image

Evaluating Bitcoin Price Volatility Forecasting Models: A Comparative Analysis

Download Paper PDF: Download pdf
Author(s):
Abstract:

This paper conducts an extensive analysis of Bitcoin return series, with a primary focus on three volatility metrics: historical volatility (calculated as the sample standard deviation), forecasted volatility (derived from GARCH-type models), and implied volatility (computed from the emerging Bitcoin options market). These measures of volatility serve as indicators of market expectations for conditional volatility and are compared to elucidate their differences and similarities. The central finding of this study underscores a notably high expected level of volatility, both on a daily and annual basis, across all the methodologies employed. However, it's important to emphasise the potential challenges stemming from suboptimal liquidity in the Bitcoin options market. These liquidity constraints may lead to discrepancies in the computed values of implied volatility, particularly in scenarios involving extreme money or maturity. This analysis provides valuable insights into Bitcoin's volatility landscape, shedding light on the unique characteristics and dynamics of this cryptocurrency within the context of financial markets.


© 2024 The Author(s). Published by RITHA Publishing. This article is distributed under the terms of the license CC-BY 4.0., which permits any further distribution in any medium, provided the original work is properly cited.


How to cite:

Chinazzo, C., & Jeleskovic, V. (2024). Evaluating Bitcoin Price Volatility Forecasting Models: A Comparative Analysis. Journal of Research, Innovation and Technologies, Volume III, 1(5), 7-29. https://doi.org/10.57017/jorit.v3.1(5).01 


References:

[1] Akaike, H. (1974). A New Look at the Statistical Model Identification. In: Parzen, E., Tanabe, K., Kitagawa, G. (eds) Selected Papers of Hirotugu Akaike. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1694-0_16 

[2] Akgiray, V. (1989). Conditional heteroscedasticity in time series of stock returns: Evidence and forecasts. The Journal of Business, 62(1), 55-80. http://www.jstor.org/stable/2353123 

[3] Akron, S., Ender Demir, E. & Roi D. Taussig (2020). Real options and asymmetric volatility in light of the firm’s growth opportunities. Investment Analysts Journal, Volume 49(2), 105-117. https://doi.org/10.1080/10293523.2020.1755928

[4] Ardia, D., Bluteau, K., & Rüede, M. (2019). Regime changes in Bitcoin GARCH volatility dynamics. Finance Research Letters, 29, 266-271. https://doi.org/10.1016/j.frl.2018.08.009

[5] Avramov, D., Chordia, T., & Goyal, A. (2006). The Impact of Trades on Daily Volatility. Review of Financial Studies, 19(4), 1241–1277. https://doi.org/10.1093/rfs/hhj027

[6] Balcilar, M., Bouri, E., Gupta, R., & Roubaud, D. (2017). Can volume predict Bitcoin returns and volatility? A quantiles-based approach. Economic Modelling, 64, 74-81. https://doi.org/10.1016/j.econmod.2017.03.019

[7] Beckers, S. (1981). Standard deviations implied in option prices as predictors of future stock price variability. Journal of Banking & Finance, 5(3), 363-381. https://doi.org/10.1016/0378-4266(81)90032-7

[8] Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of political Economy, 81(3), 637-654. https://www.jstor.org/stable/1831029

[9] Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307-327. https://doi.org/10.1016/0304-4076(86)90063-1 

[10] Bouoiyour, J., & Selmi, R. (2015). What does Bitcoin look like? Annals of Economics and Finance, 16(2), 449-492. https://down.aefweb.net/AefArticles/aef160211Bouoiyour.pdf

[11] Bouoiyour, J., Selmi, R., Tiwari, A. K., & Olayeni, O. R. (2016). What drives Bitcoin price. Economics Bulletin, 36(2), 843-850.

[12] Bunnag, T (2023). Guidelines for Econometrics and Applications: Emphasis on Tourism and Financial Economics, 211 pp. in Book Serie: Socio-Economics, Research, Innovation and Technologies (SERITHA). https://doi.org/10.57017/SERITHA.2023.GEA 

[13] Burnham, K. P., & Anderson, D. R. (2004). Multimodel Inference: Understanding AIC and BIC in Model Selection. Sociological Methods & Research, 33(2), 261-304. https://doi.org/10.1177/0049124104268644

[14] Catania, L., & Grassi, S. (2017). Modelling crypto-currencies financial time-series. CEIS Working Paper. Available at SSRN: https://ssrn.com/abstract=3084109 

[15] Chang, C. L., & McAleer, M. (2017). The correct regularity condition and interpretation of asymmetry in EGARCH. Economics Letters, 161, 52-55. https://doi.org/10.1016/j.econlet.2017.09.017

[16] Cheah, E. T., & Fry, J. (2015). Speculative bubbles in Bitcoin markets? An empirical investigation into the fundamental value of Bitcoin. Economics Letters, 130, 32-36. https://doi.org/10.1016/j.econlet.2015.02.029

[17] Cheung, A., Roca, E., & Su, J. J. (2015). Crypto-currency bubbles: an application of the Phillips–Shi–Yu (2013) methodology on Mt. Gox bitcoin prices. Applied Economics, 47(23), 2348-2358. https://doi.org/10.1080/00036846.2015.1005827

[18] Chiras, D. P., & Manaster, S. (1978). The information content of option prices and a test of market efficiency. Journal of Financial Economics, 6(2-3), 213-234. https://doi.org/10.1016/0304-405X(78)90030-2

[19] Chu, J., Chan, S., Nadarajah, S., & Osterrieder, J. (2017). GARCH modelling of cryptocurrencies. Journal of Risk and Financial Management, 10(4), 17. https://doi.org/10.3390/jrfm10040017

[20] Ciaian, P., Rajcaniova, M., & Kancs, D. A. (2016). The economics of BitCoin price formation. Applied Economics, 48(19), 1799-1815. https://doi.org/10.1080/00036846.2015.1109038

[21] Cont, R., & Da Fonseca, J. (2002). Dynamics of implied volatility surfaces. Quantitative Finance, 2(1), 45-60. https://doi.org/10.1088/1469-7688/2/1/304

[22] Corbet, S., Lucey, B., & Yarovaya, L. (2018). Datestamping the Bitcoin and Ethereum bubbles. Finance Research Letters, 26, 81-88. https://doi.org/10.1016/j.frl.2017.12.006

[23] Danielsson, J., & Zigrand, J. P. (2006). On time-scaling of risk and the square-root-of-time rule. Journal of Banking & Finance, 30(10), 2701-2713. https://doi.org/10.1016/j.jbankfin.2005.10.002

[24] Day, T. E., & Lewis, C. M. (1992). Stock market volatility and the information content of stock index options. Journal of Econometrics, 52(1-2), 267-287. https://doi.org/10.1016/0304-4076(92)90073-Z 

[25] Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366), 427-431. https://doi.org/10.2307/2286348

[26] Ding, Z., Granger, C. W., & Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance, 1(1), 83-106. https://doi.org/10.1016/0927-5398(93)90006-D

[27] Dyhrberg, A. H. (2016). Bitcoin, gold and the dollar - A GARCH volatility analysis. Finance Research Letters, 16, 85-92. https://doi.org/10.1016/j.frl.2015.10.008

[28] Engle, R. F. (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica: Journal of the Econometric Society, 987-1007. https://doi.org/10.2307/1912773

[29] Engle, R. F., & Bollerslev, T. (1986). Modelling the persistence of conditional variances. Econometric Reviews, 5(1), 1-50. https://doi.org/10.1080/07474938608800095

[30] Engle, R. F., & Mustafa, C. (1992). Implied ARCH models from options prices. Journal of Econometrics, 52(1-2), 289-311. https://doi.org/10.1016/0304-4076(92)90074-2

[31] Gaies, B., Chaâbane, N., Arfaoui, N., & Sahut, J-M. (2024). On the resilience of cryptocurrencies: A quantile-frequency analysis of bitcoin and Ethereum reactions in times of inflation and financial instability, Research in International Business and Finance, in press, Journal pre-proof. https://doi.org/10.1016/j.ribaf.2024.102302

[32] Garcia, D., Tessone, C. J., Mavrodiev, P., & Perony, N. (2014). The digital traces of bubbles: feedback cycles between socio-economic signals in the Bitcoin economy. Journal of the Royal Society Interface, 11(99), 20140623. https://doi.org/10.1098/rsif.2014.0623

[33] Glaser, F., Zimmermann, K., Haferkorn, M., Weber, M. C., & Siering, M. (2014). Bitcoin-asset or currency? revealing users' hidden intentions. Revealing Users' Hidden Intentions (April 15, 2014). ECIS 2014 (Tel Aviv) https://ssrn.com/abstract=2425247

[34] Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. The Journal of Finance, 48(5), 1779-1801. https://doi.org/10.1111/j.1540-6261.1993.tb05128.x

[35] Haas, M., Mittnik, S., & Paolella, M. S. (2004). A new approach to Markov-switching GARCH models. Journal of Financial Econometrics, 2(4), 493-530. https://doi.org/10.1093/jjfinec/nbh020

[36] Hafner, C. (2020). Testing for bubbles in cryptocurrencies with time-varying volatility. Journal of Financial Econometrics, 18(2), 233–249. https://doi.org/10.1093/jjfinec/nby023

[37] Hull, J. C. (2022). Options futures and other derivatives. 11th Edition, Pearson Education. ISBN 978-0-13-693997-9

[38] Hung, J-C., Liu, H-C., & Yang, J. J. (2020). Improving the realized GARCH’s volatility forecast for Bitcoin with jump-robust estimators, The North American Journal of Economics and Finance, Volume 52. https://doi.org/10.1016/j.najef.2020.101165 

[39] Klein, T., Thu, H. P., & Walther, T. (2018). Bitcoin is not the New Gold - A comparison of volatility, correlation, and portfolio performance. International Review of Financial Analysis, 59, 105-116. https://doi.org/10.1016/j.irfa.2018.07.010

[40] Letra, I. J. S. (2016). What drives cryptocurrency value? A volatility and predictability analysis (Doctoral dissertation, Instituto Superior de Economia e Gestão). https://www.repository.utl.pt/bitstream/10400.5/ 12556/1/DM-IJSL-2016.pdf 

[41] Natenberg, S. (1994). Option Volatility & Pricing. Advanced Trading Strategies and Techniques. McGraw-Hill Education. ISBN:978-0071508018

[42] Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the Econometric Society, 347-370. https://doi.org/10.2307/2938260 

[43] Osterrieder, J., & Lorenz, J. (2017). A statistical risk assessment of Bitcoin and its extreme tail behaviour. Annals of Financial Economics, 12(01), 1750003. https://doi.org/10.1142/S2010495217500038

[44] Peng, S., Prentice, C., Shams, S., & Sarker, T. (2024). A systematic literature review on the determinants of cryptocurrency pricing. China Accounting and Finance Review, 26(1), pp. 1-30. https://doi.org/10.1108/CAFR-05-2023-0053

[45] Pichl, L., & Kaizoji, T. (2017). Volatility analysis of bitcoin. Quantitative Finance and Economics, 1, 474-485. 10.3934/QFE.2017.4.474

[46] Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464. http://www.jstor.org/stable/2958889

[47] Taylor, S. J. (2007). Modelling Financial Time Series. 2nd Edition. ISBN: 978-9812770851. https://doi.org/10.1142/6578 

[48] Urquhart, A. (2016). The inefficiency of Bitcoin. Economics Letters, 148, 80-82. https://doi.org/10.1016/j.econlet.2016.09.019

[49] Yermack, D. (2015). Is Bitcoin a real currency? An economic appraisal. In Handbook of Digital Currency, David Lee Kuo Chuen (Ed), pp. 31-43. Academic Press. ISBN: 978-0-12-802117-0. https://doi.org/10.1016/C2014-0-01905-3

[50] Zaitsev, N. (2019). Empirical forward price distribution from Bitcoin option prices. Available at SSRN 3314682. http://dx.doi.org/10.2139/ssrn.3314682

Websites

*** Alexandre, A. (2019, May). Study: Bitcoin Derivatives Exchanges Register Record Trading Volumes. Retrieved from: https://cointelegraph.com/news/study-bitcoin-derivatives-exchanges-register-record-trading-volumes 

*** Andersson, H. (2019, May). Crypto Convexity. Retrieved from: https://www.apollocap.io/blog/2019/5/28/crypto-convexity 

*** Antos, J. (2018, March). An Efficient-Markets Valuation Framework for Crypto assets using Black-Scholes Option Theory. Retrieved from: https://medium.com/blockchain-advisory-group/an-efficient-markets-valuation-framework-for-cryptoassets-using-black-scholes-option-theory-a6a8a480e18a 

*** Brown, A. (2018, February). Bitcoin Enters Awkward Adolescence. Retrieved from: https://www.bloomberg.com/ opinion/articles/2018-02-28/bitcoin-cryptocurrency-derivatives-have-slow-uneventful-launch

*** BTC Implied Volatility at Historical Low – Time to Buy BTC Options? (2018, June). Retrieved from: https://blog.deribit.com/btc-implied-volatility-opportunity/ 

*** Crypto derivatives market color #2. (2018, November). Retrieved from: https://medium.com/@skew_options/ crypto-derivatives-market-color-2-3bb78eb10383 

*** Del Castillo, M. (2017, November). First Long-Term LedgerX Bitcoin Option Pegs Price at $10,000. Retrieved from: https://www.coindesk.com/first-long-term-ledgerx-bitcoin-option-pegs-price-10000-one-year

*** Ghalanos, A. (2019, January). ruGARCH: Univariate GARCH Models. Retrieved from: https://cran.r-project.org/web/packages/rugarch/index.html 

*** Graham, L. (2017, September). How bitcoin could overcome its wild reputation. Retrieved from: https://www.cnbc.com/2017/09/21/bitcoin-volatility-how-digital-currency-can-overcome-wild-reputation.html 

*** Hays, D. (2017, December). U.S. Regulated Bitcoin Derivatives: Blessing or Curse? Retrieved from: https://cryptoresearch.report/crypto-research/u-s-regulated-bitcoin-derivatives-blessing-curse/ 

*** Investment using virtual currency or distributed ledger technology (2015, July). Retrieved from: https://www. esma.europa.eu/press-news/consultations/investment-using-virtual-currency-or-distributed-ledger-technology

*** Lielacher, A. (2019, April). How to Trade Bitcoin Options in the United States. Retrieved from: https://www.bitcoinmarketjournal.com/bitcoin-options/ 

*** Should there be two implied volatilities, one based on bid and another on ask, or just a single one based on mid-price (calculation of the implied volatility)? (2016, March). Retrieved from: https://www.quora.com/Should-there-be-two-implied-volatilities-one-based-on-bid-and-another-on-ask-or-just-a-single-one-based-on-mid-price-calculation-of-the-implied-volatility 

*** Top 100 Cryptocurrencies by Market Capitalization (2019, July). Retrieved from: https://coinmarketcap.com