't understand before, I get a slight touch of the blues. There's this one dominant theme to financial modeling:

* pick a plausible stochastic process with parameters;

* calculate the value of securities whose prices you know;

* fix the parameters to match those prices;

* use the model to calculate values of other securities.

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Every ten years the process repeats itself:

* stock options: match stock and bond, fix volatility;

* interest rates: match bond or swap prices, fix volatilities;

* credit: match CDS prices, fix future default probabilities.

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When you get more sophisticated, you make the parameters you fixed also stochastic. Hence stochastic volatility, stochastic default probabilities, ...

Cf. Peggy Lee: Is that all there is?

Supermodels

Marek Musiela gave a very interesting talk at Columbia the other evening about trying to use a derivatives framework to handle optimal asset allocation. A discussion arose about what makes a model useful for trading derivatives. I always come back to the same answer: practitioners use models in finance to take you from the prices of liquid market-traded instruments and use them to estimate the prices of illiquid instruments. Black-Scholes takes you from stock and bond prices to options prices or convertible bond prices. In a real sense, the models are interpolators from known boundaries to the middle ground.

Ambitious theoretical models that start bottom up often have elegant theoretical variables (a stochastic pde that describes the evolution of volatility, for example) that have to be made up and don't directly relate to observed or traded quantities. You then have to use heavy machinery to calibrate the model to the value of the liquid instruments and use it to calculate the values of the illiquid ones. The link between liquid and illiquid goes through a substrate of hedden variable that is invisible. A practitioner model tries to eliminate as much of that substrate as possible. There should be a short path from calibration to value.

Therefore, it's easier for users of the models to have the inputs and their stochastic description be quantities or parameters they can have an intuitive handle on. You can work with stochastic variables that are directly observed. This is more or less what market models do.

Barrier options valuation is another example. In order to value a barrier option, you can build an arbitrage-free stochastic volatility model, calibrate it as best you can, make assumptions for correlations that you are uncertain about, and then value the exotic. Another way to go at it, that I've seen practitioners do, is to approximately replicate the exotic option out of a portfolio of vanilla options, and then let the vanilla options themselves become stochastic, and compute the effect of that stochasticity on the value of the exotic option. It's less theoretically defensible, and may violate some axioms of valuation, but it may also give a better handle on the dynamics of the exotic, since there's a shorter path from liquid to illiquid.

Options on Periodically-Settled Stocks

I posted on my web site, www.ederman.com, a 14-year-old paper we wrote in Quantitative Strategies concerned with how to value options on stocks that settle in the old European style, where all stocks bought in the next (say) 30 days settle at some fixed date in the future, say 40 days from now. You can find it at

http://www.ederman.com/new/docs/gs-periodically-settled.pdf

Why Models Work [?]

A student at another university recently sent me a question which I've often wondered about myself:

"Any introductory economics course in college will introduce the student to simple supply and demand curves; the forces of the market that determine the price of a good. If that is the case, why is there such an effort in pricing financial instruments or (as you mention in one of your interviews) trying to understand the price of a stock? Shouldn’t these prices simply be dictated by the supply and demand of the market?"

Off the bat, I had two answers.

1. The world, physical or mental, doesn’t just have to have a description on only one level. You can describe water as a bunch of molecules or as a liquid or as something without which your body dies. All descriptions are true. Similarly you can think of a person as chemistry or biology or as a mind and a body, and all of those have some validity. It depends what facets of the person you want to talk about. So far this argument isn’t an argument about why the financial laws are right, but rather about why they don’t have to be wrong.

2. More deeply, people who supply or demand often themselves use various kinds of models to figure out value. For example, when you buy a house you first look at the market's implied cost per square foot and then see if that produces a reasonable estimate of the value of the house you're interested in. Then you adjust the price about that theoretical value. In other words, price per square foot is a model, like yield to maturity for bonds, that many of the participants in the market are using, some more rigorously, some more intuitively.

In the same way, the supply and demand for options probably depend on intuitive estimates of future volatility, and then those prices lead to an implied volatility that does indeed reflect estimates of future volatility. People, even naïve people, are often using some version of the financial strategists sophisticated model too.

Supply and demand is one way of looking at things; models are a complementary view of the same phenomenon. Often, but not always, they are related, not in conflict. Fischer Black once said that the market is efficient when prices are with a factor of 1/2 and 2 of the fair value.....

One other thing I came back to add: Models are very useful when they are the only way to communicate value, and then drive supply and demand for financial assets. The value of an option is hard to estimate, almost impossible, without a model. Black-Scholes takes a linear quantity like volatility, which you can estimate with intuition and thought, and translates it into a nonlinear price, which you couldn't.

Check N = 3 before you check N = infinity

In implementing models, one of the most common mistakes I've made, and seen others make, is to check them sloppily.

For example, suppose you can write a binomial or lattice or Monte Carlo solution for the Black-Scholes model, and then check that for a very small lattice spacing it agrees with Black-Scholes solution to a high degree of accuracy for a bunch of different strikes, expirations, etc. The temptation is to say that everything is OK. But that just tells you that the average of all your calculations is roughly OK. There could still be logical errors in your algorithm that aren't showing up in this average case.

Therefore, it's good to run the program for N=3, say, and print out every intermediate number, and check each one with a calculator. It's amazing how often you can have a small mistake that doesn't show up in your simple gross tests until much later, when you do calculate something a little stranger.

Constant self-criticism, as the Red Guards used to say, and constant looking over your own shoulder.

Since everyone else is apparently beginning to put photos in their blog, I must too. This one is Central Park on an early spring evening, taken with my Treo's camera. I used to despise picture-taking cell phones, but they have their uses.

Intuition

I was looking at blogs on google and I found one that referrred to an article I once wrote on how to get a job in finance. The blog quoted something I wrote about the importance of gaining intuition:

"And, importantly, seek to gain intuition. Quantitative finance isn’t mathematics or chess; it’s not a field for brilliant idiot savants; it’s an attempt to model the world of markets and people, and you need a little wisdom and experience to know what can work."

Then, the blogger added a coda:

"There's not much there about how to "gain intuition" though, so good luck with that. While you are at it, you might try gaining super-powers and esp too."

It's a good point. In the course I teach on the vol smile at Columbia, I try hard to somehow get the intuition about the various models across to the students, rather than mathematics. But I never thought about how to systematically do that. Here are some random thoughts. I'm sure other people have other suggestions.

- Look for interesting results in papers, or in observations; then try to "derive" them qualitatively.

- Or see if you can derive the same results with much simpler mathematics.

- Or, better, first try to think about it qualitatively, and then check your reasoning with the math.

- Many papers obscure the simplicity of their approach with complex and formal mathematics. Try to see what the essence of the paper is, in terms of assumptions and methodoloty, and then see if you can get to the result yourself, qualitatively, in pictures. - Think about extreme cases where you know the answer (e.g. deep in the money, deep out) because it's obvious, then try to move a liittle away from them.

- Try to internalize the mathematics and its results in order to go one level higher.

- Use simple pictorial methods to understand how to tackle something. (That's why I like the binomial model.)

As a personal example, my colleagues and I once noticed that in the computed results of local vol models the slope of the implied vol was about half the slope of the local vol at-the-money. We thought that was interesting and then found a way to derive that approximately. Then, that half reminded us of the similar relation between yield to maturity and forward rates. In that way we got to think about implied vol as an average over local vols. That proved to be a fruitful and often accurate way to think about the model.

Next blog session I will tackle how to get super-powers.