dorsal/arxiv
View SchemaWaiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem
| Authors | Naoya Sazuka, Jun-ichi Inoue |
|---|---|
| Categories | |
| ArXiv ID | physics/0702003 |
| URL | https://arxiv.org/abs/physics/0702003 |
Abstract
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 renewal-reward theorem. Assuming that stochastic processes of the market price changes 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 Omega(s) directly for arbitrary time interval distribution (first passage time distribution) of the stochastic process P_{W}(tau) and observation time distribution P_{O}(t) of customers. Our analysis enables us to evaluate not only the first moment (the average waiting time) but also any order of the higher moments of the waiting time. Moreover, in our formalism, it is possible to model the observation of the price on the internet by the customers in terms of the observation time distribution P_{O}(t). We apply our analysis to the stochastic process of the on-line foreign exchange rate for individual customers from the Sony bank and compare the moments with the empirical data analysis.
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"abstract": "We evaluate the average waiting time between observing the price of financial\nmarkets and the next price change, especially in an on-line foreign exchange\ntrading service for individual customers via the internet. Basic technical idea\nof our present work is dependent on the so-called renewal-reward theorem.\nAssuming that stochastic processes of the market price changes could be\nregarded as a renewal process, we use the theorem to calculate the average\nwaiting time of the process. In the conventional derivation of the theorem, it\nis apparently hard to evaluate the higher order moments of the waiting time. To\novercome this type of difficulties, we attempt to derive the waiting time\ndistribution Omega(s) directly for arbitrary time interval distribution (first\npassage time distribution) of the stochastic process P_{W}(tau) and observation\ntime distribution P_{O}(t) of customers. Our analysis enables us to evaluate\nnot only the first moment (the average waiting time) but also any order of the\nhigher moments of the waiting time. Moreover, in our formalism, it is possible\nto model the observation of the price on the internet by the customers in terms\nof the observation time distribution P_{O}(t). We apply our analysis to the\nstochastic process of the on-line foreign exchange rate for individual\ncustomers from the Sony bank and compare the moments with the empirical data\nanalysis.",
"arxiv_id": "physics/0702003",
"authors": [
"Naoya Sazuka",
"Jun-ichi Inoue"
],
"categories": [
"physics.data-an",
"physics.soc-ph",
"q-fin.ST"
],
"title": "Waiting time analysis of foreign currency exchange rates: Beyond the renewal-reward theorem",
"url": "https://arxiv.org/abs/physics/0702003"
},
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