Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem

— We evaluate the average waiting time between observing the price of financial markets and the next price change, especially in an on-line foreign exchange trading service for individual customers via the internet. Basic technical idea of our present work is dependent on the so-called renewalreward theorem. Assuming that stochastic processes of the price change of markets could be regarded as a renewal process, we use the theorem to calculate the average waiting time of the process. In the conventional derivation of the theorem, it is apparently hard to evaluate the higher order moments of the waiting time. To overcome this type of difficulties, we attempt to derive the waiting time distribution Ω(s) directly for arbitrary time interval distribution (first passage time distribution) of the stochastic process PW (τ) and observation time distribution PO(t) of customers. Our analysis enables us to evaluate not only the first moment (the average waiting time) but also any order of...

• Type: Conference
• Year: 2007
• Where: FOCI
• Authors: Naoya Sazuka, Jun-ichi Inoue
• Keywords: Applied Computing, Average Waiting Time, FOCI 2007, Observation Time Distribution, Time Distribution