Some Weird Math and the Most Interesting Guy of All Time

In this post, we will not only learn about one of the most interesting people to ever have walked the earth -- a person whose life story is full of so much comedy and irony that it sounds made up -- but also explore the history (and present) of highly abstract mathematics. This is a non-technical piece, so the non-technically inclined will enjoy as well.

In order to explain what abstract algebra is, we have to go backwards in time a little. For most of human history, mathematics was viewed mainly as a tool to study science, and although some people may have focused more on the math side of things, the two ideas were inextricably joined: math was a tool used to explore science. The better they developed the tools, the better they could solve scientific problems. This was, for example, how calculus came to be; it was invented on a whim by Newton in order to solve physics problems, which were his prime area of concern. And it was this way across the disciplines, from geometry to analysis -- math was primarily done with the idea of accomplishing something tangible in mind.

But that all began to change in the mid-19th century, with the birth of an absolutely fascinating individual by the name of Evariste Galois. While in his teens, Galois became interested in math. He applied to Ecole Polytechnique, which was then and still is the MIT of France, and was rejected. He went to another French university, Ecole Normale. This is where Galois started to rock the house. When he first began the work that would soon make him famous, he attempted to get some papers published. Both were judged by Cauchy, another all-time famous French mathematician, and he turned them down. The story goes that Cauchy's issue was clerical, and truly believed in Galois' work; nonetheless, it was another kick in the groin for a young Evariste.

At this point, Galois' father commits suicide, shortly before young Evariste reapplies to Polytechnique. Naturally, he gets rejected. Keep in mind, at this point Galois is a genuine prodigy. Most attribute this to a personal offense made by Galois to the examiner; some blame it on the examiner, others on Galois. Either way, Galois returns to Ecole Normale, defeated, to continue his studies. But don't worry, much more bad luck lay in store for him there.

Galois essentially invented the field of abstract algebra, coined the mathematical term "group" (as in group theory) and solved the extremely long-standing problem of determining the necessary and sufficient conditions for a polynomial to be solvable by radicals. Basically, this means that (among other things) he figured out how to tell whether we could solve a particular polynomial equation with an elegant little formula like the "quadratic formula" from elementary school.

A bit more confident, he resubmit his work to the Academy, which Cauchy had rejected some years before. In fact, he submitted it directly to Fourier (of "Fourier transform" fame) but in line with Galois' previous luck, Fourier died soon thereafter and never reviewed it. That year, the prize was given to Jacobi and Abel, two highly deserving mathematicians. Nevertheless, Galois did succeed in getting two important papers published that gave birth to Galois theory. Another French mathematical all-star, Poisson, soon asked him to submit his work on Galois theory.

Now that something good had happened, Galois was apparently anxious to have more problems. So when the Trois Glorieuses came about, he became enthralled with the tumult of contemporary French politics, quit mathematics and joined a batallion of the National Guard. At a banquet, he gave a toast to the king that was perceived as a threat on his life and he was jailed the next day. By Bastille Day, he was released, but then promptly rearrested when he showed up to a protest covered in firearms. He was imprisoned, and shortly after arriving he received word from Poisson. Poisson derided his work as "incomprehensible" and said that his "argument is neither sufficiently clear nor sufficiently developed to allow us to judge its rigor," which is about as a tough a statement as a mathematician could make. Galois, naturally, was of poor humor during his initial days of incarceration.

After getting out of prison, young Evariste finally could return to his research. Unfortunately, true to his luck, he found himself embroiled in a torid love affair with one Mlle du Motel, whose fiance challenged him to a duel and killed him. The twist? The previous night Galois knew he was a goner, and stayed up composing his last mathematical work, which he sent to friend and mathematician Auguste Chevalier. These documents contain ideas that have enormous consequences for diverse areas of mathematics, and in fact may have influenced the future trend towards abstraction and generalization in math and science more than any other. Says Hermann Weyl, "This letter, if judged by the novelty and profundity of ideas it contains, is perhaps the most substantial piece of writing in the whole literature of mankind."

Tragically, his last words made a bleak reference to dying at the age of twenty. An obvious end to a man whose life was fraught with constant neverending disaster, which makes it all the more shocking how influential his work has become. And Galois' last word on his work? Bitterly, he says, "ask Jacobi or Gauss publicly to give their opinion, not as to the truth, but as to the importance of these theorems. Later there will be, I hope, some people who will find it to their advantage to decipher all this mess."

What was in this work, and why was it so vastly important? Galois was trying to study a problem, which basically amounts to determining whether a polynomial equation (like 4x^2=0 or 5x-1=0 or x^10-x+1=0) admits a solution. It turns out the answer can be yes or sometimes. They can always be solved for degree less than five. But higher than four (for a polynomial like x^5+x-1=0)  how can we tell, for one particular such equation, in some kind of mathematically sound way, whether it's solvable -- and how? The theory for this was laid by Galois in his short life's work. He did a few amazing things. Like Lagrange before him, he connected permutations and the roots of the polynomials (roots meaning "solutions"). What he realized was that he had to look at those permutations of the roots  that had a remarkable property: any algebraic equation of the roots (with rational coefficients) satisfied before the permutation is also satisfied after. He then makes another incredible step, formalizing the notion of a "group" as we know it.

I've put off telling you what a group is but it's the first thing in abstract algebra. A group is a set (like {1,2,3} or {a,b,c} or "all the colors in the world") together with an "operation" such that taking any two elements, and doing the "operation" on them, gives you another element in the group. Pretty simple, but pretty powerful. Rich structure can be induced from these simple criteria, based on the rules of the operation and the elements you choose. The shocking part of abstract algebra is that given two completely unrelated groups, one can define homomorphisms (which you can think of as teleports between two different mathematical objects) to go between them. That means one can apply thinking and reasoning about one space to another.

Galois noticed that permutations formed such a group. And in fact, each polynomial has something called a "Galois group". The structure of the group corresponding to a polynomial (called that polynomial's Galois group) tells you whether or not a solution exists.

What does structure mean?


This is an idea that must resonate. It is so crucial, and such a powerful concept that is, I believe, a large organizing theme in the search for human knowledge. In this sense, structure simply means that a group has particular "subgroups" -- that is, groups within the group that are themselves also a group. So for example the even integers (under addition) make a subgroup of the integers (under addition). There are many interesting things that follow from this, and basically the subgroups are what define the structure of the group. And this is the case in Galois' solution, as well.

By beginning the trend towards abstraction and generalization, Evariste Galois set mathematics on a course to decouple from the physical sciences and become a science in its own right. This begs the question -- exactly what "science" do mathematicians study? I believe they study reality. They study some kind of general fabric of our universe so fundamental to existence that it perhaps goes unnoticed -- it is a concept too vague to give a simple label, like "chemistry" or "physics." I suppose that's why we call it mathematics.

Kicking Off the Free Finance Project: Free Pairs Trading Software!

In order to kick off the Free Finance project, I've released a tutorial to guide interested parties through the creation of a statistical arbitrage screener. You can use it to analyze stocks and determine pairs that could be viable candidates for statistical arbitrage. The script works by running an Augemented Dickey-Fuller test, one of the tests for cointegration, the measure primarily used to determine whether two stocks tend to move together in time.

In order to run the script, you will need Finatica, which can be downloaded for free. The code for the screener is available at Free Finance.

Ernie Chan, Quant Trading Wizard, Backing Up SVMs?

Today Ernie Chan, who has previously been unenthused by using machine learning algorithms in trading strategies, reports on a new study by UC Berkeley that affirms the ability of support vector machines to predict markets in a statistically significant fashion using technical indicators.

http://epchan.blogspot.com/2010/10/data-mining-and-artificial-intelligence.html

As it happens, I have long been a huge SVM advocate, and believe that due to the intuitions underlying their design they are clearly the superior nonlinear regression tool, and should find a wide variety of commercial usages. Finatica provides an environment in which you can use SVMs, among a wide variety of other tools, to develop, backtest and deploy trading strategies. If you want to harness the power of SVMs quickly without a whole bunch of hassle, Finatica is the perfect choice for you. And, a free version is available!

Make sure to enter the code "JVDBLOG" for 50% off the registered version of Finatica.

GS and JNJ Earnings Are In

In my last post, I mentioned two forecasts from my model on stocks going into earnings, and discussed the implications of a model's performance during this critical time period.

GS and JNJ earnings have been reported, and our model's insight was correct in both cases. In the case of JNJ, analysts' predictions gave an average of $1.15 per share, with a low of $1.10 and a high of $1.17. In reality, JNJ reported $1.23 per share, despite a minor slip in revenue, and raised their EPS forecasts for year-end. As for GS, America's perennial investment bank, analysts averaged a forecast of $2.29, with a low of $1.81 and a high of $3.00. They came in at $2.98, just shy of the maximum forecast.

It is 9:15 right now and both stocks are down in pre-market trading, so only time will tell how the market will react. What is interesting, though, is the fact that our model's predictions were in line with true changes in the company's fair value. Whether the perceived value will change with it, of course, remains to be seen.

GS and JNJ Earnings Tomorrow

I've been working on an options trading strategy recently, which would loosely be classified as "volatility arbitrage." As an experiment, I took some of the trades it implied on two stocks entering earnings announcements: GS and JNJ. Both were long, coupled with a short position in PG. The short position is less important to the experiment, but is necessary for reasons unimportant.

The reason I find this particular moment so fascinating is because, in my opinion, it is the truest test of a strategy. When earnings are reported, equities experience a rare moment in which the full information set that determines their value is available. There is something of a "reset" to the perceived fair value, in which all market participants have the same information.

The question is, will the earnings announcement disrupt my strategy, or actually bolster it? If a model works by correctly identifying the genuine value of a security, the earnings announcement should force a convergence to fair value, which would be beneficial to the strategy. If, on the other hand, it works by predicting the changes in investors' whims, and in fact does little to determine true value, the earnings announcement should disrupt the strategy.

Naturally, the optimal strategy would fare well in both scenarios. But how could that be? We must construct portfolios that are sensitive to a likely outcome (such as convergence to fair value) but still robust and immune to other possible scenarios in which investors misread the evidence.

The St. Petersburg Paradox and the Low Hanging Fruit

The most recent trading strategy I've been researching has been based on so-called volatility arbitrage, a horrible misnomer for the strategy of trading volatility like an asset by taking a view and getting exposure (generally) through options. But since the modern options market has all but adopted a notion of equivalence between volatility and price, trading volatility really amounts to determining the true fair value of options written on a particular underlying. It's not really a forecasting problem so much as a modeling problem, although elementary forecasting does play a role in a good model.

I shared a bit of this information with a reader of this blog last night, and to my surprise, he commented that vol arb had been "picked clean" -- a term applied to strategies whose popularity has eclipsed their profitability. This term gets thrown around a lot with reference to "statistical arbitrage," a similarly misnamed strategy by which traders exploit gaps between correlated securities and bet that the gap will disappear over time.

The reason statistical arbitrage (as it is now known) is possible is because of two Nobel Prize winners named Robert Engle and Clive Granger. They won the prize for the development of a number of related time-series analysis techniques, one of which was the measure of "cointegration," which aptly embodies the "gap-ungap" property of a good stat arb pair.

The study of cointegration was borne of Engle and Granger's realization that correlation was really a terrible metric in most cases of statistical analysis. Thus, the statistical arbitrage opportunity was borne of a simple realization that one of the core beliefs of the markets -- that correlation is the correct measure of similarity -- was wrong. A paradigm shift takes place, and an opportunity arises until information diffusion has the opportunity to destroy it.

Once enough people knew how to implement a cointegration test, they could implement stat arb. And stat arb got picked flat. And it will remain flat until another paradigm shift comes along, and we are able to discover similar time series with great precision or quality, and then stat arb is back in full force.

The point is: opportunity is created by widespread misunderstanding. And to demonstrate just how much work there is left to do in quantitative finance, and how many opportunities still exist to exploit widespread ignorance, let me guide you through some of the theory of options valuation, and present some startling contradictions that you may find quite shocking.

But first, let me bore you with some mathematical history. The St. Petersburg Paradox is a problem worked on jointly by the Bernoulli brothers. It describes a lottery in which one buys a ticket, and the "dealer" of sorts flips a coin in succession until a tails comes up. If a tails comes up on the first flip, the gambler gets $1. If it comes up on the second, he gets $2, and the third, $4, and so on ad infinitum.

The problem: determine the fair price of a ticket. Most people would do this by taking expectations over the probability distribution defined by the payoffs, but get this -- the expectation is infinite! That implies that a human being would pay any price for a ticket!

Clearly, a human being wouldn't pay any price for a ticket. The Bernoulli brothers solve the problem by expressing the payoffs in terms of a diminishing marginal utility function (logarithmic) and show the fair value to be $2, which is a lot more sensible. The point of the paradox is how nonsensical an answer you can get by naively taking expectations.

Now let's turn our attention to the original work of Black and Scholes, something I intend to discuss plenty on this blog. Black and Scholes begin by dreaming up a portfolio containing a delta-hedged option position, and by no-arbitrage arguments reason that the portfolio must yield the risk-free rate, since it is itself risk-free.

This is the celebrated Black-Scholes differential equation, the form of which is the basis for the great majority of all derivative pricing methods. Since the equation has no risk-dependent parameters in it, like the stock's drift rate, they reason that the derivative's value is not dependent on the level of risk, or even the expected return, on a stock.

This is where it starts to get weird. They reason that since the derivative's value is independent of risk, that the value of an option in our world is the same as that of a derivative in a hypothetical universe called the "risk neutral world."

The risk-neutral world is a bit like Eden. All investors are 100% tolerant of risk. All securities earn the risk-free rate. Securities are all equal to their discounted expected value under the correct probability measure.

They reason that since the value of the derivative in our world is the same as in theirs, we may as well make life simple and value the derivative in their world. So they do -- they combine the differential equation obtained above with the solution to an Ito integral representing the stock price's lognormal diffusion (with drift equal to the risk free rate). That yields the Black-Scholes solution.

I hope the St. Petersburg paradox is contrasting nicely with this Nobel Prize-winning reasoning of Black and Scholes. We're going to make the comparison even more explicit by extending the discussion to the pricing of American options, which have the capability to be exercised at any point during their lifetime, not just at expiry.

The Black Scholes-style way to value an American option is using a binomial tree representation, popularized initially by Cox, Rubinstein and Ross. A tree is constructed in order to represent the lognormal process described above; each leaf node is annotated with its value; the other nodes are annotated with the discounted expected value of their children under the tree's induced probability measure.

Now, if the stock doesn't pay a dividend, we have a bizarre situation. Under the induced probability measure of the binomial tree, the discounted price process (by the Black-Scholes theory) is a martingale. Thus, we know there is no optimal stopping time. So, the value of the early exercise never exceeds the discounted expected value, and therefore is never taken. Therefore, the value of an American option on a non-dividend paying stock is equal to the value of the same European option on that stock.

You might need a minute to digest that. Yes, it's true. Under the Black-Scholes assumptions, an American option has the same value as a European one so long as there is no dividend. And these same assumptions that yield such a terrifying paradox also underlie the rest of the models used for pricing and risk management of derivative contracts.

The source of the contradiction is similar to the case of the St. Petersburg Paradox; the reckless taking of expectations, that reduction of a probability distribution to a scalar, is such a dangerous approach. And much more importantly, the idealistic assumptions of Black-Scholes don't just manifest themselves in an unrealistic price process with skinny tails, as people frequently point out, but in the very modeling of human behavior that underlies the model.

See, with European options, there's no behavior to model, since nobody really has much of a choice. The only choice happens at expiry, and you can bet your bottom dollar that the option will be exercised if and only if the option is in the money. With American options, on the other hand, the option holder is forced to make the choice of whether to exercise every second that the option is in the money. As in the case of the St. Petersburg Paradox, the assumption that humans are rational, expectations-taking automata is highly inappropriate in finance. In fact, options investors will tell you it's common knowledge to never hold an option to expiry; how ironic, then, that the behavior modeling of Black and Scholes leads to a scenario in which this is not just possible but unavoidable.

The real point of this article isn't about American options or the St. Petersburg Paradox, but the "standard of proof" in our nascent field. Will we accept gross generalizations, and ignore their shortcomings to the point we award the Nobel Prize to the mathematicians who created the above model? Or will we enforce a standard of rigor, look at problems on their face, and imagine creative solutions in real-life conditions?

The question isn't so much about proof as assumptions. It is one of the assumptions of Black and Scholes that leads to the notion of risk-neutral valuation, and hence this odd model of human behavior.

When I ask people what they think the worst assumption in Black-Scholes is, you usually get some swagger about fat tails and normal distributions, or maybe complete markets from those in the know. But here's the bigger one, the much, much bigger one:

Black and Scholes ignore transaction costs.

Is this a fair assumption? In most of economics, it is. Let's examine the case of stocks and bonds. Is it valid to ignore transaction costs when discussing a deal in stocks or bonds? I think so. It's possible that eventually transaction costs for simple assets like this will be driven to zero if humans are more able to find the appropriate counterparty due to greater access to information. And in the meantime, to be honest, it's really a fair assumption. Transaction costs here are low relative to the cost of carry and cost of buying the security, and they don't make much of a difference.

But options? Options aren't like stocks, in my mind. Remember, the basis of the Black-Scholes thinking was the delta-hedged portfolio yielding a risk-free rate. But in order to actually create that kind of portfolio, you need to hire a trader to sit there and manually hedge and re-hedge. In fact, the Black-Scholes differential equation represents a continuously re-hedged portfolio, implying virtually infinite transaction costs. And, since the derivative didn't exist in the first place, the transaction cost also includes writing the option and selling it. For options, transaction costs aren't a negligible factor -- they're everything.

It's clear that quantitative finance professionals have a long hill to climb in order to engender the kind of progress that would legitimize our work to the rest of the scientific community. But in this lack there lies a great amount of opportunity, not just for monetary gain, but for intellectual exploration and the fun of pushing the envelope. Clearly, there's something amiss about the theory underlying the most common of derivative pricing formulas. But it's unclear whether an easy solution exists. It seems there are still many questions to answer, not just mathematical, but behavioral and psychological. There is no doubt that quantitative finance has developed into a scientific discipline, but we may be surprised to find the aftertaste of other fields in papers to come.

The Difference Between a Pricing Model and a Trading Model

This morning on the brand new quant finance reddit, a user asked about the difference between a pricing model and a quant trading model. I realized that this is a question that often arises due to indiscriminate use of the world "model." And it becomes even murkier because pricing models can often play a part in quant trading models, in the sense that they are used to manage risks and potentially perform relative value analysis.

My comment and a link to the whole thread can be found here:

http://www.reddit.com/r/quantfinance/comments/d58sc/whats_the_difference_between_a_pricing_model_and/c0xnsli

I used to be rather unenthusiastic about pricing models; I wanted to learn the closely guarded secrets of the quant trading world, some kind of hidden spellbook of trading and mathematics that would teach me how to become a billionaire. But as I've learned more, and the wide world of finance has humbled me plenty, I've found that the two are more intertwined than I had thought. If nothing else, learning about pricing models helps you to think critically about the behavior of investors and markets.

Furthermore, risk, which is obviously quite related to pricing models, is fundamental to any good trading operation. In a comment (here) this morning I related a story about a meeting with a trader the other day. A few of his positions were missing their proprietary duration measures, a key interest rate risk statistic, and he remarked: "Without my risk, I'm flying blind." While quant models are extremely valuable if they can predict fundamental market occurrences like interest rate movements or stock market movements, they are worth nothing if you can't evaluate how these changes will affect your portfolio. And in that sense, risk and trading are inextricably connected.

Introducing the Quant Finance Subreddit

http://www.reddit.com/r/quantfinance/

As I've said before, quantitative finance is a truly fascinating field of study. I think it appeals most to those who are attracted to new, unexplored territory, since so much of the theory is still under heated debate and it's clear to most that the best methods have yet to come. Working on quantitative finance now -- or more specifically, computational finance -- would be like working on geometry in ancient Greece or physics in the time of Newton.

Many people mistakenly blame the financial crisis on the quants. In fact, there was an article that made the cover of Wired about how a model called the Gaussian copula was to blame for the meltdown. But it also explained that the inventor of the model had time and again protested that management didn't understand the model's limitations. They make mention of his personal anguish at seeing the risk managers herald his simple formula as the solution to modelling risk in CDOs, when he knew very well that over-reliance on his simplistic formulation could be disastrous for the CDO market. This is the reason more people need to help this field along, in order to help avoid future such disasters.

But enough of this digression -- I started the quant finance subreddit in order to allow those of us with this very niche interest to share interesting papers we come across, ideas we have or software we write. There's a wonderful community of intellectual types on reddit and it would be great to have a community for discussing this subject matter without being off topic on either programming or math reddits. So please feel free to post whatever you like!

In Support of Oracle and Java

There's been a lot of Java hate recently, particularly from the open source world, and I have always struggled to see why. Perhaps its opponents lack the pragmatism to see value in diversification. Yes, Java is not a 100% free-as-in-speech platform. But there is immense value in an open source-friendly yet commercially backed platform upon which to build our projects.

Anybody functioning within the four walls of a company knows that, when it comes to big decisions, the executives tend to want to invest in a platform that isn't going anywhere -- and that means, backed by a big bad company. A company with real, long-term economic interest in the success of the technology. And so the adage goes, nobody ever got fired for buying IBM.

But today on Reddit, one of the few places I frequent where I notice this brand of Java hate, I remarked that Mr. Mueller of FOSS Patents blog had an interesting post about the Google-Oracle dispute, available here:

http://fosspatents.blogspot.com/2010/08/oracle-vs-google-licensing-issues.html

Since my current project is written in Java, you can likely imagine I have particularly strong feelings regarding the future direction of the Java platform following Oracle's acquisition. In fact, I thought long and hard about the environment upon which to build my newest creation -- a platform for financial analytics geared towards the quantitative trader/risk manager type -- before writing a single line of code.

Certainly, Mr. Mueller, whose techno-political inclinations can swiftly be ascertained from the name of his blog, has an aptitude with the minutiae of licensing agreements and a legal expertise that I clearly lack. However, I believe that in his dedication to his principles, it's possible that he overlooks what's best for the advancement of technology as a whole. He argues that a flawed, almost duplicitous community process for the Java platform brought about a pseudo-free environment that Google misperceived as genuinely so, ultimately landing them in hot water when they tried to build a mobile Java platform that deviated from the core specification. However, it is specifically this community process that makes Java a commercially viable platform. Java's unique hybrid quality, whereby it has an obvious affinity with the open source world (think Apache projects) while still being backed commercially by a company people trust, makes it an extraordinarily valuable platform not just for open source, nor for commercial software, but for the industry in its entirety.

Droid Does
Every wonder why "Droid Does"? Because Android code is written in Java, the most popular and most commonly taught programming language in the world. That means every coder and his grandmother can write code for an Android phone, since they already know the language, and they can likely write the majority of their app without even getting the Android developer tools (everything except the graphical components).

In order to use Java code on the phones, Google (with its infinite resource) actually re-implemented the Java technologies for mobile devices, basing it on the official Java specification. However, Oracle claims that Google made changes, additions or omissions that compromised the integrity of their implementation. This is actually a violation of the license agreements for the spec itself. One thing is for certain -- Google's "Dalvik" produces .dex files, which aren't compatible with the .class files typically used by the Java platform.

It might seem curious to the non-technical why this is so vitally important to technology companies -- what does Oracle care if Google adds a new feature to their implementation of Java? The reason is compatibility. The entire cohesiveness of the community and the reliability of the platform is compromised when competing dialects get introduced into the wild. When a user downloads Java code, he no longer knows whether Oracle's JVM can run it. Perhaps it's Dalvik code, using special Dalvik-only features.

"Why do we use FinCad?"
I think the value of Java is best illustrated by an example of what I will term "Layman's Paranoia."

The Layman's Paranoia is a simple concept, and since my readers may be technically oriented, I will switch to an example about cars, about which I know absolutely nothing. When something happens to my computer, I slowly work to diagnose the problem, search for the appropriate keywords on Google, and ultimately locate a forum post or HOWTO giving me a solution. Since I am well-acquainted with the diction of the IT world, it is easy for me to handle a computer issue in a calm, collected manner.

But when my car breaks down on the side of the road, I absolutely panic. I certainly don't know how to fix a car. I don't even know enough to diagnose how big my problem is, nor what kind of specialist I may need to call, nor how long the fix will take. This uncertainty is, quite simply, an operational risk sustained by anyone as ignorant as me driving an automobile. And that's precisely the situation you're in as a manager of a technology company with little-to-no genuine technology background (save Excel macros).

Because I'm ignorant about cars, I'm flighty, scared, and prone to pay exorbitant amounts of money to AAA or some kind of insurance club in order to have a tow truck to call when my car breaks down in rural Vermont. That way, when the going gets tough, the risk (whose magnitude I cannot assess a priori) will be handled.

This creates a triangular information asymmetry between customer, mechanic and club. And these asymmetries drive the business. The situation is precisely the same as when, while working as a consultant for a large hedge fund to build a risk management solution, I suggested using a FOSS financial math library.

We were paying unheard of amounts of money to use FinCad, a commercial financial software package, and at the risk of disparaging their good work, it didn't seem to be the ideal tool for our particular application. Meanwhile, the open source option was fairly incredible, allowing us scores of different algorithms for calculating the fair value of an option, or the OAS on a mortgage.

And he said: "But who do we call when it breaks?" He was unwilling to have a non-commercial application underlie the fund's risk management operations. Because if everything goes to hell and the risk system goes down -- well, everyone's going to be looking at him.

Now, I'm not talking about support contracts. Clearly, third-party vendors can offer support for whatever FLOSS packages they please. But, the survival of a genuine platform -- in the way that Java is a platform and .NET is a platform -- requires long-term interest from a corporation with vested financial interest in the success and longevity of the technology.

The Middle Road

The strong-fisted approach to community development portrayed by Mr. Mueller is certainly no exaggeration. But how else can Oracle (previously, Sun) make good on that implicit claim to the aforementioned executives that with Java comes reliability? Java supports a thriving open source ecosystem, including a multitude of scripting and dynamic languages, none of which would ever have been possible if Java had never gained the widespread adoption that it has. 

There are some issues with the lawsuit. In basing its Android platform on Java, Google actually did a solid for Oracle and the Java community by publicizing their endorsement of the platform and precipitating yet another swathe of legacy Java code to be maintained for decades to come. Thanks to the network effect, this adds nothing but value to the Java community.

Nonetheless, I applaud Oracle for taking on Goliath in defense of the promise made to their users and shareholders. Java is something worth protecting, and something of great value to developers. Not only does it allow us to write once and run anywhere, but it actually bridges the two worlds of commercial viability and open source idealism in an elegant, if neither popular nor legally clearcut, way. It is important to keep the economic realities of intellectual property in mind, because often the survival of a technology depends on the kind of corporate stewardship Java enjoys. As a community, open source advocates need to stop pushing their ideas on people to the exclusion of all else, and instead recognize the symbiosis that can develop between the free and the proprietary.

Obligatory First Post

I'm Jason Victor. I recently graduated from my alma mater in '09  (hence the handle "Jason Victor Dartmouth") where I studied computer science. I am generally enthused by mathematics and work in or around the financial markets.

But let me start a little farther back. I started programming when I was six. By about sixteen, I had figured out the craft of programming, as it were, and began searching for a more specific interest. I found it in what was then called "artificial intelligence." Now, I call it "machine learning." But no matter. More on that later.

Anyway, I was poor, since I was a kid, and I needed free data. And one source I found was financial data -- it's abundant, it's confusing, and it provides an interesting way to test statistical techniques. Little did I know that would lead me down a much more interesting path than even I had anticipated.

To my more academic readers, please don't immediately disregard my thoughts regarding finance. It's really a fascinating field. I find a lot of similarities between finance and physics -- in practice, both involve stretching current computational and mathematical boundaries, and in theory, there's so much conflict and argument that it's abundantly clear it really hasn't been figured out yet. Just as physicists come up with theories for different pieces of physics that inherently conflict with others, grappling tirelessly for the elusive Theory of Everything, the theory of finance is equally wrought with disturbing half-truths, unrealistic assumptions, and conflicting ideologies. It's poorly understood, at best. For those with a quantitative inclination and a trailblazing ideology, the financial markets are a literal paradise.

In the following pages, I plan to record my thoughts about these wonderfully interesting subjects. And I want to accomplish a couple different things.

For one, as someone that started programming at a young age and had to teach myself for most of my life, I feel for those in the same situation. I want to document everything I wish I had access to when I was learning; I want to chart a clearer course for those looking to learn how to hack beautifully.

I want to create something similar for those looking to understand quantitative finance. That is a particularly difficult thing to get your head around. Most start with either an ill-conceived plan to make millions or a meek interest in building a career around it -- and frankly, I don't hold it against either group. But, the world around us, for some reason, does make it a pain to learn.

Here's why. There are two parts to what I will from now on call "quantness":

1. The parts that have to do with making money
2. The parts that don't have to do with making money

The second category of concepts is obviously much easier to learn, because people are willing to teach you. But it's less clear to the unsuspecting novice why in the world these concepts are useful. What are they used for? Why are they writing this? Do I really need to know this?

Really, it would be easier to start off by learning about quantitative investment strategies. But, alas, those are a whole lot harder to get anyone to explain to you. If a strategy works, the last thing anyone is going to do would be tell you about it.

So, I will try to make what little order I can of the madness that is computer science, math and quant finance. I'm no professor, and I'm certainly not an expert in anything -- but, I have managed to get my head around these concepts just enough to truly fall in love with them, and I want to help others to do the same.

All the best,

Jason Victor