The rise of the machines in commodities markets: new evidence obtained using Strongly Typed Genetic Programming

Abstract

Market regulators around the world are still debating whether or not high-frequency trading (HFT) is beneficial or harmful to market quality. We develop artificial commodities market populated with HFT scalpers and traditional commodities traders using Strongly Typed Genetic Programming (STGP) trading algorithm. We simulate real-life commodities trading at the millisecond timeframe by applying STGP to the S&P GSCI data stamped at the millisecond interval. We observe that HFT scalpers anticipate the order flow leading to severe damages to institutional traders. To mitigate the negative implications of HFT scalpers on commodities markets, we propose a minimum resting trading order period of more than 150 ms.

Appendices

Appendix 1

1.1 Strongly Typed Genetic Programming

Strongly Typed Genetic Programming (STGP) is a more sophisticated version of Genetic Programming (GP) whose application of generic functions and data types makes it more sophisticated than GP. GP represents a machine-learning method to automate the development of computer programs in terms of natural evolution (Banzhaf et al. 1998). If there are inputs X and outputs Y, a program p is generated which satisfies $Y=p(X)$ . In nearly all GP models, the programs are organized as tree genomes. For example, Fig. 1 shows a tree which describes a mathematical expression that uses the input variables $x=(a,b,c)$ where $x\in X$ . The leaf nodes of the tree in Fig. 1 are the terminals whereas the non-leaf nodes are known as non-terminals. Terminals are usually inputs to the program with no argument and the non-terminals are functions often represented with at least one argument.

Fig. 1

STGP program tree genomes (Copied from Wappler and Wegener 2006)

The fitness function of trading rules of 10,000 HFT scalpers and 90,000 traditional commodities traders are based on its ability to satisfy $Y=p(X)$ . If $Y_{\exp }$ is the expected known output and $Y_{P}$ the actual output generated by a program p with $Y_p =p(X)$, the fitness function f(p) of p has been calculated as:

$$\begin{aligned} f(p)=\sum _{i=1}^{|X|} {(p(x_i )-y_{{\exp }_{i}} )} \end{aligned}$$

(23)

Usually the nodes of the GP tree are not typed as Montana (2002) argues that many GP procedures can be formulated in a more efficient programming way by implementing a typing mechanism for GP nodes. In this way each node is connected to a particular return type and the process is known as Strongly Typed Genetic Programming (STGP). To create a parse tree one needs to take into account important additional programming criteria such as when the root node of the tree returns a value of the type required by the problem and each non-root node returns a value of the type required by the parent node as an argument (Montana 2002). While GP can be written in any programming language, the STGP is typically written in a specific programming language, which is a combination of Ada (Barnes 1982) and Lisp (Steele 1984) programming languages. The concept of generics as a method of developing strongly typed data is the critical component adopted from Ada. Additionally, Lisp incorporates the concept of having programs represented by their actual parse trees (Montana 1995).

While in conventional GP, one needs to specify all the programs and variables that can be used as nodes in a parse tree and deal with the search space of the order of $10^{30} - 10^{40}$. STGP however reduces the searching state-space size to a greater degree (Montana 1994). On the other hand, the STGP search space composes the set of all legal parse trees, which means that all functions have the correct number of parameters of the correct type. In most occasions the STGP parse tree is limited to a certain maximum depth (Table 1 illustrates that 20 is the maximum depth in the artificial commodities market in this study). We set the maximum depth to 20 in order to keep the search space finite and manageable, while not allowing the trees to grow to an extremely large size. The critical concepts in STGP are generic functions (a mechanism for specifying a class of functions), and the process of assigning generic data types for these functions (Haynes et al. 1995).

STGP has the flexibility to allow all variables, constraints, arguments and returned values to be of any type. The only strict requirement is that the type of data for each element has to be specified in the early stage of the programming process. The resulting initialization process and the various genetic operators associated with it are enabled to create syntactically correct trees. Those trees on the other hand are beneficial to the entire programming process because the search space can be significantly reduced (Haynes et al. 1996).

The STGP generates trading rules through the crossover and mutation operators. During the process of crossover, the return value type of the two selected subtrees for exchange are examined to find out whether they are from the same type and that the resulting trees are not breaching depth restrictions. In the case when either check fails, then two completely new subtrees are selected. If, after performing a finite number of selections, there are no valid crossover points, then the two parent trees are copied and transferred into the pool for the next generation (Koza 1992).

STGP trading rules for the HFT scalpers and traditional commodities traders can be described through the following crossover process. Similar to GP, randomly chosen parts of two trading rules are exchanged in order to create two new trading rules (Fig. 2).

Fig. 2

The process of crossover in STGP for generating new trading rules (Copied from Chakraborti et al. 2011)

Figure 2 illustrates that the trading strategies $S_{i}$ and $S_{j}$ are the two parents. The breaking point is based on random choice and then one-point crossover is applied to create new trading rules (children) $S_{k}$ and $S_{I}$.

The first generation of trading rules is created randomly to ensure that a large variety of possible trading rules is investigated at full capacity. The best performing trading rules from the initial selection are selected based on the Breeding Fitness return to act as parents in the crossover process. The Breeding Fitness return process represents a trailing return of a wealth moving average and is an integral part of the latency of HFT scalpers. This is in fact the return over the last n quotes of an exponential moving average of a trader’s wealth, where n could potentially have the maximum breeding value of 250. Each pair of parents generates two offspring trading rules, so the number of parents and the number of offspring are equal at all times.

In this innovative programming process the newly created trading rules replace those that are performing poorly in the initial selection based on the replacement fitness return. This type of return represents the average return of a wealth moving average per millisecond quote since the creation of the very first trading rule. In other words, this is the cumulative return of an exponential moving average of a trader’s wealth, divided by the trader’s breeding value.

Appendix 2

See Table 14.

Table 14 S&P GSCI futures daily trading volume generated by STGP trading algorithm