Tag Archives: quantitative finance

Columns, Quantitative Finance, The Wilmott Magazine, Topical

Math and Patterns

Most kids love patterns. Math is just patterns. So is life. Math, therefore, is merely a formal way of describing life, or at least the patterns we encounter in life. If the connection between life, patterns and math can be maintained, it follows that kids should love math. And love of math should generate an analytic ability (or what I would call a mathematical ability) to understand and do most things well. For instance, I wrote of a connection “between” three things a couple of sentences ago. I know that it has to be bad English because I see three vertices of a triangle and then one connection doesn’t make sense. A good writer would probably put it better instinctively. A mathematical writer like me would realize that the word “between” is good enough in this context — the subliminal jar on your sense of grammar that it creates can be compensated for or ignored in casual writing. I wouldn’t leave it standing in a book or a published column (except this one because I want to highlight it.)

My point is that it is my love for math that lets me do a large number of things fairly well. As a writer, for instance, I have done rather well. But I attribute my success to a certain mathematical ability rather than literary talent.  I would never start a book with something like, “It was the best of times, it was the worst of times.” As an opening sentence, by all the mathematical rules of writing I have formulated for myself, this one just doesn’t measure up. Yet we all know that Dickens’s opening, following no rules of mine, is perhaps the best in English literature. I will probably cook up something similar someday because I see how it summarizes the book, and highlights the disparity between the haves and the have-nots mirrored in the contrasting lead characters and so on. In other words, I see how it works and may assimilate it into my cookbook of rules (if I can ever figure out how), and the process of assimilation is mathematical in nature, especially when it is a conscious effort. Similar fuzzy rule-based approaches can help you be a reasonably clever artist, employee, manager or anything that you set your sights on, which is why I once bragged to my wife that I could learn Indian classical music despite the fact that I am practically tone-deaf.

So loving math is a probably a good thing, in spite of its apparent disadvantage vis-a-vis cheerleaders. But I am yet to address my central theme — how do we actively encourage and develop a love for math among the next generation? I am not talking about making people good at math; I’m not concerned with teaching techniques per se. I think Singapore already does a good job with that. But to get people to like math the same way they like, say, their music or cars or cigarettes or football takes a bit more imagination. I think we can accomplish it by keeping the underlying patterns on the foreground. So instead of telling my children that 1/4 is bigger than 1/6 because 4 is smaller than 6, I say to them, “You order one pizza for some kids. Do you think each will get more if we had four kids or six kids sharing it?”

From my earlier example on geographic distances and degrees, I fancy my daughter will one day figure out that each degree (or about 100km — corrected by 5% and 6%) means four minutes of jet lag. She might even wonder why 60 appears in degrees and minutes and seconds, and learn something about number system basis and so on. Mathematics really does lead to a richer perspective on life. All it takes on our part is perhaps only to share the pleasure of enjoying this richness. At least, that’s my hope.

Columns, Quantitative Finance, The Wilmott Magazine, Topical

Love of Math

If you love math, you are a geek — with stock options in your future, but no cheerleaders. So getting a child to love mathematics is a questionable gift — are we really doing them a favor? Recently, a highly placed friend of mine asked me to look into it — not merely as getting a couple of kids interested in math, but as a general educational effort in the country. Once it becomes a general phenomenon, math whizkids might enjoy the same level of social acceptance and popularity as, say, athletes and rock stars. Wishful thinking? May be…

I was always among people who liked math. I remember my high school days where one of my friends would do the long multiplication and division during physics experiments, while I would team up with another friend to look up logarithms and try to beat the first dude, who almost always won. It didn’t really matter who won; the mere fact that we would device games like that as teenagers perhaps portended a cheerleader-less future. As it turned out, the long-multiplication guy grew up to be a highly placed banker in the Middle East, no doubt thanks to his talents not of the cheerleader-phobic, math-phelic kind.

When I moved to IIT, this mathematical geekiness reached a whole new level. Even among the general geekiness that permeated the IIT air, I remember a couple of guys who stood out. There was “Devious” who also had the dubious honor of introducing me to my virgin Kingfisher, and “Pain” would drawl a very pained “Obviously Yaar!” when we, the lesser geeks, failed to readily follow a his particular line of mathematical acrobatics.

All of us had a love for math. But, where did it come from? And how in the world would I make it a general educational tool? Imparting the love math to one kid is not too difficult; you just make it fun. The other day when I was driving around with my daughter, she described some shape (actually the bump on her grandmother’s forehead) as half-a-ball. I told her that it was actually a hemisphere. Then I highlighted to her that we were going to the southern hemisphere (New Zealand) for our vacation the next day, on the other side of the globe compared to Europe, which was why it was summer there. And finally, I told her Singapore was on the equator. My daughter likes to correct people, so she said, no, it wasn’t. I told her that we were about 0.8 degrees to the north of the equator (I hope I was right), and saw my opening. I asked her what the circumference of a circle was, and told her that the radius of the earth was about 6000km, and worked out that we were about 80km to the north of the equator, which was nothing compared to 36,000km great circle around the earth. Then we worked out that we made a 5% approximation on the value of pi, so the correct number was about 84km. I could have told her we made another 6% approximation on the radius, the number would be more like 90km. It was fun for her to work out these things. I fancy her love for math has been augmented a bit.

Photo by Dylan231

Columns, Corporate Life, Quantitative Finance, The Wilmott Magazine, Topical, Work and Life

In Our Defense

The financial crisis was a veritable gold mine for columnists like me. I, for one, published at least five articles on the subject, including its causes, the lessons learned, and, most self-deprecating of all, our excesses that contributed to it.

Looking back at these writings of mine, I feel as though I may have been a bit unfair on us. I did try to blunt my accusations of avarice (and perhaps decadence) by pointing out that it was the general air of insatiable greed of the era that we live in that spawned the obscenities and the likes of Madoff. But I did concede the existence of a higher level of greed (or, more to the point, a more sated kind of greed) among us bankers and quantitative professionals. I am not recanting my words in this piece now, but I want to point out another aspect, a justification if not an absolution.

Why would I want to defend bonuses and other excesses when another wave of public hatred is washing over the global corporations, thanks to the potentially unstoppable oil spill? Well, I guess I am a sucker for lost causes, much like Rhett Butler, as our quant way of tranquil life with insane bonuses is all but gone with the wind now. Unlike Mr. Butler, however, I have to battle and debunk my own arguments presented here previously.

One of the arguments that I wanted to poke holes in was the fair compensation angle. It was argued in our circles that the fat paycheck was merely an adequate compensation for the long hours of hard work that people in our line of work put in. I quashed it, I think, by pointing out other thankless professions where people work harder and longer with no rewards to write home about. Hard work has no correlation with what one is entitled to. The second argument that I made fun of was the ubiquitous “talent” angle. At the height of the financial crisis, it was easy to laugh off the talent argument. Besides, there was little demand for the talent and a lot of supply, so that the basic principle of economics could apply, as our cover story shows in this issue.

Of all the arguments for large compensation packages, the most convincing one was the profit-sharing one. When the top talents take huge risks and generate profit, they need to be given a fair share of the loot. Otherwise, where is the incentive to generate even more profits? This argument lost a bit of its bite when the negative profits (by which I indeed mean losses) needed to be subsidized. This whole saga reminded me of something that Scott Adams once said of risk takers. He said that risk takers, by definition, often fail. So do morons. In practice, it is hard to tell them apart. Should the morons reap handsome rewards? That is the question.

Having said all this in my previous articles, now it is time to find some arguments in our defense. I left out one important argument in my previous columns because it did not support my general thesis — that the generous bonuses were not all that justifiable. Now that I have switched allegiance to the lost cause, allow me to present it as forcefully as I can. In order to see compensation packages and performance bonuses in a different light, we first look at any traditional brick-and-mortar company. Let’s consider a hardware manufacturer, for instance. Suppose this hardware shop of ours does extremely well one year. What does it do with the profit? Sure, the shareholders take a healthy bite out of it in terms of dividends. The employees get decent bonuses, hopefully. But what do we do to ensure continued profitability?

We could perhaps see employee bonuses as an investment in future profitability. But the real investment in this case is much more physical and tangible than that. We could invest in hardware manufacturing machinery and technology improving the productivity for years to come. We could even invest in research and development, if we subscribe to a longer temporal horizon.

Looking along these lines, we might ask ourselves what the corresponding investment would be for a financial institution. How exactly do we reinvest so that we can reap benefits in the future?

We can think of better buildings, computer and software technologies etc. But given the scale of the profits involved, and the cost and benefit of these incremental improvements, these investments don’t measure up. Somehow, the impact of these tiny investments is not as impressive in the performance of a financial institution compared to a brick-and-mortar company. The reason behind this phenomenon is that the “hardware” we are dealing with (in the case of a financial institution) is really human resources — people — you and me. So the only sensible reinvestment option is in people.

So we come to the next question — how do we invest in people? We could use any number of euphemistic epithets, but at the end of the day, it is the bottom line that counts. We invest in people by rewarding them. Monetarily. Money talks. We can dress it up by saying that we are rewarding performance, sharing profits, retaining talents etc. But ultimately, it all boils down to ensuring future productivity, much like our hardware shop buying a fancy new piece of equipment.

Now the last question has to be asked. Who is doing the investing? Who benefits when the productivity (whether current or future) goes up? The answer may seem too obvious at first glance — it is clearly the shareholders, the owners of the financial institution who will benefit. But nothing is black and white in the murky world of global finance. The shareholders are not merely a bunch of people holding a piece of paper attesting their ownership. There are institutional investors, who mostly work for other financial institutions. They are people who move large pots of money from pension funds and bank deposits and such. In other words, it is the common man’s nest egg, whether or not explicitly linked to equities, that buys and sells the shares of large public companies. And it is the common man who benefits from the productivity improvements brought about by investments such as technology purchases or bonus payouts. At least, that is the theory.

This distributed ownership, the hallmark of capitalism, raises some interesting questions, I think. When a large oil company drills an unstoppable hole in the seabed, we find it easy to direct our ire at its executives, looking at their swanky jets and other unconscionable luxuries they allow themselves. Aren’t we conveniently forgetting the fact that all of us own a piece of the company? When the elected government of a democratic nation declares war on another country and kills a million people (speaking hypothetically, of course), should the culpa be confined to the presidents and generals, or should it percolate down to the masses that directly or indirectly delegated and entrusted their collective power?

More to the point, when a bank doles out huge bonuses, isn’t it a reflection of what all of us demand in return for our little investments? Viewed in this light, is it wrong that the taxpayers ultimately had to pick up the tab when everything went south? I rest my case.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

Money — Love it or Hate it

Whatever its raison-d’etre may be, there is a need for more, and an unquenchable greed. And paradoxically, if you want to try to quench a bit of your greed, the best way to do it is to fan the greed in others. This is why the email scams (you know, the Nigerian banker requesting your help in moving $25 million of unclaimed inheritance, or the Spanish lottery eager to give you 67 million Euros) still hold a fascination for us, even when we know that we will never fall for it.

There is only a thin blurry line between the schemes that thrive on other people’s greed and confidence jobs. If you can come up with a scheme that makes money for others, and stay legal (if not moral), then you will make yourself very rich. We see it most directly in the finance and investment industry, but it is much more widespread than that. We can see that even education, traditionally considered a higher pursuit, is indeed an investment against future earnings. Viewed in that light, you will understand the correlation between the tuition fees at various schools and the salaries their graduates command.

When I started writing this column, I thought I was making up this new field called the Philosophy of Money (which, hopefully, somebody would name after me), but then I read up something on the philosophy of mind by John Searle. It turned out that there was nothing patentable in this idea, nor any cash to be made, sadly. Money comes under the umbrella of objective social realities that are quite unreal. In his exposition of the construction of social reality, Searle points out that when they give us a piece of paper and say that it is legal tender, they are actually constructing money by that statement. It is not a statement about its attribute or characteristics (like “This is a glass of water”) so much as a statement of intentionality that makes something what it is (like “You are my hero”). The difference between my being a hero (perhaps only to my six-year-old) and money being money is that the latter is socially accepted, and it is as objective a reality as any.

I conclude this article with the nagging suspicion that I may not have argued my point well enough. I started it with the premise that money is an unreal meta-thing, and wound up asserting its objective reality. This ambivalence of mine may be a reflection of our collective love-hate relationship with money – perhaps not such a bad way to end this column after all.

Photo by 401(K) 2013

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

Money — Why do We Crave it?

Given that the investment value is also measured and returned in terms of money, we get the notion of compound interest and “putting money to work.” Those who have money demand returns based on the investment risk they are willing to assume. And the role of modern financial system becomes one of balancing this risk-reward equation. Finance professionals focus on the investment value of money to make oodles of it. It not so much that they take your money as deposits, lend it out as loans, and earn the spread. Those simple times are gone for good. The banks make use of the fact that investors demand the highest possible return for the lowest possible risk. Any opportunity to push this risk-reward envelope is a profit potential. When they make money for you, they demand their compensation and you are happy to pay it.

Put it that way, investment sounds like a positive concept, which it is, in our current mode of thinking. We can easily make it a negative thing by portraying the demand for the investment value of money as greed. It then follows that all of us are greedy, and that it is our greed that fuels the insane compensation packages of top-level executives. Greed also fuels fraud – ponzi and pyramid schemes.

Indeed, any kind of strong feeling that you have can be bought and sold for personal gain of others. It may be your genuine sympathy for the Tsunami or earthquake victims, your voyeuristic disgust at the peccadilloes of golf icons or presidents, charitable feeling toward kidney patients of whatever. And the way money is made out of your feelings may not be obvious at all. Watching the news five minutes longer than usual because of a natural disaster may bring extra fortune to the network’s coffers. But of all the human frailties one can make money out of, the easiest is greed, I think. Well, I may be wrong; it may actually be that frailty that engendered the oldest profession. But I would think that the profession based on the lucrative frailty of greed wasn’t all that far behind.

If we want to exploit other people’s greed, the first thing to ask ourselves is this: why do we want money, given that it is a meta-entity? I know, we all need money to live. But I am not talking about the need part. Assuming the need part is taken care of, we still want more of it. Why? Say you are a billionaire. Why would you want another billion? I think the answer lies in something philosophical, something of an existential angst, although those with their billions would the last ones to admit it. The reason behind this deep-rooted need for more is a quest for a validation, or a justification for our existence, and a meaning and purpose for our life. It is all part of that metaphorical holy grail. I know, it sounds a bit nutty, but what else could it be? The Des Cartes of our time would say, “I have loads of money, therefore I am!”

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

The Ultra Rich

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Let’s first take a look at how people make money. Loads of it. Apparently, it is one of the most frequently searched phrases in Google, and the results usually attempt to separate you from your cash rather than help you make more of it.

To be fair, this column won’t give you any get-rich-quick, sure-fire schemes or strategies. What it will tell you is why and how some people make money, and hopefully uncover some new insights. You may be able to put some of these insights to work and make yourself rich – if that’s where you think your happiness lies.

By now, it is clear to most people that they cannot become filthy rich by working for somebody else. In fact, that statement is not quite accurate. CEOs and top executives all work for the shareholders of the companies that employ them, but are filthy rich. At least, some of them are. But, in general, it is true that you cannot make serious money working in a company, statistically speaking.

Working for yourself – if you are very lucky and extremely talented – you may make a bundle. When we hear the word “rich,” the people that come to mind tend to be

  1. entrepreneurs/industrialists/software moguls – like Bill Gates, Richard Branson etc.,
  2. celebrities – actors, writers etc.,
  3. investment professionals – Warren Buffet, for instance, and
  4. fraudsters of the Madoff school.

There is a common thread that runs across all these categories of rich people, and the endeavors that make them their money. It is the notion of scalability. To understand it well, let’s look at why there is a limit to how much money you can make as a professional. Let’s say you are a very successful, highly-skilled professional – say a brain surgeon. You charge $10k a surgery, of which you perform one a day. So you make about $2.5 million a year. Serious money, no doubt. How do you scale it up though? By working twice as long and charging more, may be you can make $5 million or $10 million. But there is a limit you won’t be able to go beyond.

The limit comes about because the fundamental economic transaction involves selling your time. Although your time may be highly-skilled and expensive, you have only 24 hours of it in a day to sell. That is your limit.

Now take the example of, say, John Grisham. He spends his time researching and writing his best-selling books. In that sense, he sells his time as well. But the big difference is that he sells it to many people. And the number of people he sells his product to may have an exponential dependence on its quality and, therefore, the time he spends on it.

We can see a similar pattern in software products like Windows XP, performances by artists, sports events, movies and so on. One performance or accomplishment is sold countless times. With a slight stretch of imagination, we can say that entrepreneurs are also selling their time (that they spend setting up their businesses) multiple times (to customers, clients, passengers etc.) All these money-spinners work hard to develop some kind of exponential volume-dependence on the quality of their products or the time they spend on them. This is the only way to address the scalability issue that comes about due to the paucity of time.

Investment professionals (bankers) do it too. They develop new products and ideas that they can sell to the masses. In addition, they make use of a different aspect of money that we touched upon in an earlier column. You see, money has a transactional value. It plays the role of a medium facilitating economic exchanges. In financial transactions, however, money becomes the entity that is being transacted. Financial systems essentially move money from savings and transforms it into capital. Thus money takes on an investment value, in addition to its intrinsic transactional value. This investment value is the basis of interest.

Columns, Corporate Life, Humor, Philosophy, Quantitative Finance, The Wilmott Magazine

Philosophy of Money

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Money is a strange thing. It is quite unlike any other “thing” that we know. Its value manifests itself only in a social context where we have pre-agreed conventions as to what it should be. In this sense, money is not a thing at all, but a meta-thing, which is why you are happy when your boss gives you a letter stating that you got a fat bonus even though you never actually see the physical thing. Well, if it is not physical, it is metaphysical, and we can certainly talk about the philosophy of money.

The first indication of the meta-ness of money comes from the fact that it has a value only when we assign it a value. It doesn’t possess an intrinsic value that, for instance, water does. If you are thirsty, you find that water has enormous intrinsic value. Of course, if you have money, you can buy water (or Perrier, if you want to be sophisticated), and quench your thirst.

But we may find ourselves in situations where we may not be able to buy things with money. Stranded in a desert, for instance, dying of thirst, we may not be able to buy water despite our sky-high credit limits or the hundreds of dollars we may have in our wallet. One reason for this inability of ours is obvious – we may be alone. The basic transactional value of money evaporates when we have nobody to transact with.

The second dimension of the meta-ness of money is economical. It is illustrated in the well-worn supply-and-demand principle, assuming transactional liquidity (which is a term I just cooked up to sound erudite, I confess). I mean to say, even if we have willing sellers of water in the desert, they may see that we are dying for it and jack up the price – just because we are willing and able to pay. This apparent ripping off on the part of the devious vendors of water (perfectly legal, by the way) is possible only if the commodity in question is in plentiful supply. We need commodity liquidity, as it were.

It is when the liquidity dries up that the fun begins. The last drop of water in a desert has infinite intrinsic value. This effect may look similar to the afore-mentioned supply-and-demand phenomenon, but it really is different. The intrinsic value dominates everything else, much like the strong force over short distances in particle physics. And this domination is the flipside of the law of diminishing marginal utility in economics.

The thing that looks a bit bizarre about money is that it seems to run counter to the law of diminishing marginal utility. The more money you have, the more you want it. Now, why is that? It is especially strange given its lack of intrinsic value. Great financial minds could not figure it out, but came up with pithy and memorable statements like, “Greed, for lack of a better word, is good.” Although that particular genius was only fictional, he does epitomize much of the thinking in the modern corporate and financial world. Good or bad, let’s assume that greed is an essential part of human nature and look at what we can do with it. Note that I want to do something “with” it, not “about” it – an important distinction. I, intrepid columnist that I am, want to show you how to use other people’s greed to make more money.

Photo by 401(K) 2013

Philosophy, Physics, Science

Half a Bucket of Water

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We all see and feel space, but what is it really? Space is one of those fundamental things that a philosopher may consider an “intuition.” When philosophers look at anything, they get a bit technical. Is space relational, as in, defined in terms of relations between objects? A relational entity is like your family — you have your parents, siblings, spouse, kids etc. forming what you consider your family. But your family itself is not a physical entity, but only a collection of relationships. Is space also something like that? Or is it more like a physical container where objects reside and do their thing?

You may consider the distinction between the two just another one of those philosophical hairsplittings, but it really is not. What space is, and even what kind of entity space is, has enormous implications in physics. For instance, if it is relational in nature, then in the absence of matter, there is no space. Much like in the absence of any family members, you have no family. On the other hand, if it is a container-like entity, the space exists even if you take away all matter, waiting for some matter to appear.

So what, you ask? Well, let’s take half a bucket of water and spin it around. Once the water within catches on, its surface will form a parabolic shape — you know, centrifugal force, gravity, surface tension and all that. Now, stop the bucket, and spin the whole universe around it instead. I know, it is more difficult. But imagine you are doing it. Will the water surface be parabolic? I think it will be, because there is not much difference between the bucket turning or the whole universe spinning around it.

Now, let’s imagine that we empty the universe. There is nothing but this half-full bucket. Now it spins around. What happens to the water surface? If space is relational, in the absence of the universe, there is no space outside the bucket and there is no way to know that it is spinning. Water surface should be flat. (In fact, it should be spherical, but ignore that for a second.) And if space is container-like, the spinning bucket should result in a parabolic surface.

Of course, we have no way of knowing which way it is going to be because we have no way of emptying the universe and spinning a bucket. But that doesn’t prevent us from guessing the nature of space and building theories based on it. Newton’s space is container-like, while at their heart, Einstein’s theories have a relational notion of space.

So, you see, philosophy does matter.

Books, Quantitative Finance

Principles of Quantitative Development

[This post is a review of my forthcoming book, “Principles of Quantitative Development,” to be published by John Wiley & Sons in Feb 2010. This review is written by Shayne Fletcher, Executive Director, Nomura, and author of “Financial Modelling in Python,” and is posted here with the reviewer’s permission.]

In “Principles of Quantitative Development”, Thulasidas has offered a contribution that is somewhat unique in the literature associated with the field of Quantitative Development. In that specialised, narrow domain, technical books abound. Most such titles are concerned with the intricacies of the application of specific programming language to the problems of financial engineering or, expositions of advanced mathematics as used in the pricing models of exotic financial derivative products. Thulasidas however has taken a very different tact. Focusing instead on what he terms “the big picture”, Thulasidas offers us his insights into the role of Quantitative Development in the broader context of a bank’s “trading platform”. Armed with such insights, he shows us how an understanding of the varied usages of the trading platform can and should be used to influence and shape its design.

In the opening chapters, the book is concerned with defining what is meant by the term “trading platform”. In doing so, Thulasidas necessarily reviews the “architecture” of a bank from the point of view of a Quantitative Developer. That is, he discusses the nature and interactions of the front, middle and back offices of a bank, the different roles that professionals in each of those areas satisfy and how each of their respective needs induce a different set of requirements on the trading platform. Moving on, he reviews the nature of trades, the so-called trade “life cycle” and how different views of a trade are required as a function of the life cycle and the business role of the user.

Having established a broad understanding of the requirements for a trading platform, Thulasidas turns his attention to translating those requirements into design decisions for trading platforms. Along the way he considers such aspects of design as choice of programming languages, issues relating to scalability and extensibility, security and auditing, representations for market and trade data and a trading platform’s macro architecture whilst all the way remaining focussed on ensuring that all business needs identified in the earlier chapters are given consideration and catered for.

Going from the general to the specific, Thulasidas in later chapters introduces a flexible derivatives pricing tool (the source code for which accompanies the book). This program in itself will no doubt serve as an excellent starting point for Quantitative Development teams charged with the production of an in-house trading platform. Perhaps of even greater benefit though is Thulasidas’s critique of the pricing tool, that is, in his explanation of how the supplied program fails to meet the requirements of a complete trading platform and how the program needs to be extended in order to be considered one. In this way, the line of thought of earlier chapters is reinforced and brought sharply into focus.

Throughout the book, Thulasidas manages to convey his ideas with remarkable eloquence and lucidity. Understanding is enhanced by numerous rich graphics outlining processes and their design (both in the software and work-flow sense). The reader’s attention and interest is never lost and a great deal of entertainment is to be found in the numerous side-bars, the “Big Pictures” (in effect an enjoyable mini-series of magazine style articles in their own right).

As Thulasidas himself notes, the subject matter of his book is broad. Accordingly, the potential readership of this title is equally broad. Notably, Quantitative Developers at the beginning of their careers stand most to gain from this book. The fact is though that even the most seasoned of banking professionals would profit from its reading. Quantitative Developers, Quantitative Analysts, Traders, Risk Managers, IT professionals and their Project Managers, individuals considering switching from academia or other industries to a career in banking… Readers from each and all of these groups will find Thulasidas’s work informative and thought provoking.

Columns, Corporate Life, Physics, Quantitative Finance, The Wilmott Magazine

Modeling the Models

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Mathematical finance is built on a couple of assumptions. The most fundamental of them is the one on market efficiency. It states that the market prices every asset fairly, and the prices contain all the information available in the market. In other words, you cannot glean any more information by doing any research or technical analysis, or indeed any modeling. If this assumption doesn’t pan out, then the quant edifice we build on top of it will crumble. Some may even say that it did crumble in 2008.

We know that this assumption is not quite right. If it was, there wouldn’t be any transient arbitrage opportunities. But even at a more fundamental level, the assumption has shaky justification. The reason that the market is efficient is that the practitioners take advantage of every little arbitrage opportunity. In other words, the markets are efficient because they are not so efficient at some transient level.

Mark Joshi, in his well-respected book, “The Concepts and Practice of Mathematical Finance,” points out that Warren Buffet made a bundle of money by refusing to accept the assumption of market efficiency. In fact, the weak form of market efficiency comes about because there are thousands of Buffet wannabes who keep their eyes glued to the ticker tapes, waiting for that elusive mispricing to show up.

Given that the quant careers, and literally trillions of dollars, are built on the strength of this assumption, we have to ask this fundamental question. Is it wise to trust this assumption? Are there limits to it?

Let’s take an analogy from physics. I have this glass of water on my desk now. Still water, in the absence of any turbulence, has a flat surface. We all know why – gravity and surface tension and all that. But we also know that the molecules in water are in random motion, in accordance with the same Brownian process that we readily adopted in our quant world. One possible random configuration is that half the molecules move, say, to the left, and the other half to the right (so that the net momentum is zero).

If that happens, the glass on my desk will break and it will make a terrible mess. But we haven’t heard of such spontaneous messes (from someone other than our kids, that is.)

The question then is, can we accept the assumption on the predictability of the surface of water although we know that the underlying motion is irregular and random? (I am trying to make a rather contrived analogy to the assumption on market efficiency despite the transient irregularities.) The answer is a definite yes. Of course, we take the flatness of liquid surfaces for granted in everything from the useless lift-pumps and siphons of our grade school physics books all the way to dams and hydro-electric projects.

So what am I quibbling about? Why do I harp on the possibility of uncertain foundations? I have two reasons. One is the question of scale. In our example of surface flatness vs. random motion, we looked at a very large collection, where, through the central limit theorem and statistical mechanics, we expect nothing but regular behavior. If I was studying, for instance, how an individual virus propagates through the blood stream, I shouldn’t make any assumptions on the regularity in the behavior of water molecules. This matter of scale applies to quantitative finance as well. Are we operating at the right scale to ignore the shakiness of the market efficiency assumption?

The second reason for mistrusting the pricing models is a far more insidious one. Let me see if I can present it rather dramatically using my example of the tumbler of water. Suppose we make a model for the flatness of the water surface, and the tiny ripples on it as perturbations or something. Then we proceed to use this model to extract tiny amounts of energy from the ripples.

The fact that we are using the model impacts the flatness or the nature of the ripples, affecting the underlying assumptions of the model. Now, imagine that a large number of people are using the same model to extract as much energy as they can from this glass of water. My hunch is that it will create large scale oscillations, perhaps generating configurations that do indeed break the glass and make a mess. Discounting the fact that this hunch has its root more in the financial mess that spontaneously materialized rather than any solid physics argument, we can still see that large fluctuations do indeed seem to increase the energy that can be extracted. Similarly, large fluctuations (and the black swans) may indeed be a side effect of modeling.