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Statistical arbitrage volatility trading known holiday in forex market

What is Arbitrage?

For the case of the send coinbase to coinbase pro how to buy bitcoin without pain this fluctuations, the level of overall average of cross-correlations is marked again with horizontal black dotted line at a value of 0. At its most basic, arbitrage can be defined as the concurrent purchase and sale of similar assets in different markets in all technical indicators explained software south africa to take advantage of price differentials. This is the case for exchange rates related to CHF and GBP, and this is precisely what opens windows of opportunities for the triangular arbitrage. The approach adopted in the present study has been introduced by [ 41 ]. Gopikrishnan, P. The result is consistent for a range of timescales s taken in our approach. What is Arbitrage? Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. We have found that on average the cross-correlations of exchange rates for currencies in the triangular relationship are stronger than cross-correlations between exchange rates for currencies outside the triangular relationship. Vandewalle, N. In the latter validation method, the Fourier transform of the original time series is computed and then the inverse Fourier transform is applied to the retained amplitudes, but randomly mixed phases [ 141 ]. Typically, it exhibits small daily fluctuations of currency exchange rates. This time lag could be regarded as an estimate for the time duration of window of opportunity to execute an arbitrage opportunity. In the following, we will explore in some more details statistical properties of the Forex market data in the vicinity of these events. As a result, you will need to act quickly in order to take advantage of these trading opportunities. Ducascopy Bank SA.

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How Arbitrage Opportunities Occur

Philosophy of Complex Systems. Gopikrishnan, P. Each solid line of different color demonstrates the tail behavior for the corresponding currency. Such wide interest across different fields of research in application of detrended cross-correlation analysis to nonlinear time series studies serves as an additional strong motivation for elucidating such analysis in terms of its potential and limitations. However, we have to appreciate the fact that cross-correlations between any pair of exchange rates will have some impact on the cross-correlations of other pairs through mutual connections arising from different combinations of currencies being exchanged. The middle panel of Fig. Physica A , Download references. Reports on Progress in Physics, in press. Recently, a novel predictive framework for forecasting future behavior of financial markets has been proposed by [ 20 ]. Fluctuations of high-frequency exchange rates of eight major world currencies over — period are used to study cross-correlations. The evidence we have shown clearly indicates that the multifractal cross-correlation methodology should contribute significantly to predictive modeling of temporal and multiscale patterns in time series analysis. What is more, for the shortest timescale shown here, the difference between cross-correlations for pairs that are in the triangular relations and those that are not, is the biggest. The methodology could be applicable to temporal and multiscale pattern detection in any time series. Xiong, H. Finally, we summarize and draw some general conclusions. The cross-correlations of the large fluctuations are therefore approximately two times smaller than in the case of small correlations.

London 58— The resultant tails of the probability distributions are shown in the inset of Fig. What is Slippage? What is Volatility? The time evolution of averaged cross-correlations over currency pairs with the common base for large fluctuations will be discussed later cf. In Fig. In this case, the cross-correlations are in the triangular relation the top panel of Fig. Sign Up Now. For a reference, some important global political and economic events have been indicated over the timescale. The insets show that in fact the yahoo finance vwap most profitable ea metatrader 4 rates compared red and black curves were changing so rapidly that they could not follow each. The parameter q helps to identify the range of detrended fluctuation amplitudes corresponding to the most significant correlations for these two time series [ 41 ]. However, in reality we deal with enormous amounts of data flowing at very high rates in the Forex market and. Mantegna, R. In an analogous way, the second time series of interest, Y kis obtained out of the original time series y i. Shen, C. On the bottom-left and bottom-right panels, the results are unsorted making an easier task to identify particularly high cross-correlations shown with labels for each of the both cases, the triangular and non-triangular relationship. North Holland References 1. Financial Econ. When a questrade commercial non leveraged trading uses arbitrage, they are essentially buying a cheaper asset and selling it at a higher price in a different market, thereby taking a profit without any net cash flow. We also show the overall average for the statistical arbitrage volatility trading known holiday in forex market best bollinger band settings for day trading fidelity todays biggest option trades rate pairs complying to the triangular relation the black dotted line and for currency exchange rate pairs which are not bounded by the triangular relation red dotted line. The data used in the present study have been obtained from the Dukascopy Swiss Banking Group [ 31 ]. For instance, interest rate arbitrage is a popular way to trade on arbitrage in the currency marketby selling currency from a country with low-interest rates and, at the same time, buying plus500 account gold will forex trading end currency of a country that pays high-interest rates. In order to demonstrate the origin of these deviations, we remove from our data sets a period of a half an hour in the morning on January 15,when a significant volatility of currencies exchange rates has been observed in the wake of the SNB intervention [ 9 ].

Introduction

In an analogous way, the second time series of interest, Y k , is obtained out of the original time series y i. This strategy is aimed at exploiting relative price movements of thousands of financial instruments in different markets through technical analysis. An interesting observation follows that Australlian AUD and New Zealand NZD dollars are strongly correlated—they appear together in the same clusters of exchange rates for both the small and large fluctuations. Big data, data mining, machine learning, artificial intelligence, and an algorithmic high-frequency trading are in focus of quantitative finance [ 18 ]. In what follows, we briefly state main points of this approach. We define q -dependent detrended coefficient capturing cross-correlations of two detrended time series. Introduction Dynamics of complex systems, which are typically described by many degrees of freedom and a nonlinear internal structure, as well as their specific response to significant changes in the environment are within a research focus of many areas in fundamental and applied sciences, including mathematical, physical, biological and economic sciences [ 1 ]. Seminal papers elucidating intricate complex dynamics of the foreign exchange market on short timescales include turbulent cascade approach [ 4 ], motivated by hierarchical features in hydrodynamics of turbulence, as well as those referring to multi-affine analysis of typical currency exchange rates [ 5 ] and also their sparseness and roughness [ 6 ]. In this case, the cross-correlations are in the triangular relation the top panel of Fig. Rodgers, J. Typically, we thus have approximately 2. For a reference, some important global political and economic events have been indicated over the timescale. Statistical arbitrage is derived from a collection of quantitative algorithmic investment strategies.

This somewhat unexpected result could be ascribed to mechanisms coupling economies of these two countries. Following the idea of a new cross-correlation coefficient defined in terms of detrended fluctuation analysis DFA and detrended cross-correlation analysis DCCA —[ 32 ], which has been put forward in [ 33 ], we use in the present study a multifractal detrended cross-correlation analysis MFCCA [ 34 ] with q -dependent cross-correlation coefficient. We note that all currency exchange rates with the Swiss franc CHF as base currency yield higher probability of larger absolute logarithmic returns than other exchange rates. In such a way, a pair of statistical arbitrage volatility trading known holiday in forex market is intrinsically correlated by JPY currency performance due to the triangular constraint in the exchange rates. Other methods, including weighted multifractal analysis of financial time series [ 37 ] and multiscale properties of time series based on the segmentation [ 38 ], allow for multifractal and multiscale nonlinear effects investigations. At its most basic, arbitrage can be defined as the concurrent purchase and sale of similar assets in different markets in order to take advantage of price differentials. The ultimate aim of statistical arbitrage is to generate higher than normal trading profits for larger investors. Multiscale multifractal detrended cross-correlation analysis MSMF—DXA has been proposed and subsequently employed to study dynamics of interactions in the stock market [ 36 ]. Now we are ready to construct an estimate of the covariance of both newly derived time series, each of which has those polynomial trends removed interval by interval:. Download citation. Don't miss out on the latest news and updates! Wang, F. Therefore, we may expect that occasionally, a significant fluctuation or even a temporally significant change in one exchange rate of any pair due to whatever reason will propagate to remaining pairs of currencies depending on the degree of cross-correlations between quotes for different currency pairs. Most recent works on uncovering patterns in foreign exchange markets include, but are not china forex forum warrior trading course download to, studies of lead-lag relationships [ 7 ], scaling relationships [ 8 ], multifractality and efficiency issues [ 910 ], partial correlations [ 11 ] or quote spreads in high-frequency trading [ 12 ]. Download references. This explains why averaged cross-correlations for such crypto software download makerdao fees pairs may be unexpectedly high cf. Instead, it is used for medium-frequency trading, with trading periods taking anywhere from a few hours to several days. In the latter validation method, the Fourier transform of the original time series is computed and then the inverse Fourier transform is applied to the retained amplitudes, but randomly mixed phases [ 141 ].

What is Arbitrage?

In this strategy, an investor will buy a currency and will then short the same currency in the futures market. Physica A , The results section comprises global behavior of currency rates, logarithmic return rates statistics with the focus on large fluctuations, discussion of hierarchy among currency exchange rates and the role of abrupt cross-correlation changes and large fluctuations in detecting arbitrage opportunities. All events indicated by values greater than 0 in fact could potentially offer triangular arbitrage opportunities. Finally, the bottom panel illustrates rather weak chance of exploiting triangular arbitrage opportunity—there is only one very brief in time instance when in theory this might be possible. Energy Econ. Any information or event having impact on one currency value will propagate through the Forex market by means of adjusting various other exchange rates, which could be envisaged as a sort of local pairwise currency interactions which eventually should influence globally all the currencies traded in the Forex market. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. E 84 , The indicative and executable prices differ typically by a few basis points [ 13 , 14 ]. This gives us some idea about the information propagation time through the Forex market, which is the time needed to reflect the maximum average cross-correlation between any pair of exchange currency rates. Although in our study we focus on different signatures and statistical properties of multivariate time series with respect to triangular arbitrage, one may envisage a broader picture of such analysis, whereby one would like to uncover a specific kind of cross-correlations in these time series which would help us to detect underlying interconnections useful for the system behavior prediction in future. Conclusions We have investigated currency exchange rates cross-correlations within the basket of 8 major currencies.

The results are shown in Fig. Don't miss out on the latest news and updates! Miller, T. Some pairs from outside triangular relations are, however, identified to be exceptionally strongly correlated as compared to the average strength of triangular correlations. We would like to emphasize that our method based on detrended cross-correlation analysis is quite novel and only recently a plethora of applications started to emerge across many fields of nonlinear correlations studies, including meteorological data [ 22 ], electricity spot market [ 23 ], effects of weather on agricultural market [ 24 ], stock markets [ 25 ], best bitcoin exchange fees coinbase ripple address markets [ 26 statistical arbitrage volatility trading known holiday in forex market, electroencephalography EEG signals [ 27 ], electrocardiography ECG and arterial blood pressure [ 28 ] as well as air pollution [ 2930 ]. Such events and the resultant opportunities indeed have been identified in the historical trading data for the period — Physica A The approach adopted in the present study has been introduced by [ 41 ]. The cross-correlations are quantified to be stronger on average between those exchange rate pairs that are bound within triangular relations. Hence without this single, short-termed event on the market, the tails of the distributions approximately follow the inverse-cubic behavior. E 91R Handbook of Philosophy of Science, vol. Let us first consider a model situation where we can instantly carry out a sequence of transactions with exchange rates, which all of them are known for a given time instance t. Then, we describe fundamental concepts of our statistical methods, which stem from multifractal formalism. In such a way, the bitmex best exchange goldman sachs trading bitcoin arbitrage opportunities have arisen. We also show the overall average for the currency exchange rate pairs complying to the triangular relation the black dotted line and for currency exchange rate pairs which are not bounded by ameritrade initial deposit express 30 mins account and profit and loss account triangular relation red dotted line. B 3— Such dendrograms may have important applications related to hedging, risk optimization, and diversification of the currency portfolio in the Forex market.

E 8 , We already know that the outliers of the cumulative distributions document an increased level of larger fluctuations in absolute log-returns. E 84 , Ducascopy Bank SA. Shen, C. With such a single averaged characteristics, one may have a general overview of a global temporal behavior and performance of any currency in the Forex market. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Grech, D. This indicates a possibility of building strong cross-correlations between exchange rate pairs which do not have the same common base. What is more, for the shortest timescale shown here, the difference between cross-correlations for pairs that are in the triangular relations and those that are not, is the biggest. Instead, it is used for medium-frequency trading, with trading periods taking anywhere from a few hours to several days. The insets show that in fact the exchange rates compared red and black curves were changing so rapidly that they could not follow each other.

Color online Dendrograms corresponding to Fig. The tails of the cumulative distributions of the high-frequency intra-day quotes exhibit non-Gaussian distribution of the rare events by means of the so-called fat tails large fluctuations. Such cross-correlations at least between two exchange rate time series would offer a potential opportunity of triangular arbitrage. For this plot, we take logarithmic returns deviation indicators thinkorswim twap tradingview from average bid and ask exchange rates. Additionally, for the reference both insets in Fig. Globally Regulated Broker. Search SpringerLink Search. In general, it could be a polynomial of any finite degree, depending on the nature of the signal. Miller, T. The results section comprises global behavior of currency rates, logarithmic return rates statistics with the focus on large fluctuations, discussion of hierarchy among currency exchange rates and the role of abrupt cross-correlation changes and large fluctuations in angl stock dividend questrade portfolio iq offer code arbitrage opportunities. Let us first consider a model situation where we can instantly carry out swing trading vertical debit spreads can you buy stocks through your bank sequence of transactions with exchange rates, which all of them are known for a given time instance t. Xiong, H. The arbitrage opportunities are very closely related to large fluctuations which tend to be more pronounced in the longer timescales s. E 95 Twitter data stock market fractal indicator tradingview data used in the present study have been obtained from the Dukascopy Swiss Banking Group [ 31 ].

Podobnik, B. Sign Up Now. ST] Such enormous amounts of data have to be effectively analyzed for promising patterns down to a level of small fluctuations over small timescales. For a reference, some important global political and economic events have been indicated over the timescale. In practice, however, this is difficult on real markets and in fact after the first leg of such multiple transactions, remaining trades would not be possible to complete or the price will be changed by the time they will be completed. If both time series are the same, we obtain an estimate of the detrended variance in the k -th interval from partitioning with the scale s. Chaos Solitons Fractals 88 , — We already know that the outliers of the cumulative distributions document an increased level of larger fluctuations in absolute log-returns. A similar conclusion is valid when considering GBP or JPY taken as the base currency—corresponding curves have a maximum in Instead, it is used for medium-frequency trading, with trading periods taking anywhere from a few hours to several days. In what follows, we briefly state main points of this approach. Thus, the distance for agglomerative hierarchical trees takes the following form:. Download PDF. Following the idea of a new cross-correlation coefficient defined in terms of detrended fluctuation analysis DFA and detrended cross-correlation analysis DCCA —[ 32 ], which has been put forward in [ 33 ], we use in the present study a multifractal detrended cross-correlation analysis MFCCA [ 34 ] with q -dependent cross-correlation coefficient.

Therefore, one can define a q -dependent detrended cross-correlation q DCCA coefficient using where to buy bitcoin 2009 debit card coinbase time family of such fluctuation functions [ 41 ]:. In what follows, we briefly state main points of this approach. For a given timescale swe may repeat the partitioning procedure from the other end of the time series, thus obtaining in total 2 M s time intervals, each of which will contain s data points. Wiley, New York Open a trading account in 1 minute Take advantage of trading opportunities. A similar conclusion is valid when considering GBP or JPY taken as the base currency—corresponding curves have a maximum in Financial Econ. As a result of adopting the distance given by Eq. What is a Currency Swap? Thus, the distance for agglomerative hierarchical trees takes the following form:. This could mean that the sudden overnight increase in the rates by the Bank of Canada in did not have longer lasting effect and was only causing very short term effect. The Forex market determines currency exchange rates between statistical arbitrage volatility trading known holiday in forex market traded pair of currencies through a complex and nowadays mostly machine-driven automatic system of multiple type transactions among different kinds of buyers and sellers round-the-clock. Big data, data mining, machine learning, artificial intelligence, and an algorithmic high-frequency trading are in focus of tradingview eth bt fundamental analysis for stock investment finance [ 18 ]. An interesting observation follows that Australlian AUD and New Zealand NZD dollars are strongly correlated—they appear together in the same clusters of exchange rates for open free brokerage account high dividend pipeline stocks the small and large fluctuations. Accepted : 28 October The inset shows these distributions when a short period of an extreme volatility in currency exchange rates has been removed. Cui, Z. Finally, the bottom panel illustrates rather weak chance of exploiting triangular arbitrage opportunity—there is only one very brief in time instance when in theory this might be possible. Fan, Q. Sign Up Now.

The black dotted horizontal line on the top-left panel shows the average cross-correlation of different pairs pertaining to the triangular relation. As a result of adopting the distance given by Eq. E 95 North Holland We have found that on average the cross-correlations of exchange rates for currencies in the triangular relationship are stronger than cross-correlations between exchange rates for currencies outside the triangular relationship. Nonetheless, the small fluctuations in logarithmic returns would be difficult to use in viable trading strategies, mainly due to finite spreads in bid and ask rates. Another variation on the trade of negative spread is triangular arbitrage. Arbitrage allows a trader to exploit price discrepancies in assets, but this requires speed and adequate algorithms. The present study of complexity in a system behavior is focused on the financial trade futures demo account cryptocurency charts with multicale signatures of wyckoff trading course pdf c-cex trade bot response to some major events influencing currency exchange rates. E 8

Reports on Progress in Physics, in press Noise Lett. A similar conclusion is valid when considering GBP or JPY taken as the base currency—corresponding curves have a maximum in For example, if a trader thinks that Amazon is overvalued, and Facebook is undervalued, they will open a long position on Amazon and at the same time, a short position on Facebook. In the figure, we have indicated some political or economic events on the timescale with dotted vertical line which in principle could have impact on the Forex market performance during that period of time. The most striking feature when comparing the small and large fluctuation cross-correlations over different timescales is that in the former case little is happening over different timescales considered. Ethics declarations Conflict of interest The authors declare that they have no conflict of interest. The periods of extreme variation of exchange rates are shown in the corresponding insets of Fig. Such findings are important when designing the trading strategies, both for optimizing portfolio and for its hedging. Preprint at: arXiv Attempts to predict changes in financial time series from correlation-based deep learning have been quite promising [ 19 ].

In the latter validation method, the Fourier best forex chat rooms tight stop loss forex of the original time series is computed and then the inverse Fourier transform is applied to the retained amplitudes, but randomly mixed phases [ 141 ]. Accessed 29 March 3. The evidence we have shown clearly indicates that the multifractal cross-correlation methodology should contribute significantly to predictive modeling of temporal and multiscale patterns in time series analysis. If both time series are the same, we obtain an estimate of the detrended variance in the k -th interval from partitioning with the scale s. Let us consider multiple time series of exchange rates recorded simultaneously. The otc news stock uplisting news how to invest in stock market as a student of currency pairs in the bottom panels is kept the same as in the top panels. According to the recent foreign exchange statistics published by the Bank for International Settlements, the averaged daily trade volume exceeded 5 trillion US dollars in Aprilwith currencies mostly traded including US dollars, euros and Japanese yens see—[ 2 ]. Statistical arbitrage is derived from a collection of quantitative algorithmic investment strategies. Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis. Triangular arbitrage in the Forex market Let us first consider a model situation where we can instantly carry out a sequence of transactions with exchange rates, which all of them are known for a given time instance t. Safe and Secure. Dominant multiscale cross-correlations between the exchange rates are found to typically occur at smaller fluctuation levels. Reprints and Permissions. What is Volatility? The tails of the cumulative distributions of the high-frequency intra-day quotes exhibit non-Gaussian distribution of the rare events by means of the so-called fat tails large fluctuations. In an analogous way, the second time series of interest, Y kis trading profits margin interest tips for relaxing futures trading out of the original time series y i.

Physica A , 17—27 Zhao, L. Finance From the data shown in Fig. Color online Dendrograms corresponding to Fig. What is Volatility? Ghosh, I. The growth of the overall average of cross-correlation is even more convincing for the class of pairs of currency exchange rates which are not in a strict triangular relation. Data and financial time series methodology The data used in the present study have been obtained from the Dukascopy Swiss Banking Group [ 31 ]. E 77 ,

Noise Lett. Next, we discuss a degree of triangular arbitrage opportunity in a form of a convenient coefficient derived from suitable should i invest in home depot stock crypto chat webull rates. The net difference in the two interest rates is the trading profit. Currency arbitrage occurs when financial traders use price discrepancies in the money markets to take a profit. The different spreads will create a difference in the bid and ask prices, enabling a trader to take advantage of the different rates. Big data, data mining, machine learning, artificial intelligence, and an algorithmic high-frequency trading are in focus of quantitative finance [ 18 ]. Fan, Q. Based on the methodology described, we will investigate multiscale properties for cross-correlations among time series corresponding to currency exchange rates option strategy insider banknifty intraday chart the whole period — as well as for some sub-periods. If both time series are the same, we obtain tetra tech stock forecast tradestation remove trade history chart estimate of the detrended variance in the k -th interval from partitioning with the scale s. Thus, we have in the data set all 28 exchange rates bid and ask prices among the set of 8 currencies. In order to identify promising arbitrage opportunities e. Here, the trader is taking advantage of different spreads offered by different brokers for a specific currency pair. The cross-correlations of the large fluctuations are therefore approximately two times smaller than in the case of small correlations. This in turn may have some consequences for design of statistical arbitrage volatility trading known holiday in forex market smart learning methods for neural networks and a general computational intelligence in predicting a future behavior of complex systems.

We can apply our procedure to randomly shuffled original data. Logarithmic returns and the inverse cubic law In this subsection, we will present a general picture for the financial time series dynamics with an emphasis on events which have an impact on the Forex market. Let us assume that a trader holds initially euros EUR. Color online Currency indexes as defined by Eq. We also show the overall average for the currency exchange rate pairs complying to the triangular relation the black dotted line and for currency exchange rate pairs which are not bounded by the triangular relation red dotted line. Dynamics of complex systems, which are typically described by many degrees of freedom and a nonlinear internal structure, as well as their specific response to significant changes in the environment are within a research focus of many areas in fundamental and applied sciences, including mathematical, physical, biological and economic sciences [ 1 ]. What is Slippage? This removed period a half an hour corresponds to the wake of the SNB intervention on January 15, Noise Lett. Accessed 15 Jan The magnitude of this cross-correlation measure is weakly dependent on the timescale and only slightly grows with time. The currency index given by Eq. We already know that the outliers of the cumulative distributions document an increased level of larger fluctuations in absolute log-returns. Financial Econ. Thus, the distance for agglomerative hierarchical trees takes the following form:.

This gives an idea about the range of obtained values of cross-correlation coefficient distributions for the currency pairs which are in or out the triangular relation. Additionally, for the reference both insets in Fig. This indicates a possibility of building strong cross-correlations between exchange rate pairs which do not have the same common base. Robinhood app revenue fx trading investment ai bot interesting feature of the Forex market is related to the cumulative distribution of absolute logarithmic returns:. It is worth noting that to the best of our knowledge, it is the first ever such use of the cross-correlation q -coefficient as a way to induce measure for creating a hierarchy tree a dendrogram. Energy Econ. For example, since we have demonstrated feasibility of financial trump pot stocks ishares msci eafe minimum volatility etf isin series analysis against favorable autotrade day trade scalp call covered warrant definition, we may expect future advancement in computer algorithms for financial engineering when trading tick-by-tick data are available in real time. The inset shows these distributions when a short period of an extreme volatility in currency exchange rates has been removed. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. The paper is organized as follows. The result is consistent for a range of timescales s taken in our approach.

Vandewalle, N. Pearson, K. We also show the overall average for the currency exchange rate pairs complying to the triangular relation the black dotted line and for currency exchange rate pairs which are not bounded by the triangular relation red dotted line. In general, one observes significant variations of considered currency indexes over the period of 8 years. Reprints and Permissions. It is worth noting that statistical arbitrage does not lend itself to high-frequency trading. The Forex market is highly liquid market due to its massive trading and asset volume. Next, we discuss a degree of triangular arbitrage opportunity in a form of a convenient coefficient derived from suitable exchange rates. We have looked already into the cross-correlations within fluctuation magnitude domain. Any temporal discrepancy between exchange rates for such two pairs of currencies, with one currency in common, would offer immediately an opportunity to make a profit just by means of using this window of opportunity due to favorable exchange rates. The arbitrage opportunities are very closely related to large fluctuations which tend to be more pronounced in the longer timescales s. This in turn may have some consequences for design of new smart learning methods for neural networks and a general computational intelligence in predicting a future behavior of complex systems. Fan, Q. We note that all currency exchange rates with the Swiss franc CHF as base currency yield higher probability of larger absolute logarithmic returns than other exchange rates. What is a Market Cycle? In: Ghosh, D. In this strategy, an investor will buy a currency and will then short the same currency in the futures market. Hence, financial market studies are of interest from fundamental and practical point of view for a wide community of scientists, engineers and professionals, bringing together many branches of mathematics, physics, economy and computer sciences to address some challenging issues.

Finally, our conjecture is that during significant events e. The cross-correlation for currency exchange pairs outside the triangular relation in the case of large fluctuations in logarithmic return rates grows in time, which indicates propagation of correlations in time. Any temporal discrepancy between exchange rates for such two pairs of currencies, with one currency in common, would offer immediately an opportunity to make a profit just by means of using this window of opportunity due to favorable exchange rates. References 1. In such a way, the possible arbitrage opportunities have arisen. It indicates a possibility of observing stronger correlations in exchange rates among four currencies in comparison with what we would expect on average in the case of exchange rates linked with the triangular relations. Let us now investigate the cross-correlations in the time domain. Most recent works on uncovering patterns in foreign exchange markets include, but are not limited to, studies of lead-lag relationships [ 7 ], scaling relationships [ 8 ], multifractality and efficiency issues [ 9 , 10 ], partial correlations [ 11 ] or quote spreads in high-frequency trading [ 12 ]. The cross-correlations of the large fluctuations are therefore approximately two times smaller than in the case of small correlations. Finally, let us investigate closely these brief in time periods of arbitrage opportunities we have identified by our data analysis. That is we could end up with more currency EUR than we had initially. Lin, A.