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 ...
18
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 ...
15
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 ...
14
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 ...
14
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 ...
14
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,...
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 ...
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 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
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
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,...
10
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 ...
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
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
The main application I know of is in option pricing. Peter Carr has done some research here. For an introductory article see this one:
Option valuation using the fast Fourier transform by Peter Carr and Dilip B. Madan:
In this paper the authors show how the fast Fourier transform may be used to value
options when the characteristic function of the ...
8
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 ...
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
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\...
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
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
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
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
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 ...
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
Everyone can do what HFTs do, if they spend the necessary time and money to build and run the infrastructure required. This may involve becoming a regulated broker/dealer, but it is in no way an invite-only club.
Now, to your specific question, you'll find some information on Haim Bodek's site. Bodek does content that ISO's and Day ISOs are used to gain ...
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
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 ...
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