Large-scale simulations of synthetic markets

High-frequency trading has been experiencing an increase of interest both for practi- cal purposes within financial institutions and within academic research; recently, the UK Government Office for Science reviewed the state of the art and gave an outlook analy- sis. Therefore, models for tick-by-tick financial time series are becoming more and more important. Together with high-frequency trading comes the need for fast simulations of full synthetic markets for several purposes including scenario analyses for risk evaluation. These simulations are very suitable to be run on massively parallel architectures. Aside more traditional large-scale parallel computers, high-end personal computers equipped with several multi-core CPUs and general-purpose GPU programming are gaining importance as cheap and easily available alternatives. A further option are FPGAS. In all cases, development can be done in a unified framework with standard C or C++ code and calls to appropriate libraries like MPI (for CPUs) or CUDA for (GPGPUs). Here we present such a prototype simulation of a synthetic regulated equity market. The basic ingredients to build a synthetic share are two sequences of random variables, one for the inter-trade durations and one for the tick-by-tick logarithmic returns. Our extensive simulations are based on several distributional choices for the above random variables, including Mittag-Leffer distributed inter-trade durations and alpha-stable tick-by-tick logarithmic returns.