Estimación de la distribución multivariada de los rendimientos de los tipos de cambio contra el dólar de las criptomonedas Bitcoin, Ripple y Ether

• Autores: M. Beatriz Mota Aragón, José Antonio Núñez Mora
• Localización: Revista Mexicana de Economía y Finanzas (REMEF): nueva época, ISSN-e 2448-6795, ISSN 1665-5346, Vol. 14, Nº. 3, 2019, págs. 447-457
• Idioma: español
• DOI: 10.21919/remef.v14i3.409
• Títulos paralelos:
  • Estimation of the multivariate distribution of exchange rate yields against the dollar of the Cryptocurrencies Bitcoin, Ripple and Ether
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    Resumen En este artículo se estima la distribución multivariada para analizar la dependencia del Bitcoin (BTC), Ripple (XRP) y Ether (ETH). Se utiliza la familia Hiperbólica Generalizada de distribuciones (GH) y en particular la distribución Varianza Gamma. El procedimiento para la estimación de los parámetros de la GH es a través del algoritmo EM (Expectation-Maximization). Los resultados muestran que existe una dependencia positiva entre los tres tipos de cambio respecto del dólar americano y seestima una distribución Varianza-Gamma de dimensión tres. Esta distribución es muy flexible para el ajuste de series de los rendimientos con leptocurtosis y sesgo. Esta información se considera importante para los inversionistas que conforman sus portafolios de una manera eficiente.

  • English

    Abstract In this paper we estimated the multivariate distribution among Bitcoin (BTC), Ripple (XRP) and Ether (ETH) to analyze the dependence. We used the Hyperbolic Generalized (GH) family of distributions and in particular the Variance-Gamma distribution.The procedure for the estimation of the parameters of the GH distribution is through the EM (Expectation-Maximization) algorithm. The results show that there exists a positive dependence among the three exchange rates with respect to the American dollar and a Variance-Gamma distribution of dimension three is estimated. This distribution is very flexible for the adjustment of returns with leptokurtosis and skewness. This distribution is very flexible for the adjustment of the returns with leptokurtosis and skewness. The information is important for the investors who construct their portfolios in an efficient way.

• Referencias bibliográficas
  • Barndorff, O.. (1977). Exponentially decreasing distributions for the logarithm of the particle size. Proceedings of the Royal Society. Mathematical...
  • Barndorff, O.,Mikosch, T.,Resnick, S.. (2012). Lévy processes: theory and applications. Springer Science Business Media. New York.
  • Baur, D.G.,Lucey, B.M.. (2010). Is gold a hedge or a safe haven? An analysis of stocks, bonds and gold. Financial Review. 45. 217
  • Baur, D.,Dimpfl, T.,Kuck, K.. (2017). Bitcoin, Gold and the US Dollar- A replication and Extension. Finance Researcher Letters. 25. 103
  • Baur, D.,Hong, K.,Lee, A.. (2018). Bitcoin: Medium of exchange or speculative assets?. Journal of International Financial Markets. 54. 177
  • Bouri, E.,Gil-Alana, L.A.,Gupta, R.,Roubaud, D.. (2016). Modelling Long Memory Volatility in the Bitcoin Market: Evidence of Persistence and...
  • Breymann, W.,Lüthi, D.. (2013). ghyp: A package on generalized hyperbolic distributions.
  • Cermak, Vavrinec.. (2017). Can Bitcoin become a viable alternative to fiat currencies? An empirical analysis of Bitcoin’s volatility based...
  • Cont, R.. (2001). Empirical properties of asset returns: stylized facts and statistical issues. Quantitative Finance. 1. 223
  • Corbet, S.,Lucery, B.M.,Urquhart, A.,Yarovaya, L.. (2018). Cryptocurrencies as a financial asset. A systematic analysis.
  • Corsi, F.,Sornette, D.. (2014). Follow the money: The monetary roots of bubbles and crashes. International Review of Financial Analysis. 32....
  • Demir, E.,Goznor, G.,Lau., C.K.M.,Vinge, S.A.. (2018). Does economic policy uncertainty predict the bitcoin returns? An empirical investigation....
  • Dwyer, G.P.. (2015). The economics of Bitcoin and similar private digital currencies. Journal of Financial Stability. 17. 81-91
  • Gandal, N.,Halaburda, H.. (2016). Can we predict the winner in market with network effects? Competition in cryptocurrency market. Games. 7....
  • Glaser, F.,Zimmermann, K.,Haferkorn, M. W. M.,Siering, M. (2014). Bitcoin-asset or currency? Revealing users hidden intentions. 22ndEuropean...
  • (1998). GSR. E-gold; better money; since 1996.
  • Henriques, I.,Sadorsky, P.. (2018). Can bitcoin replace gold in an investment portfolio?. Journal of Risk Financial Management. 11.
  • Chan, Stephen,Jeffrey, Chu,Saralees, Nadarajah,Joerg, Osterrieder. (2017). A statistical analysis of cryptocurrencies. Journal of Risk Financial...
  • Chaum, D.L.. (1983). Blind signatures for untraceable payments.
  • Chu, Jeffrey,Stephen, Chan,Saralees, Nadarajah,Joerg, Osterrieder. (2017). GARCH Modeling of Cryptocurrencies. School of Mathematics, University...
  • Dyhrberg, Anne Haubo. (2016). Hedging capabilities of Bitcoin. Is it the virtual gold?. Finance Research Letters. 16. 139
  • Dyhrberg, Anne Haubo. (2016). Bitcoin, gold and the dollar - A GARCH volatility analysis. Finance Research Letters. 16. 85-92
  • Garcia, D.,Tessone, C.,Mavrodiev, P.,Perony, N.. (2014). The digital traces of bubbles: Feedback cycles between socio-economic signals in...
  • Glaser, F.,Haferhorn, M.,Weber, M.C.,Zimmarmann, K.,Siering, M.b.. (2014). Bitcoin -Asset or currency? Revealing users’ hidden intentions....
  • Hu, W.. (2005). Calibration of Multivariate Generalized Hyperbolic Distributions using the EM Algorithm, with Applications in Risk Management,...
  • Konlak, V.,Wilcox, D.. (2014). A Comparison of Generalized Hyperbolic Distribution Models for Equity Returns. Journal of Applied Mathematics....
  • Kristoufek, L.. (2013). Bitcoin meets Google Trends and Wikipedia: Quantifying the relationship between phenomena of the Internet era. Scientific...
  • McAssey, M.. (2013). An empirical goodness-of-fit test for multivariate distributions. Journal of Applied Statistics. 40. 1120
  • Paolella, M.. (2007). Intermediate Probability. John Wiley Sons. West Sussex, England.
  • Protassov, R.. (2004). EM-based maximum likelihood parameter estimation for multivariate generalized hyperbolic distributions with λ fixed....
  • Ratner, M.,Chiu, C.. (2013). Hedging Stock Sector Risk with Credit Default Swaps. International Review of Financial Analysis. 30. 18-25
  • Ross, S.. (2012). Simulation. Academic Press. USA.
  • Sahoo, P.. (2017). Bitcoin as digital money: Its growth and future sustainability. Theoretical and Applied Economics. 4. 53-64
  • Shuyue. (2018). Volatility connecedness in the cryptocurrency market. Is Bitcoin a dominant cryptocurrency?.
  • Tsay, R.. (2010). Analysis of financial time series. Wiley. Cambridge, Massachusetts.
  • Xin, L.,Chong, A.. (2016). The technology and economic determinants of cryptocurrency exchange rates: determinants of cryptocurrency exchange...
  • Yermack, D.. (2013). Is Bitcoin a real currency? An economic appraisal. National Bureau of Economic Research.