On-line trading as a renewal process: Waiting time and inspection paradox

TL;DR

This paper models online financial trading as a renewal process to evaluate average waiting times between price changes, highlighting the inspection paradox where observed durations are shorter than actual waiting times.

Contribution

It introduces a renewal process approach to estimate waiting times in online trading and discusses the inspection paradox in this context.

Findings

Average waiting time can be calculated using renewal-reward theorem.

The inspection paradox causes observed durations to be shorter than true waiting times.

Application to foreign exchange trading demonstrates practical relevance.

Abstract

We briefly review our recent studies on stochastic processes modelling internet on-line trading. We present a way to evaluate the average waiting time between the observation of the price in financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. The basic method of our approach depends on the so-called renewal-reward theorem. Assuming that the stochastic process modelling the price change is a renewal process, we use the theorem to calculate the average waiting time of the process. The so-called ``inspection paradox'' is discussed, which, in general, means that the average durations is shorter than the average waiting time.