Algorithmic trading is a method of executing orders using automated pre-programmed trading instructions accounting for variables such as time, price, and volume. This type of trading attempts to leverage the speed and computational resources of computers relative to human traders. In the twenty-first century, algorithmic trading has been gaining traction with both retail and institutional traders. It is widely used by investment banks, pension funds, mutual funds, and hedge funds that may need to spread out the execution of a larger order or perform trades too fast for human traders to react to. A study in 2019 showed that around 92% of trading in the Forex market was performed by trading algorithms rather than humans.

The term algorithmic trading is often used synonymously with automated trading system. These encompass a variety of trading strategies, some of which are based on formulas and results from mathematical finance, and often rely on specialized software.

The financial landscape was changed again with the emergence of electronic communication networks (ECNs) in the 1990s, which allowed for trading of stock and currencies outside of traditional exchanges. In the U.S., decimalization changed the minimum tick size from 1/16 of a dollar (US$0.0625) to US$0.01 per share in 2001, and may have encouraged algorithmic trading as it changed the market microstructure by permitting smaller differences between the bid and offer prices, decreasing the market-makers' trading advantage, thus increasing market liquidity.

This increased market liquidity led to institutional traders splitting up orders according to computer algorithms so they could execute orders at a better average price. These average price benchmarks are measured and calculated by computers by applying the time-weighted average price or more usually by the volume-weighted average price.

A further encouragement for the adoption of algorithmic trading in the financial markets came in 2001 when a team of IBM researchers published a paper at the International Joint Conference on Artificial Intelligence where they showed that in experimental laboratory versions of the electronic auctions used in the financial markets, two algorithmic strategies (IBM's own MGD, and Hewlett-Packard's ZIP) could consistently out-perform human traders. MGD was a modified version of the “GD” algorithm invented by Steven Gjerstad & John Dickhaut in 1996/7; the ZIP algorithm had been invented at HP by Dave Cliff (professor) in 1996. In their paper, the IBM team wrote that the financial impact of their results showing MGD and ZIP outperforming human traders “...might be measured in billions of dollars annually”; the IBM paper generated international media coverage.

In 2005, the Regulation National Market System was put in place by the SEC to strengthen the equity market. This changed the way firms traded with rules such as the Trade Through Rule, which mandates that market orders must be posted and executed electronically at the best available price, thus preventing brokerages from profiting from the price differences when matching buy and sell orders. As more electronic markets opened, other algorithmic trading strategies were introduced. These strategies are more easily implemented by computers, as they can react rapidly to price changes and observe several markets simultaneously.

A third of all European Union and United States stock trades in 2006 were driven by automatic programs, or algorithms. As of 2009, studies suggested HFT firms accounted for 60–73% of all US equity trading volume, with that number falling to approximately 50% in 2012. In 2006, at the London Stock Exchange, over 40% of all orders were entered by algorithmic traders, with 60% predicted for 2007. American markets and European markets generally have a higher proportion of algorithmic trades than other markets, and estimates for 2008 range as high as an 80% proportion in some markets. Foreign exchange markets also have active algorithmic trading, measured at about 80% of orders in 2016 (up from about 25% of orders in 2006).  Futures markets are considered fairly easy to integrate into algorithmic trading, with about 20% of options volume expected to be computer-generated by 2010. Bond markets are moving toward more access to algorithmic traders.

Pairs trading or pair trading is a long-short, ideally market-neutral strategy enabling traders to profit from transient discrepancies in relative value of close substitutes. Unlike in the case of classic arbitrage, in case of pairs trading, the law of one price cannot guarantee convergence of prices. This is especially true when the strategy is applied to individual stocks – these imperfect substitutes can in fact diverge indefinitely. In theory, the long-short nature of the strategy should make it work regardless of the stock market direction. In practice, execution risk, persistent and large divergences, as well as a decline in volatility can make this strategy unprofitable for long periods of time (e.g. 2004-2007). It belongs to wider categories of statistical arbitrage, convergence trading, and relative value strategies.

In finance, delta-neutral describes a portfolio of related financial securities, in which the portfolio value remains unchanged due to small changes in the value of the underlying security. Such a portfolio typically contains options and their corresponding underlying securities such that positive and negative delta components offset, resulting in the portfolio's value being relatively insensitive to changes in the value of the underlying security.

In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices. When used by academics, an arbitrage is a transaction that involves no negative cash flow at any probabilistic or temporal state and a positive cash flow in at least one state; in simple terms, it is the possibility of a risk-free profit at zero cost. Example: One of the most popular arbitrage trading opportunities is played with the S&P futures and the S&P 500 stocks. During most trading days, these two will develop disparity in the pricing between the two of them. This happens when the price of the stocks which are mostly traded on the NYSE and NASDAQ markets either get ahead or behind the S&P Futures which are traded in the CME market.

Arbitrage is possible when one of three conditions is met:

Arbitrage is not simply the act of buying a product in one market and selling it in another for a higher price at some later time. The long and short transactions should ideally occur simultaneously to minimize the exposure to market risk, or the risk that prices may change on one market before both transactions are complete. In practical terms, this is generally only possible with securities and financial products which can be traded electronically, and even then, when first leg(s) of the trade is executed, the prices in the other legs may have worsened, locking in a guaranteed loss. Missing one of the legs of the trade (and subsequently having to open it at a worse price) is called 'execution risk' or more specifically 'leg-in and leg-out risk'. In the simplest example, any good sold in one market should sell for the same price in another. Traders may, for example, find that the price of wheat is lower in agricultural regions than in cities, purchase the good, and transport it to another region to sell at a higher price. This type of price arbitrage is the most common, but this simple example ignores the cost of transport, storage, risk, and other factors. “True” arbitrage requires that there be no market risk involved. Where securities are traded on more than one exchange, arbitrage occurs by simultaneously buying in one and selling on the other. Such simultaneous execution, if perfect substitutes are involved, minimizes capital requirements, but in practice never creates a “self-financing” (free) position, as many sources incorrectly assume following the theory. As long as there is some difference in the market value and riskiness of the two legs, capital would have to be put up in order to carry the long-short arbitrage position.

Mean reversion is a mathematical methodology sometimes used for stock investing, but it can be applied to other processes. In general terms the idea is that both a stock's high and low prices are temporary, and that a stock's price tends to have an average price over time. An example of a mean-reverting process is the Ornstein-Uhlenbeck stochastic equation.

Mean reversion involves first identifying the trading range for a stock, and then computing the average price using analytical techniques as it relates to assets, earnings, etc.

When the current market price is less than the average price, the stock is considered attractive for purchase, with the expectation that the price will rise. When the current market price is above the average price, the market price is expected to fall. In other words, deviations from the average price are expected to revert to the average.

The standard deviation of the most recent prices (e.g., the last 20) is often used as a buy or sell indicator.

Scalping is liquidity provision by non-traditional market makers, whereby traders attempt to earn (or make) the bid-ask spread. This procedure allows for profit for so long as price moves are less than this spread and normally involves establishing and liquidating a position quickly, usually within minutes or less.

A market maker is basically a specialized scalper. The volume a market maker trades is many times more than the average individual scalper and would make use of more sophisticated trading systems and technology. However, registered market makers are bound by exchange rules stipulating their minimum quote obligations. For instance, NASDAQ requires each market maker to post at least one bid and one ask at some price level, so as to maintain a two-sided market for each stock represented.

Most strategies referred to as algorithmic trading (as well as algorithmic liquidity-seeking) fall into the cost-reduction category. The basic idea is to break down a large order into small orders and place them in the market over time. The choice of algorithm depends on various factors, with the most important being volatility and liquidity of the stock. For example, for a highly liquid stock, matching a certain percentage of the overall orders of stock (called volume inline algorithms) is usually a good strategy, but for a highly illiquid stock, algorithms try to match every order that has a favorable price (called liquidity-seeking algorithms).

The success of these strategies is usually measured by comparing the average price at which the entire order was executed with the average price achieved through a benchmark execution for the same duration. Usually, the volume-weighted average price is used as the benchmark. At times, the execution price is also compared with the price of the instrument at the time of placing the order.

A special class of these algorithms attempts to detect algorithmic or iceberg orders on the other side (i.e. if you are trying to buy, the algorithm will try to detect orders for the sell side). These algorithms are called sniffing algorithms. A typical example is “Stealth”.

Some examples of algorithms are VWAP, TWAP, Implementation shortfall, POV, Display size, Liquidity seeker, and Stealth. Modern algorithms are often optimally constructed via either static or dynamic programming.

As of 2009, HFT, which comprises a broad set of buy-side as well as market making sell side traders, has become more prominent and controversial. These algorithms or techniques are commonly given names such as “Stealth” (developed by the Deutsche Bank), “Iceberg”, “Dagger”, “Monkey”, “Guerrilla”, “Sniper”, “BASOR” (developed by Quod Financial) and “Sniffer”. Dark pools are alternative trading systems that are private in nature—and thus do not interact with public order flow—and seek instead to provide undisplayed liquidity to large blocks of securities. In dark pools, trading takes place anonymously, with most orders hidden or “iceberged”.Gamers or “sharks” sniff out large orders by “pinging” small market orders to buy and sell. When several small orders are filled the sharks may have discovered the presence of a large iceberged order.

Strategies designed to generate alpha are considered market timing strategies. These types of strategies are designed using a methodology that includes backtesting, forward testing and live testing. Market timing algorithms will typically use technical indicators such as moving averages but can also include pattern recognition logic implemented using finite-state machines.

Backtesting the algorithm is typically the first stage and involves simulating the hypothetical trades through an in-sample data period. Optimization is performed in order to determine the most optimal inputs. Steps taken to reduce the chance of over-optimization can include modifying the inputs +/- 10%, shmooing the inputs in large steps, running Monte Carlo simulations and ensuring slippage and commission is accounted for.

Forward testing the algorithm is the next stage and involves running the algorithm through an out of sample data set to ensure the algorithm performs within backtested expectations.

Live testing is the final stage of development and requires the developer to compare actual live trades with both the backtested and forward tested models. Metrics compared include percent profitable, profit factor, maximum drawdown and average gain per trade.