Bitcoin-based triangular arbitrage with the Euro/U.S. dollar as a foreign futures hedge: modeling with a bivariate GARCH model

Zheng Nan; Taisei Kaizoji; Zheng Nan; Taisei Kaizoji

doi:10.3934/QFE.2019.2.347

Quantitative Finance and Economics

2019, Volume 3, Issue 2: 347-365. doi: 10.3934/QFE.2019.2.347

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Bitcoin-based triangular arbitrage with the Euro/U.S. dollar as a foreign futures hedge: modeling with a bivariate GARCH model

Zheng Nan ¹,
Taisei Kaizoji ^{1,2
,
,}

1.
Graduate School of Arts and Science, International Christian University, 3-10-2 Mitaka, Tokyo 181-8585, Japan
2.
College of Liberal Arts, International Christian University, 3-10-2 Mitaka, Tokyo 181-8585, Japan

Received: 05 March 2019 Accepted: 03 June 2019 Published: 11 June 2019
JEL Codes: G11, G12, G17

This paper proposes a bitcoin-based triangular arbitrage, combining foreign exchanges in the bitcoin market and reverse foreign exchange spot transactions. An FX futures contract is used to reduce exposure to risk as a hedging instrument. The returns of the portfolio are jointly modeled using a bivariate DCC-GARCH model with multivariate standardized student's t disturbances due to the presence of leptokurtosis and fat tails observed. Based on the time-dependent covariance matrix, a dynamic optimal hedge ratio is formed, with a conditional correlation series as a by-product. Empirical results are obtained using Euros and U.S. dollars over the period from 21 April 2014 to 21 September 2018. Multiple rolling one-step-ahead forecasts are generated. The empirical results present bitcoin-based currency strategies dominate bitcoin trading in terms of risk management.
- bitcoin,
- bitcoin exchange rate,
- triangular arbitrage,
- optimal hedge ratio,
- DCC-GARCH model
Citation: Zheng Nan, Taisei Kaizoji. Bitcoin-based triangular arbitrage with the Euro/U.S. dollar as a foreign futures hedge: modeling with a bivariate GARCH model[J]. Quantitative Finance and Economics, 2019, 3(2): 347-365. doi: 10.3934/QFE.2019.2.347

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Abstract

This paper proposes a bitcoin-based triangular arbitrage, combining foreign exchanges in the bitcoin market and reverse foreign exchange spot transactions. An FX futures contract is used to reduce exposure to risk as a hedging instrument. The returns of the portfolio are jointly modeled using a bivariate DCC-GARCH model with multivariate standardized student's t disturbances due to the presence of leptokurtosis and fat tails observed. Based on the time-dependent covariance matrix, a dynamic optimal hedge ratio is formed, with a conditional correlation series as a by-product. Empirical results are obtained using Euros and U.S. dollars over the period from 21 April 2014 to 21 September 2018. Multiple rolling one-step-ahead forecasts are generated. The empirical results present bitcoin-based currency strategies dominate bitcoin trading in terms of risk management.

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