گذار در توزیع انتظار ـ زمان رویدادهای قیمت ـ تغییر در یک نظام اجتماعی و اقتصادی جهانی
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|14798||2013||12 صفحه PDF||سفارش دهید||7012 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Volume 392, Issue 24, 15 December 2013, Pages 6458–6469
The goal of developing a firmer theoretical understanding of inhomogeneous temporal processes–in particular, the waiting times in some collective dynamical system–is attracting significant interest among physicists. Quantifying the deviations between the waiting-time distribution and the distribution generated by a random process may help unravel the feedback mechanisms that drive the underlying dynamics. We analyze the waiting-time distributions of high-frequency foreign exchange data for the best executable bid–ask prices across all major currencies. We find that the lognormal distribution yields a good overall fit for the waiting-time distribution between currency rate changes if both short and long waiting times are included. If we restrict our study to long waiting times, each currency pair’s distribution is consistent with a power-law tail with exponent near to 3.5. However, for short waiting times, the overall distribution resembles one generated by an archetypal complex systems model in which boundedly rational agents compete for limited resources. Our findings suggest that a gradual transition arises in trading behavior between a fast regime in which traders act in a boundedly rational way and a slower one in which traders’ decisions are driven by generic feedback mechanisms across multiple timescales and hence produce similar power-law tails irrespective of currency type.
From human communications and conflicts to protein production, a wealth of studies has recently appeared in the physics literature concerning the underlying dynamics of complex processes across the biological and socioeconomic sciences , , , , , ,  and . The task of developing a theory for the timing of events in socioeconomic systems is a particularly daunting one, since inherent feedback processes operate across multiple timescales; yet it is precisely this complexity in time which makes the problem such an attractive one for the statistical physics community, and one in which the statistical physicist’s toolbox may prove useful in practice. Indeed, many important everyday problems can be reduced to predicting the timing of the next event in a series of such events. This situation is particularly acute in the world’s global markets, since a decision to buy or sell can rapidly turn bad if the collective action of the other market participants produces an unfavorable price change either before or during the fulfillment of the trade. Here, we pursue this physics-driven goal of developing a mechanistic understanding of intermittent collective processes, by focusing on arguably the world’s largest socioeconomic system—the foreign exchange (FX) market , ,  and . This market handles an average daily trading volume of over four trillion US dollars. Moreover, it is a decentralized market in which financial centers around the world act as trading hubs for the buying and selling of currencies, with continuous operation from 20:15 Greenwich Mean Time (GMT) on Sunday until 22:00 GMT Friday . The FX market consists of a diverse collection of buyers and sellers: diverse both in trading behavior and geographic location. It is their collective activity which determines the relative value of currencies at any point in time , ,  and . We specifically investigate the time between price changes across multiple currencies. This is an easily measurable characteristic of a price series. Furthermore, being able to accurately model such a variable has significant practical value. Any trader who has placed a resting order at the best price has a dilemma: Should they cancel their resting order and aggress the resting liquidity on the opposite side of the book? If they do so, they incur a known transaction cost; if they do not, their resting order may be filled (resulting in a zero transaction cost) but the price may also move against them—potentially resulting in a significantly greater transaction cost. The respective merits of the two options will be strongly influenced by how long the trader believes it will be until the best price changes. A better understanding of the characteristics of this waiting-time distribution would enable this decision to be better informed. In addition to the practical interest in this particular question within the finance industry, and the rapidly growing interest within the physics community concerning waiting times in collective processes, other applications include manufacturing where the distribution of failure times has proved to be an important risk control tool . In particular, fat-tailed distributions can give rise to large fluctuations in the waiting time which exceed the mean value by many standard deviations. However, modeling the fine-grained details of human trading systems poses significant problems. There are strong and poorly understood feedback effects inherent in the system, since each decision to place or cancel an order by one market participant can influence the future behavior of all other market participants. This complex feedback remains only partially understood, both within physics and in the wider finance community. As a result, accurate models for the microstructure of such markets have so far eluded researchers. (See Ref.  for a detailed review.) However, there is still significant value in a model which, while known to be imperfect, is a quantitatively reasonable approximation to reality—particularly if this model is mathematically tractable. Clearly, how good a model needs to be will depend upon what the model will be used for. For example, those engaged in ultra-high-frequency trading will need to have a more sophisticated and in-depth understanding of the complex feedback mechanisms between orders placed within milliseconds of each other than will a trader who places orders at a much lower frequency. Pinning down the precise form of the waiting-time distribution for different currencies requires reliable trading data on a fine-grained timescale. This is made difficult by the fact that the ‘price’ shown in commercially supplied data may actually be a hybrid of quoted prices, instead of something truly representative of supply and demand, such as best bid–ask executable prices. Here, we avoid this issue using a unique dataset of best bid–ask executable prices on a second-by-second scale for all the major currencies, captured by the global FX trading desk at HSBC Bank, which is one of the world’s largest FX trading institutions. We consider three commonly suggested waiting-time distributions: the exponential distribution, the Weibull distribution, and the lognormal distribution. Of these candidates, the lognormal distribution gives the best fit to the observed data. By contrast, if we restrict our study to longer waiting times, the distribution is well described statistically by a power law, with each currency pair exhibiting a power-law exponent αα which is clustered around 3.5. For the regime of short waiting times up to approximately 11 s, the waiting-time distribution takes on a different form, which can be reproduced by a modified version of Arthur’s El Farol bar problem, an archetypal complex systems model in which boundedly rational agents compete for limited resources . Taken overall, our findings suggest that there is a crossover in trading behavior between the scale of a few seconds and the scale of minutes and beyond. We speculate that this crossover accompanies a transition between the fast second-to-second regime in which traders act in a boundedly rational way (hence generating El Farol-like dynamics ), and a slower regime in which feedback drives more considered decisions across multiple timescales (hence generating a power law). Our paper is structured as follows. Section 2 briefly reviews the literature related to financial market activity and the waiting-time distribution, while Section 3 describes the source of our data. Section 4 briefly discusses the statistical methods and corresponding models adopted in the paper, while Section 5 provides the results of the distribution fitting process and the statistical tests. Section 6 introduces a multi-agent model which mimics the market dynamics for short waiting times. Section 7 provides concluding remarks and a perspective for future work.
نتیجه گیری انگلیسی
We have obtained various results which help clarify the physical nature of intermittent processes in the world’s largest socioeconomic system. Specifically, we have explored fitting the exponential distribution, the Weibull distribution, and the lognormal distribution to the entire distribution of waiting times between executable price changes across the major currencies in the FX market, and also fitting a power-law distribution to the tail of these waiting-time distributions. We presented an agent-based model, showing that it provides a good fit for the short-waiting-time regime as well as being able to interpret the underlying parameters in terms of the properties of the individual trading entities (e.g., their memory mm and the number of strategies ss). By contrast, for long waiting times, we found that the distribution for each currency pair exhibits a power law with exponent around 3.5. This unexpected transition in the distribution as we move from short to long waiting times requires further investigation to assign a unique explanation. However, we speculate that it arises because the regime of short waiting times is dominated by traders (and algorithms) operating with little time for processing information, and hence tends to be driven by bounded rationality trading strategies as in the El Farol bar problem. By contrast, the regime of longer waiting times allows a wide range of analyses from naive to complex, and hence is liable to give rise to feedback processes across multiple timescales—and hence power-law behavior in which there is by definition no fixed single timescale. We stress that, when exploring the power-law distribution, we made sure to use the rigorous statistical testing procedure introduced by Clauset et al. . In addition to the intrinsic interest within the field of statistical physics, our findings should prove to be of interest to researchers studying the theoretical pricing of exotic securities, and for designing algorithmic trading strategies for liquidation, for example, how to break a large position into small pieces in order to disguise the overall trade.