25
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 ...
21
It seems that your question refers to the microstructure noise defined in papers about intraday volatility estimates.
Originally, it comes from the bid-ask bounce, i.e. the fact that even if the volatility is zero, you have buyers and sellers at this price and consequently you observe prices at Bid or Ask prices, and not at mid-price. Because of that, if ...
19
The main issue measuring intraday volatility is called "signature plot": when you zoom in, the volatility measure (i.e. empirical quadratic variations) explode.
Similarly you have the "Epps effect" for correlations: when you zoom in, the correlations collapse (it is at least a mechanical effect).
For the volatility a lot of models can correct this:
- first ...
17
The term has a different meaning to different people.
to econometricians, microstructure noise is a disturbance that makes high frequency estimates of some parameters (e.g. realized volatility) very unstable. Generally this strand of the literature professes agnosticism as to the its origin;
to market microstructure researchers, microstructure noise is a ...
17
Some cynical but functional definitions:
It's what you can't model if you're not using tick by tick data
It's what proper quant pricing theory doesn't know how to model yet
It's information (order book behavior) that reflects momentary fluctuations in the supply/demand of a given contract, rather than its underlying value (eg an arbitrage free price)
The ...
17
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 ...
14
The expression you have is fine. But more generally, for the intraday volatility, I don't think there "the correct definition". More like, whatever works in the given context. I found the following notes by Almgren pretty useful:
http://cims.nyu.edu/~almgren/timeseries/notes7.pdf
14
There are few things to consider.
Trading moves the price, to minimize market impact and maximize return it is generally optimal to split an order in several child orders. See the Kyle model.
Splitting optimally dependents on specific assumptions that you make. The simplest (and first) approach is that of Berstsimas and Lo (Optimal Control of Execution ...
14
There are many specialised products for HF tick data. In addition to KDB which you mentioned, there is OneTick, Vertica, Infobright, and some open-source ones like MonetDB etc. (see http://en.wikipedia.org/wiki/Column-oriented_DBMS).
My experience is that Column Oriented Databases are overrated when it comes to tick data, because very often you request the ...
13
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 ...
13
There are rigorous econometric definitions, as has already been eluded to by others. For practical purposes, microstructure noise is a component of a price process that exhibits mean reversion on some (possibly time-varying) frequency.
This reversion is particularly attractive to liquidity provisioners, who seek to profit from this noise component (along ...
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
There are typically two important metrics:
Order to Accept. This measures the round-trip time it takes your application to send an order to the exchange and get an accept, cancel, or execute back. Think of it as the minimum amount of time required for you to ask the market to do something and know whether it's been done. This plays an important role when ...
12
The best explanation/theory that I have heard about Knight's erratic trading was put forth by Nanex. I have pasted their summary of findings below.
We believe Knight accidentally released the test software they used to verify that their new market making software functioned properly, into NYSE's live system.
In the safety of Knight's test laboratory,...
12
"quote spam", "book colouring", "quote stuffing", etc encompass any mechanism to modify the shape of the orderbook by a market participant who does not intend to really buy or sell shares thanks to these orders.
It means that someone fills the bid side of the book with 10,000 shares at different levels of price and does not want to buy at all, or only 100 ...
12
I can think of an application in options pricing. I came across the following paper a long time ago but think it explains FT very eloquently as applied to pricing options under BS:
http://maxmatsuda.com/Papers/2004/Matsuda%20Intro%20FT%20Pricing.pdf
The fun starts on page 112 but it relies on the 1998 paper by Madan and Carr.
What I like about the paper ...
11
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 ...
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
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,...
10
Intraday seasonality is a major factor in comparing volatility at different times of day. Most time series display significantly higher volatility in the morning EST than mid-day. For US exchange-traded products, volatility picks up again just before 4:00 PM EST. This is known as the u-shaped volatility pattern for exchange-traded products. A proper ...
10
Joel Hasbrouck (imho, a leading expert in market microstructure) has a paper on this:
http://people.stern.nyu.edu/jhasbrou/Research/Working%20Papers/HS10-11-10.pdf
From the abstract:
Our conclusion is that increased low-latency activity improves traditional market quality measures such as short-term volatility, spreads, and displayed depth in the limit ...
10
The flickered orders are postonly bid at 15.16. The exchange slides it back to 15.15 to avoid a locked market. Submitting firm sees the slideback and cancels. Then tries again. When the 15.16 offer is executed or cancelled out, the offer moves to 15.17 then the postonly bid at 15.16 goes through at the targeted price and gains good queue position.
10
The "price protection" refers to RegNMS in the US. A stock exchange that does not have the best price must route all order flow to the exchange that does. The SIP in the figure is a consolidated feed that lists the best price among all exchanges.
Consider this example: a broker sends a market order to buy JNJ to NYSE where the best offer is \$86.97. However,...
9
Indeed, algorithmic trading is a very hidden subject.
All I can help you with are some industry-specific terms which might speed up your search for relevant papers and information:
Risk of ruin tables
(Peak-to-valley) drawdown (maximum drawdown, duration of drawdown etc.)
Number of consecutive losses
Confidence intervals
Empirical distributions (for risk ...
9
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 ...
8
There is a paper of mine answering To this question: Dealing with the Inventory Risk. A solution to the market making problem by Olivier Guéant, Charles-Albert Lehalle, Joaquin Fernandez Tapia.
8
What you are looking for is generally called "machine-readable news". Here are the ones I know about off hand:
Dow Jones Elementized News Feed
Thompson Reuters News Feed Direct
Bloomberg Event-Driven Trading Feed
NASDAQ OMX Event-Driven Analytics
Good luck getting reliable latency figures from any of those vendors though.
8
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 ...
8
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 ...
8
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 ...
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