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26 votes
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What mathematical theory is required for high frequency trading?

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 ...
Chris Taylor's user avatar
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19 votes
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Backtesting Market Making Strategy or Microstructure Strategy

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 "...
lehalle's user avatar
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18 votes

Ultra-High Frequency Trading Help

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 ...
Theodore's user avatar
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17 votes

Market impact, why square root?

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 ...
JoseOrtiz3's user avatar
17 votes

What mathematical theory is required for high frequency trading?

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 ...
Dave Harris's user avatar
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14 votes

What is C++ used for when writing code at High Frequency Trading firms?

I ran all of the research and trading at a high-frequency market making firm with well over a million lines of C++. Now I'm at Databento, where we have about 1 line of Rust for every 1.5 lines of C++ ...
databento's user avatar
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12 votes
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Understanding how market making helps investors

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 ...
nbbo2's user avatar
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12 votes
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How long do algorithmic trading strategies typically remain profitable?

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 ...
amdopt's user avatar
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11 votes
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Avellaneda -Stoikov market making model

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 + \...
RRG's user avatar
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11 votes
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Daily realized volatility and true daily volatility

To keep it brief: the realized variance estimator, $RV_t$, is only a consistent estimator of Quadratic Variation (QV) under absence of microstructure noise. Following the paper of Barndorff‐Nielsen, O....
Pleb's user avatar
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10 votes
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Market Making Strategy to Interact with IB API

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 ...
Theodore's user avatar
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9 votes

What are the main types of orders on an exchange?

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 ...
databento's user avatar
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9 votes
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Is there a HAR that deals with the leverage effect?

There exists a modification of the HAR model that accounts for leverage effect (á la GJR-GARCH) in a high-frequency setting. The semi-variance HAR model, termed the SHAR model of Patton and Sheppard (...
Pleb's user avatar
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9 votes
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Modelling queue position

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 ...
databento's user avatar
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8 votes
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Order Book Dynamics

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 ...
lehalle's user avatar
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8 votes

Infinite horizon agent in Avellaneda-Stoikov model

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). ...
cjm2671's user avatar
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8 votes
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Beginner to high-frequency trading

My advice would be to read some books. To start with: Algorithmic Trading and DMA: An introduction to direct access trading strategies, by Johnson Market Microstructure in Practice, 2nd edition by L ...
lehalle's user avatar
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8 votes

Alternatives to RDBMS for options backtesting

My answer is similar to the one given for this other question. If you are mainly using the data for backtesting, there's very little reason to store the data in a MySQL database. The data generally ...
databento's user avatar
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8 votes

Stochastic equation in "High Frequency Trading in LoB, Sasha Stoikov and Marco Avellaneda"

First part of your question: The solution comes from solving the SDE specified in the paper and then using the moment generating function of a normal random variable. Formally, let us define the SDE ...
Pleb's user avatar
  • 4,661
7 votes
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How to measure the Sharpe Ratio of a high frequency trading strategy?

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. ...
chrisaycock's user avatar
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7 votes

Market impact, why square root?

My understanding (devoid of any mathematical grounding) is as follows. v = Turnover PER UNIT TIME n = Shares you need to execute therefore ...
hjw's user avatar
  • 359
7 votes

definition of mid price in literature

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 ...
Attack68's user avatar
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7 votes

What is C++ used for when writing code at High Frequency Trading firms?

I read your question here on stackexchange and was curious myself, so I did a little digging and came across this: A thread on Quora Where can I learn C++ for HFT? Theodore Weld Smith (programming ...
Pierre Merstab's user avatar
6 votes
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What are some quantitative trading strategies used by high-frequency trading companies to make a killing on a market crash day on 24Aug2015?

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 ...
madilyn's user avatar
  • 5,240
6 votes

HFT to blame for Flash Crashes?

I can't say what other HFT operations do, but I can give you a description of how our automated systems worked and that may give some insight into what goes on. From 1999 to 2007 I ran an HFT and ...
drobertson's user avatar
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6 votes
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What are flickering orders?

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 ...
Chris Taylor's user avatar
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6 votes
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Why circuit breakers can't prevent a flash crash

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 ...
lehalle's user avatar
  • 12.4k
6 votes

How do market participants know intentions of other players

First of all, you may have a look at two other papers Mean-Field Game Strategies for Optimal Execution by Huang, Jaimungal and Nourian. Mean Field Game of Controls and An Application To Trade ...
lehalle's user avatar
  • 12.4k
6 votes

Insoluble Enigma

Your question is too broad to give anything but a very general answer. Data mining in the raw form won't do any good. At the minimum, you will pick up thousands of spurious correlations. You cannot ...
Dave Harris's user avatar
  • 4,309
6 votes
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Formerly profitable algorithmic trading strategies?

Take a look at compilations such as 151 Trading Strategies. I wouldn't expect this information to be widely disclosed. After all, a non-profitable strategy is a supermartingale which means there is an ...
Sergei Rodionov's user avatar

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