# Key Roles of Crypto-Exchanges in Generating Arbitrage Opportunities

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Methodology

#### 3.1. Arbitrage Definition

- There are no taxes, i.e., $fe{e}_{i}^{c}=0$ and ${C}_{ij}^{c}=0$, for all crypto-currencies c and all exchanges $i,j=1,\dots ,N$;
- Taxes are taken into account, i.e., $fe{e}_{i}^{c}>0$ and ${C}_{ij}^{c}>0$, for all crypto-currencies c and all exchanges $i,j=1,\dots ,N$.

#### 3.2. Network Model of Arbitrage Flows

- Hubs and authorities are used to determine the relevance of crypto-exchange in the network [42]. A good hub represents a crypto-exchange having a terminal Buyer role (that points to many other exchanges), and a good authority represents a crypto-exchange having a terminal Seller role (that is linked by many different exchanges). The authority scores of the vertices are defined as the principal eigenvector of ${A}^{T}A$, while the hub scores of the vertices are defined as the principal eigenvector of $A{A}^{T}$. Recall that matrix A defines the adjacency matrix. The value of scores ranges between 0 to 1, where a larger value shows the higher importance of the crypto-exchange as a Seller or Buyer, respectively;
- PageRank centrality was introduced by the founders of Google to rank web-pages in search engine results. It is a variant of eigencentrality [43], but the importance of a vertex (crypto-exchange) is determined through the number of edges it receives, as well as the edge propensity and the centrality of its neighbors [44]. In mathematical terms, the Pagerank centrality is defined by:$${x}_{i}=\alpha \sum _{j}{A}_{ij}\frac{{x}_{j}}{{k}_{j}^{out}}+\beta ;$$
- Strength centrality is defined as the sum of edge values of the adjacent edges from each vertex [45]. For the network of crypto-exchanges, it describes overall arbitrage turnover of crypto-currency that has occurred in this exchange;
- Diversity measure shows a vertex’s connections to communities outside of its own community. Specifically, the vertex with many connections to other communities will have a higher diversity value [46]. Mathematically, the diversity of a vertex is defined as the Shannon entropy of the edge value (weights) of its incident edges:$${D}_{i}=-\sum ({p}_{ij}log\left({p}_{ij}\right),j=1\dots {k}_{i})/log\left({k}_{i}\right);$$
- Betweenness centrality can be understood as a probability of crypto-exchange to occur on a randomly chosen shortest path between two crypto-exchanges [47]. In case of application, crypto-exchanges with high betweenness centrality may have a considerable influence within a network by virtue of their role over flows passing between others. Formally, the betweenness of vertex i is defined as follows:$${B}_{i}=\sum _{j\ne k\ne i}\frac{{n}_{jk}^{i}}{{n}_{jk}}$$

#### 3.3. Canonical Correlation Analysis

## 4. Results

#### 4.1. Data

#### 4.2. Pairwise Analysis of Crypto-Exchanges

#### 4.3. Crypto-Network Topology Analysis

#### 4.4. Arbitrage Opportunities Excluding Bitcoin

#### 4.5. Relationship between Arbitrage and Some Crypto-Market Variables

## 5. Discussion

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

- Varian, H. The Arbitrage Principle in Financial Economics. J. Econ. Perspect.
**1987**, 1, 55–72. [Google Scholar] [CrossRef] [Green Version] - Billingsley, R.S. Understanding Arbitrage: An Intuitive Approach to Financial Analysis; Pearson Education, Inc.: Hoboken, NJ, USA, 2006. [Google Scholar]
- Herschberg, M. Limits to Arbitrage: An introduction to Behavioral Finance and a Literature Review. Palermo Bus. Rev.
**2012**, 7, 7–21. [Google Scholar] - Barberis, N.; Thaler, R. Chapter 18 A survey of behavioral finance. In Financial Markets and Asset Pricing; Handbook of the Economics of Finance; Elsevier: Amsterdam, The Netherlands, 2003; Volume 1, pp. 1053–1128. [Google Scholar] [CrossRef]
- Wątorek, M.; Drożdż, S.; Kwapień, J.; Minati, L.; Oświęcimka, P.; Stanuszek, M. Multiscale characteristics of the emerging global cryptocurrency market. Phys. Rep.
**2021**, 901, 1–82. [Google Scholar] [CrossRef] - Pele, D.T.; Wesselhöfft, N.; Härdle, W.K.; Kolossiatis, M.; Yatracos, Y. Phenotypic convergence of cryptocurrencies. In IRTG 1792 Discussion Paper 2019-018; Humboldt-Universität zu Berlin: Berlin, Germany, 2019. [Google Scholar]
- Tan, Z.; Huang, Y.; Xiao, B. Value at risk and returns of cryptocurrencies before and after the crash: Long-run relations and fractional cointegration. Res. Int. Bus. Financ.
**2021**, 56, 101347. [Google Scholar] [CrossRef] - Kurka, J. Do cryptocurrencies and traditional asset classes influence each other? Financ. Res. Lett.
**2019**, 31, 38–46. [Google Scholar] [CrossRef] [Green Version] - Kim, M.J.; Canh, N.P.; Park, S.Y. Causal relationship among cryptocurrencies: A conditional quantile approach. Financ. Res. Lett.
**2020**, 101879. [Google Scholar] [CrossRef] - Mokni, K.; Ajmi, A.N. Cryptocurrencies vs. US dollar: Evidence from causality in quantiles analysis. Econ. Anal. Policy
**2021**, 69, 238–252. [Google Scholar] [CrossRef] - Yarovaya, L.; Matkovskyy, R.; Jalan, A. The effects of a “black swan” event (COVID-19) on herding behavior in cryptocurrency markets. J. Int. Financ. Mark. Inst. Money
**2021**, 101321. [Google Scholar] [CrossRef] - Figá-Talamanca, G.; Focardi, S.; Patacca, M. Regime switches and commonalities of the cryptocurrencies asset class. North Am. J. Econ. Financ.
**2021**, 101425. [Google Scholar] [CrossRef] - Caporale, G.M.; Kang, W.Y.; Spagnolo, F.; Spagnolo, N. Non-linearities, cyber attacks and cryptocurrencies. Financ. Res. Lett.
**2020**, 32, 101297. [Google Scholar] [CrossRef] - Ghosh, A.; Gupta, S.; Dua, A.; Kumar, N. Security of Cryptocurrencies in blockchain technology: State-of-art, challenges and future prospects. J. Netw. Comput. Appl.
**2020**, 163, 102635. [Google Scholar] [CrossRef] - Ferdous, M.S.; Chowdhury, M.J.M.; Hoque, M.A. A survey of consensus algorithms in public blockchain systems for crypto-currencies. J. Netw. Comput. Appl.
**2021**, 182, 103035. [Google Scholar] [CrossRef] - Makarov, I.; Schoar, A. Trading and arbitrage in cryptocurrency markets. J. Financ. Econ.
**2020**, 135, 293–319. [Google Scholar] [CrossRef] [Green Version] - Shynkevich, A. Bitcoin arbitrage. Financ. Res. Lett.
**2020**, 101698. [Google Scholar] [CrossRef] - Hattori, T.; Ishida, R. The Relationship Between Arbitrage in Futures and Spot Markets and Bitcoin Price Movements: Evidence From the Bitcoin Markets. J. Futur. Mark.
**2021**, 41, 105–114. [Google Scholar] [CrossRef] - Krückeberg, S.; Scholz, P. Decentralized Efficiency? Arbitrage in Bitcoin Markets. Financ. Anal. J.
**2020**, 76, 135–152. [Google Scholar] [CrossRef] - Vidal-Tomás, D. Transitions in the cryptocurrency market during the COVID-19 pandemic: A network analysis. Financ. Res. Lett.
**2021**, 101981. [Google Scholar] [CrossRef] - Somin, S.; Altshuler, Y.; Gordon, G.; Pentland, A.S.; Shmueli, E. Network Dynamics of a Financial Ecosystem. Sci. Rep.
**2020**, 10, 4587. [Google Scholar] [CrossRef] [PubMed] - Aspembitova, A.T.; Feng, L.; Chew, L.Y. Behavioral structure of users in cryptocurrency market. PLoS ONE
**2021**, 16, e0242600. [Google Scholar] [CrossRef] [PubMed] - Caporale, G.M.; Kang, W.Y.; Spagnolo, F.; Spagnolo, N. Cyber-attacks, spillovers and contagion in the cryptocurrency markets. J. Int. Financ. Mark. Inst. Money
**2021**, 101298. [Google Scholar] [CrossRef] - Forbes, K.J.; Rigobon, R. No Contagion, Only Interdependence: Measuring Stock Market Comovements. J. Financ.
**2002**, 57, 2223–2261. [Google Scholar] [CrossRef] - Chen, Y.; Giudici, P.; Hadji Misheva, B.; Trimborn, S. Lead Behaviour in Bitcoin Markets. Risks
**2020**, 8, 4. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yilmaz, K. Better to give than to receive: Predictive directional measurement of volatility spillovers. Int. J. Forecast.
**2012**, 28, 57–66. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yılmaz, K. On the network topology of variance decompositions: Measuring the connectedness of financial firms. J. Econom.
**2014**, 182, 119–134. [Google Scholar] [CrossRef] [Green Version] - Diebold, F.X.; Yilmaz, K. Trans-Atlantic equity volatility connectedness: US and European financial institutions, 2004–2014. J. Financ. Econom.
**2015**, 14, 81–127. [Google Scholar] [CrossRef] [Green Version] - Ji, Q.; Bouri, E.; Kristoufek, L.; Lucey, B. Realised volatility connectedness among Bitcoin exchange markets. Financ. Res. Lett.
**2021**, 38, 101391. [Google Scholar] [CrossRef] - Ji, Q.; Bouri, E.; Lau, C.K.M.; Roubaud, D. Dynamic connectedness and integration in cryptocurrency markets. Int. Rev. Financ. Anal.
**2019**, 63, 257–272. [Google Scholar] [CrossRef] - Umar, M.; Rizvi, S.K.A.; Naqvi, B. Dance with the devil? The nexus of fourth industrial revolution, technological financial products and volatility spillovers in global financial system. Technol. Forecast. Soc. Chang.
**2021**, 163, 120450. [Google Scholar] [CrossRef] - Shahzad, S.J.H.; Bouri, E.; Kang, S.H.; Saeed, T. Regime specific spillover across cryptocurrencies and the role of COVID-19. Financ. Innov.
**2021**, 7, 5. [Google Scholar] [CrossRef] - Duan, K.; Li, Z.; Urquhart, A.; Ye, J. Dynamic efficiency and arbitrage potential in Bitcoin: A long-memory approach. Int. Rev. Financ. Anal.
**2021**, 101725. [Google Scholar] [CrossRef] - Bouri, E.; Gil-Alana, L.A.; Gupta, R.; Roubaud, D. Modelling long memory volatility in the Bitcoin market: Evidence of persistence and structural breaks. Int. J. Financ. Econ.
**2019**, 24, 412–426. [Google Scholar] [CrossRef] [Green Version] - Hu, Y.; Valera, H.G.A.; Oxley, L. Market efficiency of the top market-cap cryptocurrencies: Further evidence from a panel framework. Financ. Res. Lett.
**2019**, 31, 138–145. [Google Scholar] [CrossRef] - Al-Yahyaee, K.H.; Mensi, W.; Ko, H.U.; Yoon, S.M.; Kang, S.H. Why cryptocurrency markets are inefficient: The impact of liquidity and volatility. North Am. J. Econ. Financ.
**2020**, 52, 101168. [Google Scholar] [CrossRef] - Siu, T.K. The risks of cryptocurrencies with long memory in volatility, non-normality and behavioural insights. Appl. Econ.
**2021**, 53, 1991–2014. [Google Scholar] [CrossRef] - Wei, W.C. Liquidity and market efficiency in cryptocurrencies. Econ. Lett.
**2018**, 168, 21–24. [Google Scholar] [CrossRef] - Sensoy, A. The inefficiency of Bitcoin revisited: A high-frequency analysis with alternative currencies. Financ. Res. Lett.
**2019**, 28, 68–73. [Google Scholar] [CrossRef] - Kristoufek, L. On Bitcoin markets (in)efficiency and its evolution. Phys. A Stat. Mech. Appl.
**2018**, 503, 257–262. [Google Scholar] [CrossRef] - Newman, M. Networks: An Introduction; Oxford University Press: Oxford, UK, 2010. [Google Scholar]
- Kleinberg, J.M. Hubs, Authorities, and Communities. ACM Comput. Surv.
**1999**, 31, 5-es. [Google Scholar] [CrossRef] - Bonacich, P. Power and Centrality: A Family of Measures. Am. J. Sociol.
**1987**, 92, 1170–1182. [Google Scholar] [CrossRef] - Gleich, D.F. PageRank Beyond the Web. SIAM Rev.
**2015**, 57, 321–363. [Google Scholar] [CrossRef] - Opsahl, T.; Agneessens, F.; Skvoretz, J. Node centrality in weighted networks: Generalizing degree and shortest paths. Soc. Netw.
**2010**, 32, 245–251. [Google Scholar] [CrossRef] - Eagle, N.; Macy, M.; Claxton, R. Network Diversity and Economic Development. Science
**2010**, 328, 1029–1031. [Google Scholar] [CrossRef] - Freeman, L.C. A Set of Measures of Centrality Based on Betweenness. Sociometry
**1977**, 40, 35–41. [Google Scholar] [CrossRef] - Hotelling, H. Relations between two sets of variates. Biometrika
**1936**, 28, 321–377. [Google Scholar] [CrossRef] - Härdle, W.K.; Simar, L. Canonical Correlation Analysis. In Applied Multivariate Statistical Analysis; Springer International Publishing: Berlin/Heidelberg, Germany, 2019; pp. 431–442. [Google Scholar] [CrossRef]
- Trimborn, S.; Härdle, W.K. CRIX or Evaluating Blockchain Based Currencies; SFB 649 Discussion Paper 2015-048. Available online: https://www.econstor.eu/handle/10419/122006 (accessed on 9 April 2021). [CrossRef] [Green Version]
- Balcilar, M.; Bouri, E.; Gupta, R.; Roubaud, D. Can volume predict Bitcoin returns and volatility? A quantiles-based approach. Econ. Model.
**2017**, 64, 74–81. [Google Scholar] [CrossRef] [Green Version] - Naeem, M.; Bouri, E.; Boako, G.; Roubaud, D. Tail dependence in the return-volume of leading cryptocurrencies. Financ. Res. Lett.
**2020**, 36, 101326. [Google Scholar] [CrossRef]

**Figure 5.**After-tax arbitrage amount after taxes in case of two roles of the exchange: Buyer and Seller. Arrows indicate the decrease (%) of arbitrage after taxes.

Exchange | Opened | Country of HQ | Position (Ranking) * | Potential Arbitrage, €M | |
---|---|---|---|---|---|

Buyer | Seller | ||||

BitBay | 2014 | Estonia | 147 | 35.999 | 23.994 |

Bitfinex | 2012 | Hong Kong | 5 | 0.000001 | 0.000033 |

Bitlish | 2015 † | UK | - | 51.043 | 33.755 |

Bitmarketlt | 2013 | Lithuania | – | 18.604 | 13.500 |

Bitsane | 2016 † | Ireland | - | 21.364 | 2.083 |

Bitstamp | 2011 | UK | 7 | 70.566 | 20.393 |

CEX.IO | 2013 | Gibraltar | – | 46.901 | 68.556 |

Coindeal | 2018 | Malta | 114 | 92.702 | 30.415 |

CoinFalcon | 2017 | UK | 238 | 11.337 | 2.833 |

Coinfloor | 2012 | UK | 48 | 94.697 | 6.073 |

CoinMate | 2014 | Slovakia | 125 | 8.220 | 1.692 |

Coinroom | 2016 † | Poland | - | 5.451 | 1.560 |

DSX | 2014 † | UK | - | 18.895 | 220.335 |

EXMO | 2013 | UK | 31 | 4.953 | 169.058 |

Gatecoin | 2015 † | Hong Kong | - | 22.411 | 1.165 |

IncoreX | 2018 | Estonia | - | 1.624 | 1.643 |

Kraken | 2011 | USA | 4 | 112.277 | 26.907 |

Quoinex | 2014 | Japan | 12 | 8.658 | 3.261 |

SingularityX | 2018 | Lithuania | - | 0.782 | 0.096 |

TheRock | 2011 | Italy | 108 | 5.269 | 4.434 |

Total | 631.753 | 631.753 |

Crypto Currency | Ticker | ICO Date (White Paper) | Capitalisation *, €B | Potential Arbitrage, €M | Potential Profit after Taxes, % |
---|---|---|---|---|---|

Bitcoin | BTCEUR | 09.01.2009 ^{1} | 482.627 | 414.9901 | 69.58 |

BTCGBP | 73.9420 | 83.41 | |||

BTCPLN | 2.1793 | 60.72 | |||

BTCUSD | 97.1858 | 65.88 | |||

Bitcoin Cash | BCHEUR | 01.08.2017 ^{2} | 6.519 | 0.0034 | 61.04 |

Ethereum | ETHEUR | 30.07.2015 ^{3} | 110.691 | 38.2707 | 66.15 |

Litecoin | LTCEUR | 07.10.2011 ^{4} | 7.563 | 0.0005 | 26.71 |

STELLAR | XLMEUR | 25.02.2016 ^{5} | 4.825 | 0.0003 | 50.83 |

Ripple | XRPEUR | 20.02.2018 ^{6} | 9.939 | 5.1809 | 68.48 |

Total | 622.164 | 631.753 | 61.42 ** |

^{1}https://bitcoin.org/bitcoin.pdf;

^{2}https://bitcoincash.org/bitcoin.pdf;

^{3}https://github.com/ethereum/wiki/wiki/White-Paper;

^{4}https://icoholder.com/en/whitepaper/litecoin-token-28667;

^{5}https://www.stellar.org/papers/stellar-consensus-protocol;

^{6}https://arxiv.org/abs/1802.07242.

Exchange | Average Rate | |
---|---|---|

Buyer | Seller | |

BitBay | 0.3956 | 0.4604 |

Bitlish | 0.5373 | 0.6464 |

Bitmarketlt | 0.6351 | 0.5762 |

Bitsane | 0.7978 | 0.6194 |

Bitstamp | 0.4543 | 0.5248 |

CEX.IO | 0.4711 | 0.5300 |

Coindeal | 0.4994 | 0.3749 |

CoinFalcon | 0.5332 | 0.5227 |

Coinfloor | 0.4501 | 0.2758 |

CoinMate | 0.4471 | 0.3748 |

Coinroom | 0.6281 | 0.5023 |

DSX | 0.4315 | 0.7341 |

EXMO | 0.5962 | 0.8490 |

Gatecoin | 0.5899 | 0.4363 |

IncoreX | 0.5845 | 0.3855 |

Kraken | 0.4216 | 0.4285 |

Quoinex | 0.5586 | 0.6126 |

SingularityX | 0.4893 | 0.5792 |

TheRock | 0.5009 | 0.4955 |

Exchange | Diversity | Betweenness | Strength, €M | Pagerank | Authority Score | Hub Score | Arbitrage Ratio |
---|---|---|---|---|---|---|---|

BitBay | 0.6758 | 0 | 59.993 | 0.0555 | 0.0769 | 0.3026 | 0.2001 |

Bitlish | 0.6767 | 0 | 84.799 | 0.0384 | 0.1447 | 0.3896 | 0.2039 |

Bitmarketlt | 0.6950 | 0 | 32.104 | 0.0225 | 0.0471 | 0.1025 | 0.1590 |

Bitsane | 0.5164 | 0.0359 | 23.447 | 0.0098 | 0.0062 | 0.1408 | 0.8224 |

Bitstamp | 0.6768 | 0 | 90.959 | 0.0694 | 0.0430 | 0.4260 | 0.5516 |

CEX.IO | 0.7597 | 0 | 115.457 | 0.109 | 0.2095 | 0.3523 | −0.1876 |

Coindeal | 0.7831 | 0 | 123.117 | 0.0722 | 0.1058 | 0.4643 | 0.5059 |

CoinFalcon | 0.6134 | 0 | 14.170 | 0.0114 | 0.0093 | 0.0944 | 0.6001 |

Coinfloor | 0.3504 | 0.0523 | 100.770 | 0.0143 | 0.0193 | 1 | 0.8795 |

CoinMate | 0.4615 | 0.0556 | 9.912 | 0.0094 | 0.0061 | 0.0892 | 0.6586 |

Coinroom | 0.5951 | 0 | 7.011 | 0.0099 | 0.0054 | 0.0348 | 0.5549 |

DSX | 0.6705 | 0 | 239.230 | 0.2186 | 1 | 0.0537 | −0.8420 |

EXMO | 0.7283 | 0 | 174.012 | 0.2173 | 0.5235 | 0.0263 | −0.9431 |

Gatecoin | 0.6033 | 0 | 23.576 | 0.0091 | 0.0043 | 0.0451 | 0.9011 |

IncoreX | 0.6573 | 0.3856 | 3.267 | 0.0096 | 0.0055 | 0.0111 | −0.0059 |

Kraken | 0.6490 | 0 | 139.184 | 0.0817 | 0.0617 | 0.7884 | 0.6134 |

Quoinex | 0.7009 | 0.2026 | 11.919 | 0.0237 | 0.0093 | 0.0351 | 0.4528 |

SingularityX | 0.3227 | 0.9314 | 0.878 | 0.0080 | 0.0003 | 0.0047 | 0.7806 |

TheRock | 0.6497 | 0.2026 | 9.703 | 0.0104 | 0.0062 | 0.0325 | 0.0860 |

**Table 5.**Network characteristics for all crypto-exchanges that generated arbitrage on ETHEUR and XRPEUR.

ETHEUR | XRPEUR | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Diversity | Betweenness | Strength, €M | Page Rank | Authority Score | Hub Score | Arbitrage Ratio | Diversity | Betweenness | Strength, €M | Page Rank | Authority Score | Hub Score | Arbitrage Ratio | |

BitBay | 0.666 | 0 | 2.343 | 0.089 | 0.051 | 0.093 | −0.436 | 0.690 | 0.046 | 0.286 | 0.050 | 0.109 | 0.032 | −0.664 |

Bitlish | 0.438 | 0.25 | 7.276 | 0.230 | 0.053 | 1 | 0.672 | 0.770 | 0 | 1.223 | 0.170 | 0.476 | 0.193 | −0.367 |

Bitmarketlt | 0.649 | 0 | 1.838 | 0.022 | 0.015 | 0.181 | 0.646 | 0.526 | 0.065 | 0.240 | 0.026 | 0.017 | 0.179 | 0.696 |

Bitsane | 0.381 | 0.333 | 2.899 | 0.013 | 0.003 | 0.394 | 0.943 | |||||||

Bitstamp | 0.653 | 0 | 4.563 | 0.043 | 0.039 | 0.426 | 0.420 | 0.679 | 0 | 1.623 | 0.194 | 0.057 | 1 | 0.516 |

CEX.IO | 0.756 | 0.071 | 5.996 | 0.089 | 0.281 | 0.207 | −0.403 | 0.670 | 0 | 1.980 | 0.245 | 1 | 0.040 | −0.783 |

Coindeal | 0.880 | 0 | 1.876 | 0.045 | 0.045 | 0.073 | 0.107 | |||||||

EXMO | 0.646 | 0 | 13.917 | 0.347 | 1 | 0.001 | −0.991 | |||||||

Gatecoin | 0.780 | 0 | 0.908 | 0.031 | 0.016 | 0.043 | 0.355 | |||||||

IncoreX | 0.258 | 0.199 | 0.211 | 0.011 | 0.000 | 0.034 | 0.972 | |||||||

Kraken | 0.644 | 0 | 5.755 | 0.037 | 0.015 | 0.533 | 0.622 | 0.616 | 0 | 1.341 | 0.074 | 0.032 | 0.940 | 0.730 |

Quoinex | 0.595 | 0.25 | 1.928 | 0.015 | 0.006 | 0.018 | 0.810 | 0.809 | 0 | 0.404 | 0.035 | 0.062 | 0.102 | 0.511 |

SingularityX | 0.165 | 0.718 | 0.097 | 0.011 | 0.000 | 0.018 | 0.884 | |||||||

TheRock | 0.704 | 0.269 | 1.023 | 0.017 | 0.009 | 0.082 | 0.545 |

Average | Standard Deviation | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

BTCEUR | BTCUSD | ETHEUR | XRPEUR | USDEUR | GBPEUR | CRIX | BTCEUR | BTCUSD | ETHEUR | XRPEUR | USDEUR | GBPEUR | CRIX | ||

Pre-tax arbitrage | |||||||||||||||

BTCEUR | Aggregated arbitrage value | −0.11 | −0.11 | −0.07 | −0.06 | −0.01 | −0.06 | −0.06 | 0.03 | 0.05 | 0.15 | 0.00 | −0.06 | 0.15 | 0.05 |

Number of transactions | −0.16 | −0.16 | −0.09 | −0.06 | −0.06 | 0.10 | −0.12 | −0.19 | −0.18 | −0.09 | −0.19 | −0.25 | 0.10 | −0.18 | |

Average transaction value | −0.07 | −0.07 | −0.08 | −0.10 | 0.03 | −0.18 | −0.04 | 0.42 | 0.42 | 0.36 | 0.34 | 0.28 | 0.10 | 0.37 | |

ETHEUR | Aggregated arbitrage value | −0.02 | −0.04 | 0.03 | −0.03 | 0.03 | −0.08 | 0.02 | 0.03 | 0.06 | 0.18 | 0.06 | 0.16 | 0.08 | 0.11 |

Number of transactions | −0.09 | −0.09 | −0.02 | −0.02 | −0.04 | 0.12 | −0.03 | −0.23 | −0.21 | −0.07 | −0.17 | −0.14 | 0.16 | −0.20 | |

Average transaction value | 0.00 | −0.02 | 0.02 | −0.06 | 0.11 | −0.14 | −0.01 | 0.27 | 0.27 | 0.28 | 0.27 | 0.39 | −0.04 | 0.30 | |

XRPEUR | Aggregated arbitrage value | −0.03 | −0.06 | −0.05 | −0.04 | 0.12 | −0.08 | −0.05 | 0.36 | 0.38 | 0.40 | 0.38 | 0.19 | −0.05 | 0.41 |

Number of transactions | −0.03 | −0.06 | −0.06 | −0.08 | 0.10 | −0.05 | −0.08 | 0.24 | 0.27 | 0.28 | 0.25 | 0.15 | 0.00 | 0.30 | |

Average transaction value | −0.02 | −0.05 | −0.02 | 0.00 | 0.09 | −0.15 | 0.00 | 0.38 | 0.38 | 0.42 | 0.39 | 0.24 | −0.05 | 0.40 | |

After-tax arbitrage | |||||||||||||||

BTCEUR | Aggregated arbitrage value | −0.09 | −0.09 | −0.08 | −0.07 | 0.01 | −0.10 | −0.05 | 0.10 | 0.12 | 0.22 | 0.07 | 0.03 | 0.17 | 0.14 |

Number of transactions | −0.09 | −0.10 | −0.08 | −0.07 | −0.03 | −0.04 | −0.06 | −0.06 | −0.04 | 0.13 | −0.03 | 0.00 | 0.15 | 0.03 | |

Average transaction value | −0.07 | −0.06 | −0.05 | −0.04 | 0.03 | −0.14 | 0.00 | 0.31 | 0.32 | 0.29 | 0.24 | 0.10 | 0.13 | 0.27 | |

ETHEUR | Aggregated arbitrage value | −0.05 | −0.08 | −0.02 | −0.07 | 0.07 | −0.09 | −0.02 | 0.07 | 0.10 | 0.26 | 0.18 | 0.27 | 0.07 | 0.18 |

Number of transactions | −0.08 | −0.09 | −0.06 | −0.06 | −0.04 | −0.02 | −0.04 | −0.12 | −0.09 | 0.13 | 0.03 | 0.03 | 0.06 | 0.02 | |

Average transaction value | −0.06 | −0.08 | −0.02 | −0.10 | 0.13 | −0.17 | −0.04 | 0.24 | 0.24 | 0.28 | 0.27 | 0.40 | 0.02 | 0.25 | |

XRPEUR | Aggregated arbitrage value | −0.03 | −0.06 | −0.05 | −0.04 | 0.11 | −0.08 | −0.06 | 0.38 | 0.40 | 0.41 | 0.38 | 0.19 | −0.07 | 0.42 |

Number of transactions | −0.03 | −0.05 | −0.06 | −0.08 | 0.09 | −0.06 | −0.07 | 0.25 | 0.29 | 0.29 | 0.25 | 0.15 | 0.00 | 0.32 | |

Average transaction value | −0.02 | −0.04 | −0.03 | 0.00 | 0.08 | −0.11 | 0.00 | 0.42 | 0.42 | 0.47 | 0.44 | 0.23 | −0.10 | 0.44 |

Canonical | Wilks’ Lambda Test | |||
---|---|---|---|---|

Correlation | Stat | Approx | p-value | |

(${U}_{1}$, ${V}_{1}$) | 0.8527 | 0.0150 | 1.5450 | 0.000004 |

(${U}_{2}$, ${V}_{2}$) | 0.7178 | 0.0549 | 1.1661 | 0.070809 |

(${U}_{3}$, ${V}_{3}$) | 0.6369 | 0.1132 | 0.9886 | 0.531021 |

_{i}is a linear combination of crypto-market variables X, V

_{1}is a linear combination of arbitrage variables Y.

${\mathit{U}}_{1}$ | ${\mathit{V}}_{1}$ | ||
---|---|---|---|

Canonical Loading | Cross Loading | ||

Average | BTCEUR | −0.2059 | −0.1756 |

BTCUSD | −0.2374 | −0.2025 | |

ETHEUR | −0.1910 | −0.1628 | |

XRPEUR | −0.1587 | −0.1353 | |

USDEUR | 0.2758 | 0.2352 | |

GBPEUR | −0.5587 | −0.4764 | |

CRIX | −0.2126 | −0.1813 | |

Standard deviation | BTCEUR | 0.7994 | 0.6817 |

BTCUSD | 0.7794 | 0.6646 | |

ETHEUR | 0.7169 | 0.6113 | |

XRPEUR | 0.4607 | 0.3928 | |

USDEUR | 0.6452 | 0.5501 | |

GBPEUR | 0.4196 | 0.3578 | |

CRIX | 0.7313 | 0.6236 |

${\mathit{U}}_{1}$ | ${\mathit{V}}_{1}$ | ||
---|---|---|---|

Cross Loading | Canonical Loading | ||

Pre-tax arbitrage | |||

BTCEUR | Aggregated arbitrage value | 0.5937 | 0.5062 |

Number of transactionss | −0.0249 | −0.0213 | |

Average transaction value | 0.5037 | 0.4295 | |

ETHEUR | Aggregated arbitrage value | 0.0960 | 0.0818 |

Number of transactions | −0.0234 | −0.0200 | |

Average transaction value | 0.1636 | 0.1395 | |

XRPEUR | Aggregated arbitrage value | 0.2101 | 0.1792 |

Number of transactions | 0.2439 | 0.2080 | |

Average transaction value | 0.2560 | 0.2183 | |

After-tax arbitrage | |||

BTCEUR | Aggregated arbitrage value | 0.7147 | 0.6095 |

Number of transactions | 0.2689 | 0.2293 | |

Average transaction value | 0.6025 | 0.5138 | |

ETHEUR | Aggregated arbitrage value | 0.0992 | 0.0846 |

Number of transactions | 0.0690 | 0.0589 | |

Average transaction value | 0.0902 | 0.0769 | |

XRPEUR | Aggregated arbitrage value | 0.1666 | 0.1420 |

Number of transactions | 0.2543 | 0.2169 | |

Average transaction value | 0.1486 | 0.1268 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kabašinskas, A.; Šutienė, K.
Key Roles of Crypto-Exchanges in Generating Arbitrage Opportunities. *Entropy* **2021**, *23*, 455.
https://doi.org/10.3390/e23040455

**AMA Style**

Kabašinskas A, Šutienė K.
Key Roles of Crypto-Exchanges in Generating Arbitrage Opportunities. *Entropy*. 2021; 23(4):455.
https://doi.org/10.3390/e23040455

**Chicago/Turabian Style**

Kabašinskas, Audrius, and Kristina Šutienė.
2021. "Key Roles of Crypto-Exchanges in Generating Arbitrage Opportunities" *Entropy* 23, no. 4: 455.
https://doi.org/10.3390/e23040455