Transmission of Trading Orders through Communication Line with Relativistic Delay

Peter B Lerner

doi:10.3390/ijfs9010012

Abstract

The notion of “relativistic finance” became ingrained in the public imagination and has been asserted in many mass-media reports. However, despite an observed drive of the most reputable Wall Street firms to establish their servers ever closer to the trading hubs, there is surprisingly little concrete information related to the relativistic delay of the trading orders. There is an underlying assumption that faster electronics are always beneficial to the stability of the network. In this paper, the author proposes a modified M/M/G queue theory to describe the propagation of the trading signal with finite velocity. Based on this theory, we demonstrate that, even if the reaction time of the system is negligible, the propagating signal is distorted by simple acts of trading along the transmission line.

Highlights

High-frequency trading (HFT) became feasible and popular with the advent of cheap, relocated computing power and memory
The opportunity provided by the modern technology leads to faster and faster trading, until the time of reaction of electronics became small with respect to the relativistic time of propagation of signal between major financial centers (New York–Chicago, 3.8 ms; New York–London, 18.7 ms; New York–Tokyo, 36.2 ms)
The characteristic time of the first response to a trading signal is τ ≈ 2–3 ms, which roughly corresponds to the computer messages cycling the circumference of New York City and vicinity with the speed of light (Hasbrouck 2016)

Summary

Introduction

High-frequency trading (HFT) became feasible and popular with the advent of cheap, relocated computing power and memory. Unlike a standard queue theory, we introduce a signed measure to describe the propagation of quotes. This change, trivial in our context, makes a big difference if a network has a non-trivial topology, the case currently under investigation. We obtain, in the simplest case of a one-share quote submission, a system of two integrodifferential equations, which can be solved part analytically and part numerically. This system explicitly contains the speed of signal propagation, as well as the delay time in a trading network. Despite an observed drive of the most reputable Wall Street firms to establish their servers ever closer to the trading hubs, concrete information related to the relativistic delay of the trading orders is surprisingly scarce

Literature Review

Representation of the Propagating Signal

Discussion

Conclusions