High-Frequency Trading and Probability Theory

The following sections are included:

• Contents
• Foreword to East China Normal University Scientific Reports
• Preface
• About the Authors

In recent years, high-frequency trading (HFT) became an extremely hot topic in capital markets around the world. Normally, HFT has the following attributes …

Algorithms of high-frequency trading (HFT) are heavily based on the market. A profitable algorithm in one market may not work in another market. That is the reason why we need to study the market microstructure on which our algorithms are based.

We explain in this chapter a few basic high-frequency trading (HFT) strategies, most of which are seen in various literatures. The further discussion needs some background in probability theory and statistics. Therefore, we can only start the related discussion from Section 5.4.

The IT system plays a core role in high-frequency trading (HFT). All the trading, management and research are based on IT systems. In this chapter, we will discuss the details of IT system design.

We find that the high-frequency trading (HFT) is closely related to the ergodic theory of stationary processes [12]. As we have shown in the previous chapters, in most HFT cases, the trader cannot guarantee to make profit in each of his trades. However, if a trader can repeatedly apply the same algorithm with positive expected profit to trade, then the strong ergodic theorem will lead to a steadily increasing accumulated profit as the total sum, if the profit series forms an ergodic stationary time series. That is the main thing we will explain in the next four chapters…

There are basically two methods to analyze the asset price: (i) fundamental analysis and (ii) technical analysis. Fundamental analysts examine earnings, dividends, new products, potential of the industry and the like. Technical analysts use charts to identify price patterns and market trends in financial markets and attempt to exploit those patterns. Technicians study technical indicators, momentum, and look for forms such as lines of support, resistance, channels and more obscure formations such as flags, pennants, balance days and cup and handle patterns. Contrasted with fundamental analysis, technical analysis holds that the prices already reflect all such trends before investors are aware of them. Uncovering those trends is what technical indicators are designed to do, imperfect as they may be. Some traders use technical or fundamental analysis exclusively, while others use both types to make trading decisions. Technical analysts do not attempt to measure a security's intrinsic value, but instead use various technical indicators to identify patterns that can suggest future activity…

As we have noticed in Section 5.4, the paired trading needs successful execution of four orders for two assets. Therefore, it is natural to ask if a trader can make profit just from repeatedly trading one single financial derivative. There is a big debate on profitability of market timing.We are not interested in taking part in this debate but have a remark as follows. Investors use day or month as the timescale to see the change of the fundamentals, while the time unit is a seconds in high-frequency trading (HFT). When the time is measured by a seconds, the most information one can based on is the momentum shown by technical indicators. From mathematical point of view, the only available information is the stationarity of certain pattern, which can be justified by statistics…

The bid-ask spread is the difference between the prices quoted for an immediate purchase (ask) and an immediate sell (bid). In Section 3.2.2, we have a few graphs to show the relative position of bid-ask-last price. For the statistical arbitrage using paired products, one needs to buy at the ask price and to sell at the bid price to increase the rate of successes. However, the profit of each trade is so thin in high-frequency trading (HFT). When one trade Chinese stocks index futures contracts, one tick (0.2 point) of difference will be roughly the profit of each trade. Thus, it is natural to ask if there is other way to give the trading order. That is an important problem in HFT…

The Financial Engineering (FE) is a multidisciplinary field involving financial theory, the methods of engineering, the tools of mathematics and the practice of programming. It has also been defined as the application of technical methods, especially from mathematical finance and computational finance, in the practice of finance. A lot of high technology has been applied in FE, which is why one calls it as engineering. FE is quite different from traditional financial study. In broadest definition, anyone who uses technical tools in finance could be called a financial engineer, for example, any computer programmer in a bank or any statistician in a government economic bureau. However, most practitioners restrict the term to someone educated in the full range of tools of modern finance and whose work is informed by financial theory. It is sometimes restricted even further, to cover only those originating new financial products and strategies…

If you ever searched the phrase “day trader” online before this century, you would be told that more than 99% of day traders lost their money finally. This was possibly true at that time and is possibly partially true nowadays. The advance of science and technology changed all, including the definition of “day trader”. High-frequency trading (HFT) is one of those day trading activities…

The following sections are included:

• References
• Index