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Steve Shreve on Pablo Triana’s The Flawed Math of Financial Models


Staff member

In his article The flawed math of financial models, Financial Times, November 29, Pablo Triana seeks to fix a large portion of blame for the world-wide financial crisis on "quants'' in the finance industry and the programs that educate them. Mr. Pablo recommends radical reform in such programs. Others, carrying these ideas farther, call for a diminished role for quants in finance.

Any discussion of quants in finance must begin with the recognition that the global integration of economies and the associated complexity of our financial system has made the use of mathematical models an indispensable tool. Rules-of-thumb and intuition will not suffice when multi-national firms face exchange rate risk, funding risk and commodity price risk, when insurance companies and pension funds face longevity risk, when financial institutions are called upon to mediate these risks, and when regulators are charged to oversee these institutions. This was recognized in the recent U.S. financial reform legislation, which authorized a government Office of Financial Research whose task in 2008 would have been to alert policy makers to the ridiculously large naked position in credit default swaps held by AIG and to predict the effect of the failure of Lehman Brothers. Such an office must necessarily be populated by quants, people who can build models into which information about financial institutions is fed.

What then is the appropriate training for quants? I believe we should focus on three aspects.

Most importantly, a quant must be competent in the technical disciplines of mathematics, statistics and computer programming, and she must be knowledgeable about financial markets. Achieving competence across this broad spectrum is a tall order. But it must be done because a well-intentioned incompetent quant is as dangerous to the financial system as a well-intentioned incompetent doctor is to personal health. The primary focus of the educational programs at Carnegie Mellon will remain the creation of competent graduates. This is what we do best.

But a good quant also needs good judgment. A wise quant takes to heart Albert Einstein's words, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'' All models are wrong. Judgment is needed to know when an admittedly wrong model can be helpful and when it is dangerous. This kind of judgment is acquired primarily through experience, but we can begin teaching it in the classroom. Since the financial crisis, we have invited participants in the crisis to speak in detail to our students about deals that went bad, describing how the deal was analyzed, why it was approved, and what was overlooked.

Finally, we need people with integrity managing our financial systems. Teaching ethics is difficult, and guaranteeing that listeners will implement those teachings is impossible. It is not easy for a quant to sound the alarm that his models are being stretched beyond their limits, knowing that if he is taken seriously it will result in the loss of business to competing firms and may result in the loss of his job. We cannot instill in sixteen short months behavior that properly requires years of nurturing and mentoring. We do what we can, leading by example, penalizing students for academic dishonesty, setting and enforcing rules for ethical conduct when interacting with potential employers, posing ethical dilemmas for classroom discussion, and encouraging our graduates to consult with fellow graduates when facing tough ethical decisions.

A lesson that can be learned from the present crisis is that if everyone implements the same good idea, their collective action can invalidate the assumptions that made the idea good. If everyone assumes that U.S. housing prices cannot decline and makes large bets based on that assumption, their collective action will ultimately bring about a decline in housing prices. This is not a new lesson; it is the lesson of every bubble. A feature of the most recent bubble is that quantitative analysis contributed to a false sense of security that encouraged firms to scale up risks. In some cases senior managers and even quants themselves did not appreciate the limitations in the models on which they based their risk analysis. Our students do not begin their careers at the level where the disastrous decisions were taken, and only a handful of them will ever reach those positions of power. Nonetheless, in the short time they are in our care, we seek to the extent possible to make them competent quants who exercise sound ethical judgment.

About the Author
Steven Shreve's books Stochastic Calculus for Finance I: The Binomial Asset Pricing Model and Stochastic Calculus for Finance II: Continuous-Time Models are the required textbooks for many MFE programs' Stochastic Calculus courses. He is a professor at Carnegie Mellon University and one of the co-founders of the M.S. in Computational Finance at Carnegie Mellon.

Editor's note: Following Prof. Shreve's article, we received a response from Mr. Triana on Jan 10 which we have published in full. It can be seen directly after Prof. Shreve's article.
The following is a response by Mr. Triana sent to Quantnet on Jan 10, 2010.


Let me first say that I deeply admire Professor Shreve. Though my mathematical background does not empower me to fully appreciate his scientific prowess (not that his unparalleled global reputation would ever necessitate my feedback as further support), I am aware that in replying to his analysis of my recent FT article on quant education I am addressing most possibly the world´s leading light when it comes to stochastic calculus and mathematical finance. And far from an aloof researcher, Professor Shreve is also a very successful and ingenius academic entrepreneur, having taken a leading role in the development and management of one of the most exciting and path-breaking university graduate programs ever devised. To top it all, I can personally attest to his human generosity and kindness, getting misty-eyed as I recall the time when Professor Shreve, now about a decade ago, kindly accepted my invitation (as President of NYU Stern´s Financial Engineering Association) to regale us with a wonderful lecture and an even more pleasant follow-up dinner at a fancy Soho restaurant. I vividly recall him being impressed by my thorough knowledge of and interest in his legendary Computational Finance program at Carnegie Mellon, to the point of asking me why I had chosen NYU instead (I didn´t even try to apply to terrifyingly intimidating Carnegie Mellon, acutely aware of my negligible chances at getting in; I ain´t no rocket scientist, folks!).

In sum, it is not only my responsibility but also my pleasure to try to address Professor Shreve´s rebuttal as respectfully as possible, given the caliber of the counterparty. I hope I manage to succeed at this, if not so much at triumphing in the debate.

Some initial clarifications are in order. I don´t really blame quants and quant programs for the crisis. I blame the use of certain models for the crisis. I don´t really care if those using, peddling, and imposing the deleterious models were quants, traders, salesmen, or fast food caterers. My goal is not to target specific groups of people, my goal is to target specific analytical concoctions. Having said that, it is true that a lot of quants vouch for those models both inside and outside the financial industry and, much more critically, vouch fanatically for the quantification of finance in general. As long as such belief is held and enthusiastically pushed, we can get in trouble because the potential for bad models to infiltrate the markets would be made that much larger. We need to create much more restrictive filters when it comes to welcoming mathematical finance wizardry into the realm of practice. Quants and quant programs could and should have been much less permissive and much more critical. Roadblocks to dangerous models should have been forcefully built by those who best understand the mechanics. So, yes, quants and quant programs could in the end be subjected to one type of accusation: neglect.

Everything stated in Professor Shreve´s response makes a ton of sense, and one can´t help but wholeheartedly agree. But, like other famed quants too graced with the ability to muse gracefully and the valour to challenge flawed quanty practices, Professor Shreve does not go far enough. Just like Emanuel Derman, Paul Wilmot, or Ricardo Rebonato, Professor Shreve needs to get closer to Nassim Taleb (and, maybe, my very humble self) and take things a step or two further and engage in a healthy dose of loud name-calling and unabashed denunciation. It is not enough to state that quantitative analysis played a role in the crisis by encouraging misplaced confidence or that many misunderstood the maths. It is imperative to endlessly fingerpoint the main culprits, essentially VaR and Gaussian Copula (to Professor Shreve´s credit, he went after the latter in a recent piece), and to make sure that such utterly failed tools are never again given the keys to the risk kingdom. Demonstrably flawed and lethal models should be banned from the land, and the real reasons for their original embracement intrusively inquired. VaR can no longer be part of banking regulations. These things can´t continue being taught, unless they are presented as the bad that can emerge from the quant lab. More pressing still, those failures must serve as catalyst to force everyone to revisit whether finance can and should indeed by mathematized. Are VaR, Gaussian Copula, Black-Scholes, Portfolio Theory, or Financial Econometrics isolated cases of failure, or rather inescapable proof that financial theory is bound to be at best useless and at worst crisis-igniting? We urgently need a Mathematical Finance Council of Nicaea, so that these pressing questions are answered once and for all. I wrote my Lecturing Birds On Flying in a naively idealistic attempt to help kick-start such process. Will the best that the discipline has to offer, like Professor Shreve, pick up the gauntlet?

This is no time for mincing words, it´s time to act. Back in 1994, Carnegie Mellon showed untold innovativeness and courage by correctly embracing the forcefully emerging field of financial engineering. It became the indisputable world beater. Now, with the discipline in tatters and accused of horrible crimes, the same institution should once more display one-of-a-kindness and lead the second quant finance revolution, the one that ought to make sure that models and financial stability can coexist side by side and the one not afraid to terminally castigate those naughty analytical concoctions that wreak havoc.

About the Author

Pablo Triana is the author of Lecturing Birds on Flying: Can Mathematical Theories Destroy the Financial Markets?
Steve Shreve’s makes two exellent points regarding the difficulties faced by quants.

What's the solution to this? How to get around these issues ? How to ensure safety of quants, especially at the lower levels who would be more keen to voice dissatisfaction on his models being misused ? The junior quants have less to gain and have a more ethical sense as they are new to business.

1.) "It is not easy for a quant to sound the alarm that his models are being stretched beyond their limits, knowing that if he is taken seriously it will result in the loss of business to competing firms and may result in the loss of his job."

2.) Our students do not begin their careers at the level where the disastrous decisions were taken, and only a handful of them will ever reach those positions of power. Nonetheless, in the short time they are in our care, we seek to the extent possible to make them competent quants who exercise sound ethical judgment.
In Triana’s case it is “excitingly obvious” that many “thinkers and doers (most of the time thinker-doers)” have “influenced the ideas and contents of this book”. New to quantitative finance however Triana was forced to identify the “thinker-doers” at break-neck pace and “immerse myself for a few months in equation-laden papers” while also having to “research the activities of theoreticians and quantitative professionals”. On the other hand, the author admits that he “didn’t contact (bother) too many third parties when penning this work” and therefore “It was, in the most explicit sense of the term, a solo effort”. Some urgency is understandable, given the “insultingly unpostponable” relevance of the topic which “seridipitously but sadly, was made exponentially more urgent by the neverending, ever-escalating unfolding of the credit crisis”. It was inevitable that a “book like this would require from the author a larger-than-desirable number of hours in the (intellectual) company of dogmas and dogmatics” but we should not presume inevitability of the author’s findings.

Or perhaps we should. “I do not particularly enjoy theoretical adventures”, writes the brave volunteer, laying it on just a little thick. “I can think of hundreds of better (and more productive, let alone enjoyable) things to do than read or, worse, compose a theoretical treatise. I don’t believe much in the power of theory when it comes to finance, either. And (orthodox, dogmatic) financial economists most likely would not be among my first choices for companionship on a deserted island, or a restaurant table”.

Triana relies on verbal bread crumbs like 'gaussian' to weave his way to lunacy. But by all means take this remotely seriously ...
Of some concern are the opinions expressed by Professor Steven Shreve in responding to Triana. Shreve is one of the great contributors to the field of financial mathematics but risks giving credence to the 'quants blew up the system' meme:

In some cases senior managers and even quants themselves did not appreciate the limitations in the models on which they based their risk analysis

Really? Professor Shreve would know, I am sure, just how silly the industry standard model was (and is) and for anyone with an ounce of mathematical intuition the limitations were more than evident a long, long time ago. I happen to have some insight as to the reasons why the normal copula model was nonetheless popular at one major investment bank however because I was responsible for creating it (the feeble mathematical tricks that made it practical, its physical embodiment in the form of a trading calculator, and the choice of colors for buttons - that is). Yet to suggest the limitations were not apparent to quants is just a little beyond the pale and, after wrestling with management for several years on the topic I became so incensed I wrote up an internal polemic.

To avoid accusations of hindsight I repeat here, verbatim, a small section. This was written in 2004 as best I recall:

The general absence of progress in this field is not likely explained by an absence of interest, experience or financial intuition amongst those who have contributed to a rapidly expanding literature. A more likely explanation is that most reasonable approaches channel into hard problems of mathematical or algorithmic nature for which no solutions are known - or circulated. It is not surprising that avoiding these problems leads to rather silly models, and we predict that firms not directly confronting these issues will rapidly asymptote to a rather poor level of quantitative risk management if they have not already done so.

Hardly a ringing endorsement for the status quo.

Still, well done to Professor Shreve for taking the time to counter Pablo Triana and the results of his "inquiry". Mr Triana has taken offense to my comments above about his research methodology. It is a shame that Mr Triana can't take as well as he gives, but just in case someone who has insulted an entire population of people has had his own feelings hurt, I've written a full apology at www.QuantApology.com