Research article Special Issues

Volatility Analysis of Bitcoin Price Time Series

  • Received: 10 September 2017 Accepted: 19 November 2017 Published: 13 December 2017
  • Bitcoin has the largest share in the total capitalization of cryptocurrency markets currently reaching above 70 billion USD. In this work we focus on the price of Bitcoin in terms of standard currencies and their volatility over the last five years. The average day-to-day return throughout this period is 0.328%, amounting in exponential growth from 6 USD to over 4,000 USD per 1 BTC at present. Multi-scale analysis is performed from the level of the tick data, through the 5 min, 1 hour and 1 day scales. Distribution of trading volumes (1 sec, 1 min, 1 hour and 1 day) aggregated from the Kraken BTCEUR tick data is provided that shows the artifacts of algorithmic trading (selling transactions with volume peaks distributed at integer multiples of BTC unit). Arbitrage opportunities are studied using the EUR, USD and CNY currencies. Whereas the arbitrage spread for EUR-USD currency pair is found narrow at the order of a percent, at the 1 hour sampling period the arbitrage spread for USD-CNY (and similarly EUR-CNY) is found to be more substantial, reaching as high as above 5 percent on rare occasions. The volatility of BTC exchange rates is modeled using the day-to-day distribution of logarithmic return, and the Realized Volatility, sum of the squared logarithmic returns on 5-minute basis. In this work we demonstrate that the Heterogeneous Autoregressive model for Realized Volatility Andersen et al. (2007) applies reasonably well to the BTCUSD dataset. Finally, a feed-forward neural network with 2 hidden layers using 10-day moving window sampling daily return predictors is applied to estimate the next-day logarithmic return. The results show that such an artificial neural network prediction is capable of approximate capture of the actual log return distribution; more sophisticated methods, such as recurrent neural networks and LSTM (Long Short Term Memory) techniques from deep learning may be necessary for higher prediction accuracy.

    Citation: Lukáš Pichl, Taisei Kaizoji. Volatility Analysis of Bitcoin Price Time Series[J]. Quantitative Finance and Economics, 2017, 1(4): 474-485. doi: 10.3934/QFE.2017.4.474

    Related Papers:

  • Bitcoin has the largest share in the total capitalization of cryptocurrency markets currently reaching above 70 billion USD. In this work we focus on the price of Bitcoin in terms of standard currencies and their volatility over the last five years. The average day-to-day return throughout this period is 0.328%, amounting in exponential growth from 6 USD to over 4,000 USD per 1 BTC at present. Multi-scale analysis is performed from the level of the tick data, through the 5 min, 1 hour and 1 day scales. Distribution of trading volumes (1 sec, 1 min, 1 hour and 1 day) aggregated from the Kraken BTCEUR tick data is provided that shows the artifacts of algorithmic trading (selling transactions with volume peaks distributed at integer multiples of BTC unit). Arbitrage opportunities are studied using the EUR, USD and CNY currencies. Whereas the arbitrage spread for EUR-USD currency pair is found narrow at the order of a percent, at the 1 hour sampling period the arbitrage spread for USD-CNY (and similarly EUR-CNY) is found to be more substantial, reaching as high as above 5 percent on rare occasions. The volatility of BTC exchange rates is modeled using the day-to-day distribution of logarithmic return, and the Realized Volatility, sum of the squared logarithmic returns on 5-minute basis. In this work we demonstrate that the Heterogeneous Autoregressive model for Realized Volatility Andersen et al. (2007) applies reasonably well to the BTCUSD dataset. Finally, a feed-forward neural network with 2 hidden layers using 10-day moving window sampling daily return predictors is applied to estimate the next-day logarithmic return. The results show that such an artificial neural network prediction is capable of approximate capture of the actual log return distribution; more sophisticated methods, such as recurrent neural networks and LSTM (Long Short Term Memory) techniques from deep learning may be necessary for higher prediction accuracy.


    加载中
    [1] Andersen TG, Bollerslev T, Diebold FX, et al. (2000) Exchange Rate Returns Standardized by Realized Volatility are (Nearly) Gaussian. Multinatl Financ J 4: 159–179. doi: 10.17578/4-3/4-2
    [2] Andersen TG, Bollerslev T, Diebold FX, et al. (2001) The distribution of realized stock return volatility. J Financ Econ 61: 43–76. doi: 10.1016/S0304-405X(01)00055-1
    [3] Andersen TG, Bollerslev T, Diebold FX (2007) Roughing it up: including jump components in measuring, modeling and forecasting asset return volatility. Rev Econ Stat 89: 701–720. doi: 10.1162/rest.89.4.701
    [4] Balcilar M, Bouri E, Gupta R, et al. (2017) Can volume predict Bitcoin returns and volatility? A quantiles-based approach. Econ Model 64: 74–81.
    [5] Bariviera AF, Basgall MJ, Hasperué W, et al. (2017) Some stylized facts of the Bitcoin market, Physica A: Stat Mechanics Appl 484: 82–90.
    [6] Barndorff-Nielsen OE, Shephard N (2004) Power and Bipower Variation with Stochastic Volatility and Jumps. J Financ Econom 2: 1–37. doi: 10.1093/jjfinec/nbh001
    [7] Blau BM (2017) Price dynamics and speculative trading in bitcoin. Res Int Bus Financ 41: 493–499. doi: 10.1016/j.ribaf.2017.05.010
    [8] Boudt K, Cornelissen J, Payseur S, et al. (2017) high frequency: Tools for High frequency Data Analysis. R package version 0.5. Available from: https://CRAN.R-project.org/package=highfrequency.
    [9] Bouri E, Azzi G, Dyhrberg AH (2017a) On the return-volatility relationship in the Bitcoin market around the price crash of 2013. Econ 11: 1–16.
    [10] Bouri E, Molnár P, Azzi G, et al. (2017b) On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier? Financ Res Letters 20: 192–198.
    [11] Bradbury D (2013) The problem with Bitcoin. Comput Fraud Security 2013: 5–8.
    [12] Brandvold M, Molnár P, Vagstad K, et al. (2015) Price discovery on Bitcoin exchanges. J Int Financ Mark, Inst Money 36: 18–35. doi: 10.1016/j.intfin.2015.02.010
    [13] Cheah ET, Fry J (2015) Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Econ Lett 130: 32–36.
    [14] Dwyer GP (2015) The economics of Bitcoin and similar private digital currencies. J Financ Stab 17: 81–91.
    [15] Dyhrberg AH (2016) Hedging capabilities of Bitcoin. Is it the virtual gold? Financ Res Lett 16: 139–144.
    [16] Extance A (2015) Bitcoin and beyond. Nature 526: 21–23. doi: 10.1038/526021a
    [17] Franzke C (2012) Predictability of extreme events in a nonlinear stochastic-dynamical model. Physical Rev E 85.
    [18] Fritsch S, Guenther F (2016) neuralnet: Training of Neural Networks. R package version 1.33. Available online: https://CRAN.R-project.org/package=neuralnet.
    [19] Hawkes AG, Oakes D (1974) A Cluster Process Representation of a Self-Exciting Process. J Appl Prob 11: 493–503.
    [20] Hsieh WW (2009) Machine Learning Methods in the Environmental Sciences, Cambridge University Press, Cambridge, UK.
    [21] Katsiampa P (2017) Volatility estimation for Bitcoin: A comparison of GARCH models. Econ Lett 158: 3–6.
    [22] Kim YB, Kim JG, Kim W, et al. (2016) Predicting Fluctuations in Cryptocurrency Transactions Based on User Comments and Replies. PLoS ONE 11.
    [23] Kristoufek L (2013) BitCoin meets Google Trends and Wikipedia: Quantifying the relationship between phenomena of the Internet era. Scientific rep 3.
    [24] Kristoufek L (2015) What Are the Main Drivers of the Bitcoin Price? Evidence from Wavelet Coherence Analysis. PLoS One 10.
    [25] Urquhart A (2016) The inefficiency of Bitcoin. Econ Lett 148: 80–82. doi: 10.1016/j.econlet.2016.09.019
    [26] Urquhart A (2017) Price clustering in Bitcoin. Econ Lett 159: 145–148. doi: 10.1016/j.econlet.2017.07.035
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(11724) PDF downloads(2523) Cited by(66)

Article outline

Figures and Tables

Figures(5)  /  Tables(1)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog