26

Hah! There is no such thing as the “rigorous mathematical underpinning” of high frequency trading - because HFT, like all trading, is not primarily a mathematical endeavour. It’s true that many people who work in HFT have a mathematical background, but that’s because the tools of applied math and statistics are useful when analysing the large amounts of ...


19

The primary quant skill needed to make the market is optimal control (a typical paper is Guéant, O., L, and J. Fernandez-Tapia (2013, September). Dealing with the inventory risk: a solution to the market making problem. Mathematics and Financial Economics 4 (7), 477-507), because you need to control your inventory and adjust your quotes accordingly: be more ...


16

This question has been re-opened again after (rightly) being closed as too broad for the purpose of clearing some misconceptions regarding one of the answers here. The main idea that is to be stressed here is this: When it comes to high frequency trading, biggest or "as many as you can get" is rarely true. Not only is it false, it is impossible in terms of ...


16

I would argue, taking a note from John von Neumman, that quantitative finance lacks rigorous underpinnings. Von Neumann warned in 1953 that many things that look like proofs in economics and finance depended on problems that were yet to be solved in mathematics, and where economists were assuming solutions into existence. As the problems were solved in math,...


15

This is a very difficult question. First of all you should read Almgren's slides on the topic: Using a Simulator to Develop Execution Algorithms. First you need to backtest your strategy against a "replayer". Ok it is not perfect, but it gives you information anyway. Provided you add some "sanity limitation" to this simulator (i.e. do not allow you ...


13

Here's a way to think about it: imagine you can do something in an ASIC (i.e. directly in hardware). However, the process of fabrication is in itself expensive, and you get a design that you cannot change afterwards. ASICs make sense for predefined tasks such as Bitcoin mining, well-known data processing algorithms, etc. On the other hand we have ordinary ...


12

Using months of proprietary data that labels participants by their participant ID, it has been found that during periods of significant volatility, the composition of HFT participants in the book remains mostly constant as a fraction of the total BBO composition. What really changes, it was found, was that the fraction of low-frequency traders aggressing on ...


12

I found this power point and this paper to be an excellent source on this topic. Here is a quote from the paper: A square-root singularity for small traded volumes is highly non-trivial, and certainly not accounted for in Kyle’s classical model of impact [11], which predicts a linear impact ∆ ∝ Q. A concave impact function is often thought of as a ...


11

Successful strategies in both areas can have the same math requirement. It just depends on the algorithm. PhD level mathematics is not a requirement in either area, despite the impression you may get from academic papers (note that a lot of these papers use math to build a sim market, which is completely dislocated from what a researcher needs to do). I feel ...


11

I didn't quite understand your objection. Most theories of market making are derived from a famous paper by Jack Treynor (The Economics of the Dealer Function). In the theory, there are initially no market makers, but there is a backstop seller (in this case someone willing to sell large amounts at 10.10) and a backstop buyer (a Warren Buffet ready to buy ...


11

Is there a typical "half-life" of a strategy? This is a really subjective question, and I don't think any singular answer will generalize well. That being said, I will give some examples from personal experience. I have made hundreds of trading models in my career. I have only deployed 9 into live trading in the last ~25 years. Of those 9, 2 of ...


10

Pete's seven year old answer is just as relevant now as it was in 2011. None of the limiting factors of their API has changed since then, so this is essentially an extensive reiteration. The Interactive Brokers API is not suitable for high frequency trading execution. However the main reason that this is the case is not necessarily what would come to mind ...


9

Unfortunately, the ability and tools to develop a low latency trading system are extremely commoditized and will be insufficient for you to make a living in this field. An overwhelming majority of electronic market makers are staffed 100% by PhDs because trading experience and research compose their primary differentiators, e.g.: SIG EMM - 100% PhD. DRW EMM ...


9

The market-maker makes a bid-ask spread $\delta$ around the reservation price $r$. So at any time, the market-maker quotes the bid price $$ p_b = r - \delta/2, $$ and the ask price $$ p_a = r + \delta/2. $$ Bid price is hence always below the reservation price and ask price is always above the reservation price. The reservation price $$ r = s - q\gamma\...


9

No, you have to build your model empirically with data. Suppose $p(x)$ denotes the probability of cancel in front of you when your order is positioned $0 \leq x \leq 1$ through the queue, there are a few trivial cases: If you just joined the queue, any reduction in depth at the level must come from in front, i.e. $p(x=1)=1$ If you are at the front of the ...


8

The Queue Reactive Model (by Huang, L and Rosenbaum) is an improvement of what Cont and de Larrard (CL) did. This model is capturing the inflows and outflows in each queue given the current state of the orderbook (it is one of your remark) but more importantly, once one queue depletes, the discovered quantity is not taken at random (like in the CL model) ...


8

I'm doing this from memory, but as I recall $q_{\text{max}}$ is the maximum inventory on any side that you wish to take (otherwise you might build up a huge position if you are adversely selected). Later papers such as this one https://arxiv.org/pdf/1105.3115.pdf helped my understanding. As it actually happens, I implemented these algorithms and had a go ...


8

As @chrisaycock mentioned, there's many permutations of parameters, especially when it comes to venue routing instructions, so it's hard to write an exhaustive list. But most of the time, the exceptions you're looking for will fall into 4 categories. 1. Intermarket sweep orders (ISOs) This allows a destination trading center to execute against other orders ...


7

I think it's alive and well. I don't think there's a specific "decoupling" time, but if you look at e.g. Munnix et al. "Statistical causes for the Epps effect in microstructure noise", it seems that the biased correlation is about 60% of the real value for 1 min data and about 90% for 5 min data, so you could say that 5 min is pretty safe, but 1 min is ...


7

Very interesting question. I am not an expert on the subject, however, I was able to find a collection of papers on the subject that should get you started. Here is a good and very informative paper that walks you through several tick by tick volatility estimators that seek to reduce the volatility imposed by market micro-structure: Efficient estimation of ...


7

If I was in your position I would start to research how I can create a web server is C++ and expose calls to create a REST service. In other words, can you make your code status output to HTTP? From there, the rest should be easy. You would just need to create a GUI that can access REST services, which virtually all modern languages can. You could focus on ...


7

As someone who has contributed to literature, I am purposefully vague with the use of mid price. Not that I don't define it but that it is difficult to state which definition is the best in which context. Here are an example of a few definitions of mid price: Last Trade: The physical price at which the most recent trade physically took place. This is ...


6

I have created some Fourier Analysis of stocks here: http://www.gregthatcher.com/Stocks/Default.aspx I turn the raw data into a series of sines and cosines, show the Fourier approximation as a graph, and then allow you to "turn off" the various sines and cosines, so that you can see how the various "frequencies" contribute to the graph of the stocks values. ...


6

Quick summary: Your model should still be well specified, as long as: 1) You do the analysis on a heavily traded asset, e.g. IBM on NYSE, and 2) You use heteroskedasticity-consistent standard errors in your estimation framework, e.g. White's standard errors. I'm going to start the long answer by re-stating the question to make sure I've got it right. Let ...


6

On aggregate, large shops like Virtu are involved in market making strategies. There's various classes of market making strategies, and it is unnecessary to distinguish further here for the purpose of answering your question. For your curiosity however, Virtu is especially known for pure arb market making strategies. Without diving into technical ...


6

Financial modeling is often considered as a mixture of art and science. That is a way how you model your data depends on you. You can choose several approaches, for example: calculate max - min price for a given minute data - a very simple approach, calculate the standard deviation of minute-by-minute stock data, calculate GARCH family models for measuring ...


6

A "flickering" order is one which is repeatedly submitted and cancelled (whether it's at the top of book or not). The answer from @chollida mentions that "the goal typically is to either slow down competitors quotes by flooding the gateway interface with noise" but I don't think that's necessarily true. Rather, I think many flickering quotes are caused by ...


6

As a preamble. There are two types of "circuit breakers" if the price goes outside a (long term or static) corridor defined as yesterday close +/-p% (very often p is a multiple of the long term volatility): "stop the market" and "reopen"; if the price goes outside a (short term or dynamic) corridor defined as previous trade price +/-q%: "stop the market" ...


6

Use daily P&L rather than return rate1. $$ Sharpe = \frac{\mu}{\sigma} $$ To annualize, multiply by the square root of the number of trading days in the year. For US equities, that would be 252. $$ Annualized\ Sharpe = \frac{\mu}{\sigma} \times \sqrt{252} $$ As for what kind of Sharpe you should target, the lowest I've seen is 5 in practice. A good ...


6

My understanding (devoid of any mathematical grounding) is as follows. v = Turnover PER UNIT TIME n = Shares you need to execute therefore n/v = Number of units of time required to execute your size at the normal turnover rate Realized vol follows a SQRT(T) heuristic. Given that we can now rewrite the transaction cost formula purely in terms of vol ...


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