Category Archives: Topical

Includes posts on physics, philosophy, sciences, quantitative finance, economics, environment etc.

Humor, Philosophy

If Time Died Now, I Would Be Happy

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I dream strange dreams. Thankfully, I don’t usually remember them. But at times, I do remember some, and they provide a lot of entertainment. One recent dream was of a TV interview, going on in a mall. The person being interviewed was a stranger, as the protagonists of my dreams tend to be. This guy was middle-eastern, either Iraqi or Iranian, and was talking about a kid who he was about to adopt. The kid turned out to be a child prodigy, and was flying away somewhere for specialized training. The interviewee, though a bit sad, was philosophical about it. At that moment, there was a background song in the mall that went like, “If time died now, I would be happy.” And the man says, “Yes, that is the way I feel!”

I remember feeling, in my dream, “Yeah, right! The right song just happened to be playing!” Way too skeptical even in my dreams. Not to mention that there is not such song (as far as I know). If you think this dream is weird, I once dreamed up an unknown (and non-existent) word while reading a book. I even tried looking up the word when I woke up, but in vain, of course.

One of my top dreams was when I was invited to the White House by President Bush (junior) right after his inauguration. As I stepped into what appeared to be a decent sized living room, the President was walking down a flight of stairs. And he asked me, “So. Do you still think I’m dumb?” Now, how did he know how I felt?

Coming back to my time-dying dream, there is something else that is a bit weird. I mean, one would normally say, “If I died now, I would die a happy man” or something to that effect. Why would “time” die? Is it my secret conviction that when one dies, one’s “time” also dies? That there is no common, universal time, but only our own, individual, personal times? Perhaps. I’m not talking about Newton’s universal times vs. Einstein’s relative time. There is something philosophical here that is just beyond my grasp. Like a name at the tip of your tongue. These are deep waters, and I really need to learn more. Back to school, some day…

The fanciest of my dreams? I was James Bond once. Complete with a bicycle that turned into a wooden canoe when I hit the local beach.

Books, Philosophy, Physics, Science

On Rationality and Delusions

This post started as a reply to M Cuffe’s comment on my post on The God Delusion. M Cuffe suggested that I’m merely asserting an individual’s right to be irrational, or ignorant. Yes, I am indeed saying that one has the right to be irrational. But that statement stems from something that I believe is deeper. It stems from what we mean by rationality, and why we think it is a good thing to be rational. I know it sounds “irrational,” but I’m talking about rationality as Persig talked about it in Zen and the Art of Motorcycle Maintenance.

Stepping back a bit, rationality is quintessentially a worldview. By rational, we mean things that seem normal to our commonsense. So the notion of a nuclear bomb moving or obliterating a mountain is rational, although we have never seen it. You believe it because it is consistent with your worldview. I believe it too, trust me. I was a nuclear physicist not too long ago. đŸ™‚

And a god (or faith) moving mountains is clearly ludicrous to our rationality. I’m not asking people to give equal rational weight to faith and bomb moving mountains. I’m merely encouraging them to examine why they believe in one and not the other. Calling one more rational is just another way of saying that you choose to believe one more than the other. Why?

Thinking along those lines, I come to the conclusion that it is only a question of worldviews or belief systems. I personally subscribe to your worldview based on rationality as well, which is why I consider myself also an atheist (although one of my readers thought I was merely confused :-))

A god as an old man hiding behind the clouds is not consistent with our worldview. But it may have been a metaphor for something else. Let me explain. We have these abstract concepts of happiness, perfection, grief etc. Are these things real? Should we believe they exist? Such questions don’t make too much sense because these concepts are all in our minds. But then, what isn’t?

Let’s take perfection, for instance. Let’s say we assign some human form to it, so that we could explain it to a child or something. We then call it, say, the goddess of perfection or whatever. Over generations, for whatever reason, the notion of perfection disappears from our awareness, but the metaphor of the goddess remains. Now, to somebody who believes in the reality perfection, and therefore the existence of the goddess, it is not a delusion. In that belief system, in that context and worldview, it makes perfect sense. But in the absence of the abstract concept of perfection, the goddess becomes a delusion.

I believe that a large part of our collective wisdom is handed down in the form of such metaphors. Instead of dismissing them as delusions because their context is gone, we should perhaps try harder to rediscover the lost concepts. I also believe such metaphors exist in other fields that seem to work well. Take, for instance, the Qi concept in traditional Chinese medicine, the five elements (or three body types) in Ayurveda and so on. To the extent that traditional Chinese medicine and Ayurveda work, there has to be some knowledge buried in those practices. If we write off their basis merely because their metaphors are not consistent with our rationality, we may be writing off some potential sources of new or forgotten knowledge.

In addition, I believe that some of our smarter geniuses indeed see delusional metaphors in what we take to be supremely real.

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.

Quantitative Finance, Work and Life

How to Make Money

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After my musings on God and atheism, which some may have found useless, let’s look at a supremely practical problem — how to 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 post 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 true. 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 (a) entrepreneurs/industrialists/software moguls — like Bill Gates, Richard Branson etc., (b) celebrities — actors, writers etc., (c) investment professionals — Warren Buffet, for instance, and (d) 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, and 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 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.

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.) 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 angle that we discussed in the Philosophy of Money. They 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.

There is 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 money. You 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.

Books, Philosophy, Physics, Science

Blind-Sight

In my post on A Plausible God, I cited blind-sight as an example of sensing that does not lead to conscious perception. This remarkable neurological syndrome illustrates the tight interconnection between our sense of reality and consciousness. Larry Weiscrantz and Alan Cowey discovered blind-sight at Oxford about 25 years ago.

Blindness can be physiological, when the physical eye is not functioning properly. Or it can be neurological, when the eye is fne but the visual signal processing is impaired. For example, if our right visual cortex is damaged, we are blind on the left side. When examining a patient with such a neurological blindness on one side, Weiscrantz shined a little spot of light on the patient’s blind side. Weiscrantz then asked the patient to point to it. The patient protested that he could not see it and could not possibly point to it. Weiscrantz asked him to try anyway. The patient then proceeded to point accurately to the spot of light that he could not consciously perceive.

After hundreds of trials, it became obvious that the patient could point correctly in ninety-nine percent of trials, even though he claimed on each trial that he was only guessing. How did the patient determine the location of an invisible object and point to it accurately? The neurological reason is that we all have two visual pathways. The new visual pathway goes through the visual cortex. The old, backup pathway runs through our brain stem to the superior colliculus.

The cause of our patient’s blindness was that his visual cortex was damaged, and it did not get the signals from one eye and its optic nerves. But the signals took the parallel route to the superior colliculus, using the old pathway. This rerouting allowed him to locate the object in space and guide his hand accurately to point to the invisible object. What this syndrome of blind-sight shows us is that only the new visual pathway leads to a conscious experience. While the old pathway is perfectly usable (for survival, for instance), it does not lead to a conscious experience of vision.

An interesting neurological condition, no doubt. But blind-sight is more than that. It is a rather confounding philosophical conundrum. The spot of light that the patient could see — was it real? Sure, we know it was real. But what if all of us were blind-sighted? If some of us started developing a semblance of awareness as a result of our blind-sight, would we believe them, or call them delusional? If there are senses that we can be unaware of, how sure can we be of the “sensed”? Or of our “delusions”?

This post is an edited version of section in The Unreal Universe. The information comes from The Emerging Mind: Reith Lectures on Neuroscience (BBC Radio, 2003) given by V. S. Ramachandran, the director of the Center for Brain and Cognition, San Diego, CA, USA. My book refers to several examples of physiological brain anomalies and their perceptual manifestation from this lecture series.

Books, Philosophy, Physics, Science

A Plausible God

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In my review of The God Delusion, I promised to post a plausible concept of God. By “a plausible concept,” I mean a concept that doesn’t violate the known principles of science, and should therefore be consistent with the so-called scientific worldview. Mind you, the plausibility of the concept says nothing about its veracity; but it may say something about it being a delusion.

Of all the sciences, physics seems to be the one most at odds with the God concept. Clearly, evolutionary biology is none too happy with it either, if Dawkins is anything to go by. But that analysis is for another post.

Let’s start by analyzing a physicist’s way of “proving” that there is no God. The argument usually goes something like this:

If there is a God who is capable of affecting me in any way, then there should be some force exerted by that God on me. There should be some interaction. Since the interaction is big enough to affect me, I should be able to use this particular interaction to “measure” the God-intensity. So far, I haven’t been able to measure any such God-related force. So either there is no God that affects me in any way, or there is a God that affects me through deviously disguised interactions so that whenever I try to measure the interaction, I’m always fooled. Now, you tell me what is more likely. By Occam’s Razor, the simplest explanation (that there is no God that can affect me) has the highest chance of being right.

While this is a good argument (and one I used to make), it is built on a couple of implicit assumptions that are rather tricky to spot. The first assumption is that we cannot be affected by an interaction that we cannot sense. This assumption is not necessarily true.

Modern cosmology needs at least one other kind of interaction to account for dark matter and dark energy. Let’s call this unknown interaction the dark interaction. Even though we cannot sense the dark interaction, we are subject to it exactly as all other (known) matter is. The existence of this interaction beyond our senses is sufficient to break the physicist’s proof. A plausible God can affect us, without our being able to sense it, through dark interactions.

But that is not the end of the story. The physicist can still argue, “Fine, if we cannot sense this God, how would we know he exists? And why do so many people claim they can feel him?” This argument is based on the assumptions on conscious experience and sensing. The hidden assumptions in the physicist’s questions (again, not necessarily true) are:

  1. Sensing should lead to a conscious perception.
  2. All humans should have the same sense modality.

An example of sensing that does not lead to conscious perception is the syndrome of blind sight. (I will post more on it later). A patient suffering from blind sight can point to the light spot he cannot consciously see. Thus, sensing without conscious perception is possible. The second assumption that all men are created equal (in terms of sensory modality) does not have any a priori reason to be true. It is possible that some people may be able to sense the dark interaction (or some other kind of interaction that God chooses) without being conscious of it.

So it is possible to argue that there is a God that affects us through a hitherto unknown interaction. And that some 95% of us can sense this interaction, and the others are atheists. What this argument illustrates is the plausibility of God. More precisely, it demonstrates the consistency of a concept of God with physics. It is not meant to be a proof of the existence of God. And that is why, despite the plausibility of God, I am still an atheist.

In retrospect, this argument did not have to be so complicated. It boils down to saying that there are limits on our knowledge, and to what is knowable. There is plenty of room for God outside these limits. It is also a classic argument by those who believe in God — you don’t know everything, so how do you know there isn’t a God?

Books, Creative, Philosophy, Science

The God Delusion

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I am an atheist. So I agree completely with all the arguments of The God Delusion. As a review of the book, that statement should be the end of it. But somehow the book gave me a strange feeling of dissatisfaction. You see, you may believe in God. Or you may not. Or you may actively believe that there is no God. I fall in this the last category. But I still know that it is only my belief, and that thought fills me with a humility that I feel Dawkins lacks.

Now, it is one thing to say that the concept of God is inconsistent with the worldview you have developed, perhaps with the help of science. The concept is indeed very inconsistent with my own personal worldview, which is why I am an atheist. But it is quite a different matter to discount the concept as a delusion. I believe that our knowledge is incomplete. And that there is plenty of room for a possible God to hide beyond the realms of our current knowledge. Does it mean that we should call our ignorance God and kneel before it? I don’t think so, but if somebody does, that is their prerogative.

You see, it is all a question of what your worldview is. And how much rigor and consistency you demand of it. So, what is a worldview? In my opinion, a worldview is the extension of your knowledge. We all have a certain amount of knowledge. We also have a lot of sensory data that comes in every moment that we have to process. We do most of this processing automatically, without conscious effort. But some of the higher level data and information that we encounter merit a closer analysis. How do we do it, given that we may not know much about it? We use our commonsense, our pre-conceived notions, the value systems our parents and teachers left in us and so on. One of these things that we use, or perhaps the totality of these things, is our worldview.

Let’s take an example. Douglas Adams tells us that dolphins are actually smarter than us and have regular inter-galactic communication. Well, we have no way of refuting this claim (which, of course, is only a joke). But our worldview tells us that it is unlikely to be true. And we don’t believe it — as though we know it is not true.

Another example, one that Bertram Russell once cited. Scripture tells us that faith can move mountains. Some people believe it. Science tells us that a nuclear blast can, well, move mountains. Some people believe that too. Note that most people haven’t directly witnessed either. But even for those who believe in the faith-mountain connection, nuclear energy moving mountains is far more plausible a belief. It is just a lot more consistent with our current worldview.

Now, just because God is a delusion according to Dawkins’s worldview (or mine, for that matter), should you buy it? Not unless it is inconsistent with yours as well. Worldviews are hard to change. So are our stances vis-a-vis God and science, when seen as belief-systems — as the movie Contact vividly illustrates. If you missed it, you should watch it. Repeatedly, if needed. It is a good movie anyway.

It is true what they say about a scientific worldview being inconsistent with any sensible notion of a god. But worldviews are a funny thing. Nothing prevents you from tolerating inconsistencies in your worldview. Although Dawkins goes to some length to absolve Einstein of this lack of consistency, the conventional wisdom is that he did believe in God. The truth of the matter is that our collective knowledge (even after adding Einstein’s massive contribution) is limited. There really is plenty of room beyond its limits for God (or eight million gods, if I were to believe my parents), as I will try to show in my next post.

That, however, is only the tip of the iceberg. Once we admit that there are limits to our knowledge, and to what is knowable, we will soon find ourselves staring at other delusions. What is the point it discounting a God delusion, while embracing a space-delusion? In a universe that is unreal, everything is a delusion, not just God. I know, you think it is just my sanity that is unreal, but I may convince you otherwise. In another post.

Books, Philosophy

Helen Keller

The story of Helen Keller is the story of the dark reality that traps you in the absence of your senses. It is also an illustration of the role of language in breaking out of that darkness. Born a healthy child on June 27, 1880 in Alabama, Helen Keller was a perfectly happy baby — until the tender age of 19 months, when she was stricken with a strange illness that “they called acute congestion of the stomach and brain.” The terrible illness left her blind and deaf — “closed my eyes and ears and plunged me into the unconsciousness of a new-born baby,” as she would later write in her autobiography.

Disconnected from the physical world, Helen was trapped in her dark, silent reality (or the lack thereof). She did not even have thoughts or words in her mind, because the tragedy happened before she started talking. She could not learn from her parents like normal children, because she was blind and deaf. There were no special schools at that time for disadvantaged children like her. When she was seven, Helen’s parents contacted Alexander Graham Bell, the inventor of the telephone, who was also an educator of the deaf. Through his help, they found Anne Sullivan to tutor Helen. Anne Sullivan had special methods of making hand signs to spell out objects. Sadly, none of these tricks worked with Helen for a few frustrating months. She could not make the connection between the hand movements and the objects. It looked as though Helen would be doomed to her dark reality for ever. Here is how she made the connection and broke free from darkness. (This block quote is from Helen Keller’s autobiography “The Story of my Life,” which was ffirst published in 1903 and is in the public domain according to the US copyright laws.)

One day, while I was playing with my new doll, Miss Sullivan put my big rag doll into my lap also, spelled “d-o-l-l” and tried to make me understand that “d-o-l-l” applied to both. Earlier in the day we had had a tussle over the words “m-u-g” and “w-a-t-e-r.” Miss Sullivan had tried to impress it upon me that “m-u-g” is mug and that “w-a-t-e-r” is water, but I persisted in confounding the two. In despair she had dropped the subject for the time, only to renew it at the first opportunity. I became impatient at her repeated attempts and, seizing the new doll, I dashed it upon the floor. I was keenly delighted when I felt the fragments of the broken doll at my feet. Neither sorrow nor regret followed my passionate outburst. I had not loved the doll. In the still, dark world in which I lived there was no strong sentiment or tenderness. I felt my teacher sweep the fragments to one side of the hearth, and I had a sense of satisfaction that the cause of my discomfort was removed. She brought me my hat, and I knew I was going out into the warm sunshine. This thought, if a wordless sensation may be called a thought, made me hop and skip with pleasure.

We walked down the path to the well-house, attracted by the fragrance of the honeysuckle with which it was covered. Some one was drawing water and my teacher placed my hand under the spout. As the cool stream gushed over one hand she spelled into the other the word water, first slowly, then rapidly. I stood still, my whole attention fixed upon the motions of her fingers. Suddenly I felt a misty consciousness as of something forgotten — a thrill of returning thought; and somehow the mystery of language was revealed to me. I knew then that “w-a-t-e-r” meant the wonderful cool something that was flowing over my hand. That living word awakened my soul, gave it light, hope, joy, set it free! There were barriers still, it is true, but barriers that could in time be swept away.

The mystery of language is at the genesis of reality; it is what sweeps away the dark barriers standing between us and our conscious awareness of reality. It took Helen Keller out of nothingness into a world of reality, and if it is not the Word in “The Word was God,” I will never know what is.

Photo by The Library of Congress

Philosophy

What is the Word?

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I know very little about religion. Although my smart-ass comments may appear, once in a while, as profound, I’m really ignorant in matters of theology and religion. After all, I have no formal background in these fields that scholars spend their whole life exploring. So, forgive me if this post comes across as pontificating on something I’d better leave to the scholars; but I cannot help wondering what the Word is. I mean, when they say, “In the beginning, there was the Word,” what exactly is the word?

The verse, John 1:1 “In the beginning was the Word, and the Word was with God, and the Word was God”, is again something people have spent much time researching and pondering over. My cursory search unearthed a couple of lines of thought. These lines were mostly concerned with the accuracy of the translation of the verse from Greek, which was complicated by the lack of “the” or “a” articles in the original language. So the verse could be translated as, for instance, “The Word was the God,” consistent with the monotheist notion of Christianity. Or it could be “The Word was a god,” giving quite a different, perhaps pagan, coloration to the issue.

For obvious (atheistic) reasons, I am not interested in this aspect of the verse, nor in these lines of thought. I found another translation, allegedly more literal, that went like, “When the beginning began, the Word was already there.” This suited my purpose better. Still, what exactly was this Word?

My understanding of this statement is as follows. In the philosophy of language, it can be argued that life, universe and everything exists in language, in thoughts, in your brain. The term “language” as defined here doesn’t just mean the communication tool, it also encompasses your thoughts and ideas. It is the vehicle of your thought process. In the absence of language, you have no thoughts, only animal instincts. You have no conscious awareness, only unthinking reactions to your surroundings. You don’t know that you exist, you don’t know that the world exists. The nothingness that engulfs you in the absence of a language is most poignantly depicted in the inspiring story of Helen Keller, coming up in a few days.

In my view, the “Word” that was there in the beginning is language, the ensemble of your thoughts and ideas, and the thought-processing mechanism. It creates our reality. Before we had language, we had no reality; we had nothing. And John 1:1 is a statement of intention to attribute this world of reality, or the opposite of nothingness, created by language to God. And, to me, this statement is the clearest proof that the saint knew how god was born. Obviously, I am rushing in where angels fear to tread. This view of mine will not be embraced (or even tolerated) by anybody who believes in the theological meaning attached to this text of scripture. And to them, I humbly point out that it is just a view, a mere mortal’s view at that! It probably only goes to show that “The devil can cite Scripture for his purpose!”

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.