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Open AccessArticle

GARCH Generated Volatility Indices of Bitcoin and CRIX

by Pierre J. Venter 1,2,* and Eben Maré 3,*
1
Department of Actuarial Science, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
2
Department of Finance and Investment Management, University of Johannesburg, P.O. Box 524, Aucklandpark 2006, South Africa
3
Department of Mathematics and Applied Mathematics, University of Pretoria, Private Bag X20, Hatfield 0028, South Africa
*
Authors to whom correspondence should be addressed.
J. Risk Financial Manag. 2020, 13(6), 121; https://doi.org/10.3390/jrfm13060121
Received: 21 April 2020 / Revised: 3 June 2020 / Accepted: 4 June 2020 / Published: 11 June 2020
In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset. View Full-Text
Keywords: cryptocurrency index; Bitcoin; GARCH; volatility index cryptocurrency index; Bitcoin; GARCH; volatility index
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Venter, P.J.; Maré, E. GARCH Generated Volatility Indices of Bitcoin and CRIX. J. Risk Financial Manag. 2020, 13, 121.

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