Navigation
Academic Papers and Books
Accepted and Published Papers
- The Minimal Model of Financial Complexity »
Quantitative Finance forthcoming.
Download PDF. - Regulation Simulation »
European Journal of Finance and Banking Research 2009, vol. 2, no. 2, pp.1-12.
Download PDF. - The Hazards of Propping Up: Bubbles and Chaos »
International Journal of Business and Finance Research 2009, vol. 3, no. 2, pp.83-93.
Download PDF. - Prospect Theory and Fat Tails »
Risk and Decision Analysis 2009, vol. 1, no. 3, pp.187-195.
Download PDF.
Textbooks
- Financial Hacking
World Scientific Publishing forthcoming. Scheduled Fall 2011.
Working Papers
- Any Regulation of Risk Increases Risk (with Zak Maymin) »
- Markets are Efficient If and Only If P = NP »
- Self-Imposed Limits to Arbitrage »
- Schizophrenic Representative Investors »
- Music and the Market: Song and Stock Volatility »
- Metanoia »
The Lambda-Q Calculus for Quantum Computation
- Extending the Lambda Calculus to Express Quantumized Algorithms »
- The Lambda-Q Calculus Can Efficiently Simulate Quantum Computers »
- Programming Complex Systems »
The Minimal Model of Financial Complexity
A representative investor generates realistic and complex security price paths by following this trading strategy: if, a few ticks ago, the market asset had two consecutive upticks or two consecutive downticks, then sell, and otherwise buy. This simple, unique, and robust model is the smallest possible deterministic model of financial complexity, and its generalization leads to complex variety. Compared to a random walk, the minimal model generates time series with fatter tails and more frequent crashes, thus more closely matching the real world. It does all this without any parameter fitting.Available on SSRN and on arXiv. Also see this introductory poster.
To be published in Quantitative Finance, forthcoming.
Download PDF but please note:
Author Posting. (c) Taylor & Francis, 2010.The minimal models can best be understood through live demonstrations.
This is the author's version of the work. It is posted here by permission of Taylor & Francis for personal use, not for redistribution.
The definitive version was published in Quantitative Finance, 2010.
doi:10.1080/14697681003709447.
 Step-by-step trader dynamics |
 Prices Generated by Rule 54 |
 Explore All Rules
|
See some videos of these demonstrations:
Regulation Simulation
A deterministic trading strategy by a representative investor on a single market asset, which generates complex and realistic returns with its first four moments similar to the empirical values of European stock indices, is used to simulate the effects of financial regulation that either pricks bubbles, props up crashes, or both. The results suggest that regulation makes the market process appear more Gaussian and less complex, with the difference more pronounced for more frequent intervention, though particular periods can be worse than the non-regulated version, and that pricking bubbles and propping up crashes are not symmetrical.Available on SSRN and on arXiv.
Published in the European Journal of Finance and Banking Research 2009, vol. 2, no. 2, pp.1-12. Download PDF.
This paper uses the minimal model of financial complexity above to explore the effects of different regulatory environments. It also shows how the simulated price series resemble the actual price history in European equity markets.
The Hazards of Propping Up: Bubbles and Chaos
In the current environment of financial distress, many governments are likely to soon become major holders of financial assets, but the policy debate focuses only on the likelihood and extent of short-term market stabilization. This paper shows that government intervention and propping up are likely to lead to long-term bubbles and even wildly chaotic behavior. The discontinuities occur when the committed capital reaches a critical amount that depends on just two parameters: the market impact of trading and the target exposure percentage.Available on SSRN and on arXiv.
Published in The International Journal of Business and Finance Research 2009, vol. 3, no. 2, pp.83-93. Download PDF.
See the interactive demonstration.
See a video of the demonstration:
Media and Press
Daily Finance: Bull market or bubble? History suggests brace for the 'pop'. Excerpt:Intuitively, it's almost too pretty a story: "This time it's different because of China."Phil Maymin, professor of finance and risk engineering at the Polytechnic Institute of New York University, doesn't buy that line for a second. "Wasn't it the early 80s when we were all enamored of Japan, the Rising Sun, the Eastern miracle? And the 90s was Taiwan and Thailand and Indonesia," Maymin says. "So now it's China. Bubbles, bubbles everywhere."
Yes, China's already a much bigger deal on a fundamental and economic basis than Japan or the Asian Tiger's ever could have hoped to be, but we wonder if investors aren't overpricing the would-be effects of the Middle Kingdom, if that is indeed the case.
We're going to have to go with Maymin -- not to mention Gluskin Sheff's David Rosenberg, star bank analyst Meredith Whitney and Nouriel "Dr. Doom" Roubini -- on this one. Like the fizzy lifting drink scene in Willy Wonka and the Chocolate Factory, we see bubbles, bubbles everywhere -- and fear they are propelling us right into the spinning blades of a fan.
Prospect Theory and Fat Tails
A behavioral representative investor who evaluates a single risky asset based on cumulative prospect theory will often induce high kurtosis, negative skewness, and persistent autocorrelation into the distribution of market returns even if the asset payoffs are merely a sequence of independent coin tosses. These findings continue to hold even when the investor is simply loss averse.Available on SSRN.
Published in Risk and Decision Analysis 2009, vol. 1, no. 3, pp.187-195. Download PDF.
Media and Press
Forbes Magazine: How to Protect Investments from Cataclysmic 'Fat Tails'
I wrote an article for Forbes (with Gregg S. Fisher) which refers to my research here.
Excerpt:
"And get the bits together, the fat tail, every good part." Ezekiel 24:4If you traveled back in time thousands of years to tell Abraham, Moses or Ezekiel that you had some fat tails, they would have been delighted. In ancient times, the fat tails of certain Middle Eastern sheep were considered a delicacy. Today, they're more often associated with investment cataclysms.
...
Recent research suggests that in certain cases, investors subject to these two biases--loss aversion and mental accounting--will generate fat tails via their trading activity. In trying to avoid losses and compartmentalize investment decisions, they can exacerbate moves upward and down. For example, when earnings randomly rise, investors buy more; and when earnings fall, they sell. This is not very logical, but it is very human.
Any Regulation of Risk Increases Risk (with Zak Maymin)
We show that any objective risk measurement algorithm mandated by central banks for regulated financial entities will result in more risk being taken on by those financial entities than would otherwise be the case. Furthermore, the risks taken on by the regulated financial entities are far more systemically concentrated than they would have been otherwise, making the entire financial system more fragile. This result leaves three directions for the future of financial regulation: continue regulating by enforcing risk measurement algorithms at the cost of occasional severe crises, regulate more severely and subjectively by fully nationalizing all financial entities, or abolish all central banking regulations including deposit insurance to let risk be determined by the entities themselves and, ultimately, by their depositors through voluntary market transactions rather than by the taxpayers through enforced government participation.Available on SSRN and on arXiv.
Media and Press
- American Banker: Viewpoint: An Experiment in Securities Risk. Download PDF.
- LewRockwell.com: The War on Risk.
- Fairfield County Weekly: Listen Up, Chris Dodd.
Blogs and Discussions
- Modeled Behavior
- Reddit:
- Reddit Main Site (8 comments)
- Reddit Economics (26 comments)
Markets are Efficient If and Only If P = NP
I prove that if markets are weak-form efficient, meaning current prices fully reflect all information available in past prices, then P = NP, meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can "program" the market to solve NP-complete problems. Since P probably does not equal NP, markets are probably not efficient. Specifically, markets become increasingly inefficient as the time series lengthens or becomes more frequent. An illustration by way of partitioning the excess returns to momentum strategies based on data availability confirms this prediction.Available on SSRN and on arXiv.
Blogs and Discussions
- Marginal Revolution (22 comments)
- Reddit:
- Reddit Economics (108 comments)
- Reddit Programming (23 comments)
- Reddit Math (11 comments)
- YCombinator Hacker News (58 comments)
My TEDxNSIT presentation on this topic:
Self-Imposed Limits to Arbitrage
I document a multi-billion dollar discrepancy that lasted from 1992 to 1999 between two otherwise identical share classes of HSBC that did not suffer from the external limits to arbitrage that traditionally explain such other mispriced pairs as 3Com/Palm or Royal Dutch-Shell. Instead, I describe how self-imposed, internal limits to arbitrage such as restrictions on position size can result in persistent mispricings.I also show that relatively more trading volume coincides with relatively lower prices in HSBC, and the same effects holds for 3Com/Palm, Royal Dutch-Shell, and other large mispriced pairs. An increase of one standard deviation in their relative volume coincides with a decrease of about one quarter of a standard deviation in their relative price. Self-imposed limits to arbitrage explain this phenomenon as well, so long as the more expensive security also tends to have greater daily volume: a higher relative price, or a wider discrepancy, leads to more arbitrage activity, and arbitrageurs trade equal volume in both securities, bringing the relative volume down closer to one.
Finally, I distinguish self-imposed limits to arbitrage from limits imposed as a result of market transactions costs or risk measures by calculating the market implied overall maximum position size of arbitrageurs for mispriced pairs spanning different time periods and countries and having different volume characteristics. The results are roughly constant at about one hundred days of typical trading volume, consistent with self-imposed limits.
View the complete manuscript. Also available on SSRN. Also available are presentation slides.
Schizophrenic Representative Investors
Representative investors whose behavior is modeled by a deterministic finite automaton generate complexity both in the time series of each asset and in the cross-sectional correlation when the rule governing their behavior is schizophrenic, meaning the investor holds multiple seemingly contradictory beliefs simultaneously, either by switching between two different rules at each time step, or computing different responses to different assets.Available on SSRN and on arXIv.
Music and the Market: Song and Stock Volatility
I compare the annual average beat variance of the songs in the US Billboard Top 100 since its inception in 1958 through 2007 to the standard deviation of returns of the S&P 500 for the same year and find that they are significantly negatively correlated. With the recent high stock volatility, people should now prefer less volatile music. Furthermore, the beat variance appears able to predict future market volatility, producing 2.5 volatility points of profit per year on average.Available on SSRN. Thanks to Larry Ribstein for a useful reference.
Media and Press
- Article on SmartMoney.com: Can Music Predict the Stock Market's Volatility?
- Slideshow on SmartMoney.com: Music to Buy, Sell, or Hold By.
- Interview with The Takeaway on WNYC: Music to Invest By. Download MP3.
- Article in the Guardian (UK): Beyonce's new single spells economic doom.
- Interview on BBC Radio Ulster: Arts Extra (from 25:12 on).
- Article in the German-language Swiss daily Tages-Anzeiger.
- Interview with NYU-Poly website: Rickrolling Explained.
- Washington Square News: Prof. links music with poor economy.
- Interview on NPR's All Things Considered: Volatile Markets? Try Lada GaGa to Calm Down. Download MP3.
- Newsweek Poland: Muzyczne spadki.
- Financial Times Deutschland: Britney als schlechtes Omen. Print edition PDF.
- Boston Globe: Pop Goes the Market. Interactive graphic.
- Interview with Studio 360: Recession Pop. Download MP3.
- Interview with NPR's Here and Now: Do Billboard Hits Reflect the Economy? Download MP3.
- Slideshow on CNBC: Eleven Surprising Stock Market Indicators.
- Interview with Laptop Rockers: Michael Jackson's Music Good for the Economy?
- Other appearances: WABC, CJAD, Sirius/XM.
- Other mentions: The Rachel Maddow Show on MSNBC.
- Story on USA Today: Could the pop-culture mood mirror stock market swings?
Download cover (PDF, teaser at middle left).
Download front page of Money section (PDF, teaser at top).
Download main article (PDF, page B3). - Pop quiz on USA Today: Test your music knowledge.
The New York Post asked me to write a piece about my research and, more generally, the links between popular culture and the financial markets. Here it is. Flop Culture: How Music, Skirts, and the Weather Move Markets.
Can you perceive the relationship? Suggestive video on YouTube:
Metanoia and the Market
If investors randomly switch between being rational and irrational, then eventually the market will be half rational and half irrational, even if all investors start off rational, no matter how low the switching probability is. Thus, mispricings can persist even with continued volume between two fundamentally identical investments. Multiple survey results for hypothetical investment scenarios support this metanoia model. In short, the law of one price will be violated so long as there is any probability of switching: identical assets will have different prices.Available on SSRN.
Lambda-Q Calculus (1996-1997)
Extending the Lambda Calculus to Express Quantumized Algorithms
I introduce a formal metalanguage called the lambda-q calculus for the specification of quantum programming languages. This metalanguage is an extension of the lambda calculus, which provides a formal setting for the specification of classical programming languages.As an intermediary step, I introduce a formal metalanguage called the lambda-p calculus for the specification of programming languages that allow true random number generation. I demonstrate how selected randomized algorithms can be programmed directly in the lambda-p calculus.
I also demonstrate how satisfiability can be solved in the lambda-q calculus.
View the complete manuscript. Available on arXiv.
The Lambda-Q Calculus Can Efficiently Simulate Quantum Computers
I show that the lambda-q calculus can efficiently simulate quantum Turing machines by showing how the lambda-q calculus can efficiently simulate a class of quantum cellular automaton that are equivalent to quantum Turing machines.I conclude by noting that the lambda-q calculus may be strictly stronger than quantum computers because NP-complete problems such as satisfiability are efficiently solvable in the lambda-q calculus but there is a widespread doubt that they are efficiently solvable by quantum computers.
View the complete manuscript. Available on arXiv.
Programming Complex Systems
Classical programming languages cannot model essential elements of complex systems such as true random number generation. I develop a formal programming language called the lambda-q calculus that addresses the fundamental properties of complex systems. This formal language allows the expression of quantumized algorithms, which are extensions of randomized algorithms in that probabilities can be negative, and events can cancel out.View the complete manuscript. Available on arXiv.