High frequency trading: Sinatra sings and stochastic processes swing

-August 16, 2012

Earlier in my career, my “Phd mentor/boss” always chided me to “move out of your comfort zone”. As engineers, scientists and geeks, we tend to stay with what we know.  Anything out of our ecosphere that we are not comfortable or familiar with is “off limits”.

So when I was invited to attend “The 4th Annual Modeling High Frequency Data in Finance Conference” (July 19-22, 2012), I decided to take the challenge. The conference venue was at Stevens Institute of Technology in Hoboken, New Jersey.

Hoboken is the birthplace of Frank Sinatra (see Figure 1) and the first officially recorded game of baseball took place in Hoboken in 1846 between Knickerbocker Club and New York Nine at Elysian Fields.


 Figure 1 Frank Sinatra Image from Wikipedia and impressive New York City skyline view from Stevens Institute’s Babbio Center for Technology overlooking Sinatra Drive.

This four-day conference gathered key experts in academia, industry and government from across the globe in the areas of mathematical finance, financial engineering, quantitative finance, and stochastic processes. With over sixty (60) presentations, keynote speeches, poster papers and panel discussions, the conference program was focused on sharing the latest research and applications of models for data sampled with high frequency.

The conference chairs are listed below:

The first question you might ask is what is High Frequency data in finance?

“The frequency of the submission of orders has increased and the time to execute market orders on these electronic markets has dropped from more than 25 ms in 2000 to less than 1 ms in 2010. As shown in Table I, thousands of orders are submitted in a 10-s interval, resulting in frequent updates in bid and ask quotes, up to 100,000 times a day, as well as frequent changes in transaction prices. Transaction data record trades that occur on an exchange, each record being associated with a time stamp, a price, and quantity (trade volume, in number of shares)” [1].


Table I Average number of Price changes and Orders on (June 26th, 2008) [1].

Table II describes the hierarchy of time scales. There is no “official” definition of High Frequency data.  “However, if we use the analogy of time for humans to physically react in a chess game versus a trader to make a decision on a trade then we can compare it to the time a chess grandmaster (approximately 650 milliseconds) recognizes that he is in trouble (i.e. his king is in checkmate). In many areas of human activity, the quickest that someone can notice such a cue and physically react, is approximately 1000 ms (1 second)” [2].


Table II A hierarchy of time scales [1].


How do they model?


“The large volume of data available, the presence of statistical regularities in the data and the mechanical nature of execution of orders makes order-driven markets interesting candidates for statistical analysis and stochastic modeling” [1].

To model these stochastic processes, a variety of mathematical and probability algorithms are used such as Fractional Brownian motion, Markov Decision Processes, Lévy process, semimartingale, Queuing Theory[1], Fourier and Laplace transforms, Ordinary Differential Equations (ODE), Partial Differential Equations (PDE), Partial Integro-Differential Equations (PIDE) and many other mathematical functions.


What does an algorithm look like?

A very simplified algorithm is shown in Figure 2.


 Figure 2 Simplified Algorithm [3]

The “imbalance process”, θ (t), is the trade secret of many algorithmic trading companies [3].

Why do they study these HF trading applications & algorithms?

“These programs are designed to trade enormous volumes of stocks, bonds and other financial instruments at superfast speeds, taking advantage of second-to-second fractional price shifts and market trends.”[4]. What this means is millions of dollars in profits for the traders with the smartest algorithms, most efficient software running on the fastest computers.

For HFT hardware, computer processors are tailored for these algorithms. “GPU computing has become very popular in quantitative finance and many financial institutions are moving their CPU based applications to the GPU platform”[5].

As shown in Figure 3, a significant throughput improvement (~ 46 X) is made using an Nvidia GTX 480 GPU based processor over the 64 bit Intel® Core™2 Quad Processor Q6700 (8M Cache, 2.66 GHz, 1066 MHz front side bus (FSB) speed).

Figure 3 Acceleration of program code on GPU’s for HFT. [6]


Terry Stratoudakis, Wall Street FPGA, Co-Founder/ and Executive Director, in his presentation “An Overview of High Performance Computing in Financial Services”[7] described how a single FPGA chip could achieve the same performance as hundreds of nodes in a server farm. (see Figure 4a & 4b)

Figure 4a - Typical High Performance Computing Applications in Financial Services



Figure 4b -  Block  Diagram of Trading Infrastructure  (Courtesy TABB Group) link (http://www.tabbgroup.com/)


With money as no object, one new computer chip, named iX-eCute  (see Figure 5), was designed specifically for high-frequency trading and can prepare trades in 740 nanoseconds; a proposed $300 million transatlantic cable is being built just to shave 6 milli-seconds off the current 65milli-second transaction times between New York City and London.)”[2].


 Figure 5-New high-speed custom chip (iX-eCute) from Fixnetix a UK company.

 Is High Frequency Trading Wall Street’s Doomsday Machine

“High frequency (HF) trading firms represent approximately 2% of the nearly 20,000 trading firms operating in the U.S. markets, but since 2009 they have accounted for over 70% of the volume in U.S. equity markets and are fast approaching 50% of the volume in futures markets”[8].

The speed and volume of these trades has changed the market microstructure as shown in Figure 6. Do we really know [9] what caused the “flash crash” in 2010 (see Figure 7)? Or, what caused “the recent August 3, 2012 near collapse of Knight Capital Partners – in which a software bug in one of its high-frequency trading algorithms caused the firm to lose $440 million?”


 Figure 6 Amount of high frequency trading in the stock market from January 2007 to January 2012. Screen shot for 9/28/2011. (See article by Felix-Salmon for live day by day view over that time period)


Figure 7 Flash Crash of May 6, 2010

There was no specific answer to this question at the conference.

Commissioner Scott D. O’Malia, U.S. Commodity Futures Trading Commission, in his keynote remarks stated “I believe technology must play a larger and more foundational role in the Commission's execution of its market oversight responsibilities, risk management and in the protection of customer funds”[10]. He also “outlined several specific short, medium and long term changes that can be made that would improve customer protection and protect the system against operational risk going forward. I stand by those proposals, and I hope that the Commission and Congress will address each and every one of them going forward”[11].

After four days of intensive mathematics and financial complexity, I was totally amazed and “wowed” at the field of quantitative finance and financial engineering.  So, if you can learn something new, don’t forget what you learned yesterday then you are moving ahead.

Finally, I asked one of the speakers do you do any trading? He said, “Heck no”!


The information presented in this blog is provided for educational purposes only and does not constitute investment advice.

For Further Reading and Study:

“Handbook of Modeling High-Frequency Data in Finance” by Frederi G. Viens, Maria C. Mariani, Ionut Florescu

Wiley books on High Frequency trading and Modeling

Springer Books on High Frequency trading and Modeling

4TH Annual Modeling High Frequency Data in Finance Conference”

A 20% discount is available from Wiley and Springer and is also a great list of references material on HFT, background financial mathematics and models.


For Information on Financial Engineering Programs at Stevens Institute





[1] Rama Cont, “Statistical Modeling of High-Frequency of Financial Data -Facts, Models, and Challenges”, IEEE Signal Processing Magazine, pp. 16-25, September 2011


[2] Neil Johnson, Guannan Zhao, Eric Hunsader, Jing Meng, Amith Ravindar, Spencer Carran and Brian Tivnan, “Financial Black Swans Driven by Ultrafast Machine Ecology”, The 4th Annual Modeling High Frequency Data in Finance Conference, July 19, 2012


[3] Sasha Stoikov (joint work with Rolf Waeber), “Optimal Asset Liquidation using Limit Order Book Information”, The 4th Annual Modeling High Frequency Data in Finance Conference, July 19, 2012


[4] Brandon Keim,“Nanosecond Trading Could Make Markets Go Haywire”, Wired - Weird        Science Online, February 16, 2012


[5] Giray Okten, Monte Carlo and Randomized Quasi-Monte Carlo methods on GPU, The 4th Annual Modeling High Frequency Data in Finance Conference, July 19, 2012


[6] Tobias Preis, “Quantifying Financial Market Fluctuations Using Big Data”, The 4th Annual Modeling High Frequency Data in Finance Conference, July 19, 2012


[7] Terry Stratoudakis, Wall Street FPGA, “An Overview of High Performance Computing in Financial Services”, The 4th Annual Modeling High Frequency Data in Finance Conference, July 22, 2012


[8] David Easley, Marcos Lopez de Prado, Maureen O’Hara, “Flow Toxicity and Liquidity in a High Frequency World”, Review of Financial Studies, Vol. 25, No. 5, pp. 1457-1493, February 20, 2012.



[9] SEC-CFTC Release, Preliminary Findings in Review of May 6 Market Events”, September 30, 2010

[10] Commissioner Scott D. O’Malia, U.S. Commodity Futures Trading Commission, “The True Sign of Intelligence”, The 4th Annual Modeling High Frequency Data in Finance, Conference, July 19, 2012

[11] Commissioner Scott D. O’Malia, “Where Are We? And Where Should We Be? Thoughts on MF Global and High Frequency Trading”, Address by Commissioner Scott D. O’Malia at the Center on Financial Services Law of New York Law School, January 31, 2012


What is ‘High-Frequency Trading - HFT from Investopedia'’“A program trading platform that uses powerful computers to transact a large number of orders at very fast speeds. High frequency trading uses complex algorithms to analyze multiple markets and execute orders based on market conditions. Typically, the traders with the fastest execution speeds will be more profitable than traders with slower execution speeds. ”


What is Financial Engineering from Columbia Graduate School?
“Financial Engineering is a multidisciplinary field that requires familiarity with financial theory, the methods of engineering, the tools of mathematics and the practice of programming. Undergraduate and graduate studies in Financial Engineering provide students training in the application of engineering methodologies and quantitative methods for finance. It is designed for students who wish to obtain positions in the securities, banking, and financial management and consulting industries, or as quantitative analysts in corporate treasury and finance departments of general manufacturing and service firms.”


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