IDEAS home Printed from https://ideas.repec.org/a/gam/jdataj/v8y2023i7p122-d1201466.html
   My bibliography  Save this article

A Wavelet-Decomposed WD-ARMA-GARCH-EVT Model Approach to Comparing the Riskiness of the BitCoin and South African Rand Exchange Rates

Author

Listed:
  • Thabani Ndlovu

    (Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa)

  • Delson Chikobvu

    (Department of Mathematical Statistics and Actuarial Science, University of the Free State, Bloemfontein 9300, South Africa)

Abstract

In this paper, a hybrid of a Wavelet Decomposition–Generalised Auto-Regressive Conditional Heteroscedasticity–Extreme Value Theory (WD-ARMA-GARCH-EVT) model is applied to estimate the Value at Risk (VaR) of BitCoin (BTC/USD) and the South African Rand (ZAR/USD). The aim is to measure and compare the riskiness of the two currencies. New and improved estimation techniques for VaR have been suggested in the last decade in the aftermath of the global financial crisis of 2008. This paper aims to provide an improved alternative to the already existing statistical tools in estimating a currency VaR empirically. Maximal Overlap Discrete Wavelet Transform (MODWT) and two mother wavelet filters on the returns series are considered in this paper, viz., the Haar and Daubechies (d4). The findings show that BitCoin/USD is riskier than ZAR/USD since it has a higher VaR per unit invested in each currency. At the 99% significance level, BitCoin/USD has average values of VaR of 2.71% and 4.98% for the WD-ARMA-GARCH-GPD and WD-ARMA-GARCH-GEVD models, respectively; and this is slightly higher than the respective 2.69% and 3.59% for the ZAR/USD. The average BitCoin/USD returns of 0.001990 are higher than ZAR/USD returns of −0.000125. These findings are consistent with the mean-variance portfolio theory, which suggests a higher yield for riskier assets. Based on the p -values of the Kupiec likelihood ratio test, the hybrid model adequacy is largely accepted, as p -values are greater than 0.05, except for the WD-ARMA-GARCH-GEVD models at a 99% significance level for both currencies. The findings are helpful to financial risk practitioners and forex traders in formulating their diversification and hedging strategies and ascertaining the risk-adjusted capital requirement to be set aside as a cushion in the event of the occurrence of an actual loss.

Suggested Citation

  • Thabani Ndlovu & Delson Chikobvu, 2023. "A Wavelet-Decomposed WD-ARMA-GARCH-EVT Model Approach to Comparing the Riskiness of the BitCoin and South African Rand Exchange Rates," Data, MDPI, vol. 8(7), pages 1-24, July.
    • Handle: RePEc:gam:jdataj:v:8:y:2023:i:7:p:122-:d:1201466
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2306-5729/8/7/122/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2306-5729/8/7/122/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Christoph Schleicher, 2002. "An Introduction to Wavelets for Economists," Staff Working Papers 02-3, Bank of Canada.
    2. Tetsuya Takaishi, 2017. "Statistical properties and multifractality of Bitcoin," Papers 1707.07618, arXiv.org, revised May 2018.
    3. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    4. Benhmad, François, 2013. "Bull or bear markets: A wavelet dynamic correlation perspective," Economic Modelling, Elsevier, vol. 32(C), pages 576-591.
    5. Bouri, Elie & Molnár, Peter & Azzi, Georges & Roubaud, David & Hagfors, Lars Ivar, 2017. "On the hedge and safe haven properties of Bitcoin: Is it really more than a diversifier?," Finance Research Letters, Elsevier, vol. 20(C), pages 192-198.
    6. Bauwens, Luc & De Backer, Bruno & Dufays, Arnaud, 2014. "A Bayesian method of change-point estimation with recurrent regimes: Application to GARCH models," Journal of Empirical Finance, Elsevier, vol. 29(C), pages 207-229.
    7. Dyhrberg, Anne Haubo, 2016. "Bitcoin, gold and the dollar – A GARCH volatility analysis," Finance Research Letters, Elsevier, vol. 16(C), pages 85-92.
    8. Viviana Fernandez, 2003. "Extreme Value Theory and Value at Risk," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 18(1), pages 57-85, June.
    9. James Ming Chen, 2018. "On Exactitude in Financial Regulation: Value-at-Risk, Expected Shortfall, and Expectiles," Risks, MDPI, vol. 6(2), pages 1-28, June.
    10. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    11. Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Marcin Wk{a}torek, 2023. "What is mature and what is still emerging in the cryptocurrency market?," Papers 2305.05751, arXiv.org.
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Panagiotidis, Theodore & Stengos, Thanasis & Vravosinos, Orestis, 2019. "The effects of markets, uncertainty and search intensity on bitcoin returns," International Review of Financial Analysis, Elsevier, vol. 63(C), pages 220-242.
    2. Flori, Andrea, 2019. "News and subjective beliefs: A Bayesian approach to Bitcoin investments," Research in International Business and Finance, Elsevier, vol. 50(C), pages 336-356.
    3. Kwon, Ji Ho, 2020. "Tail behavior of Bitcoin, the dollar, gold and the stock market index," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 67(C).
    4. Telli, Şahin & Chen, Hongzhuan, 2020. "Structural breaks and trend awareness-based interaction in crypto markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    5. Garcia-Jorcano, Laura & Benito, Sonia, 2020. "Studying the properties of the Bitcoin as a diversifying and hedging asset through a copula analysis: Constant and time-varying," Research in International Business and Finance, Elsevier, vol. 54(C).
    6. Telli, Şahin & Chen, Hongzhuan, 2020. "Multifractal behavior in return and volatility series of Bitcoin and gold in comparison," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Kakinaka, Shinji & Umeno, Ken, 2021. "Exploring asymmetric multifractal cross-correlations of price–volatility and asymmetric volatility dynamics in cryptocurrency markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    8. Panayiotis Theodossiou & Polina Ellina & Christos S. Savva, 2022. "Stochastic properties and pricing of bitcoin using a GJR-GARCH model with conditional skewness and kurtosis components," Review of Quantitative Finance and Accounting, Springer, vol. 59(2), pages 695-716, August.
    9. Hamed Tabasi & Vahidreza Yousefi & Jolanta Tamošaitienė & Foroogh Ghasemi, 2019. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models," Administrative Sciences, MDPI, vol. 9(2), pages 1-17, May.
    10. Canh, Nguyen Phuc & Wongchoti, Udomsak & Thanh, Su Dinh & Thong, Nguyen Trung, 2019. "Systematic risk in cryptocurrency market: Evidence from DCC-MGARCH model," Finance Research Letters, Elsevier, vol. 29(C), pages 90-100.
    11. Park, Sangjin & Jang, Kwahngsoo & Yang, Jae-Suk, 2021. "Information flow between bitcoin and other financial assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    12. Claudeci Da Silva & Hugo Agudelo Murillo & Joaquim Miguel Couto, 2014. "Early Warning Systems: Análise De Ummodelo Probit De Contágio De Crise Dos Estados Unidos Para O Brasil(2000-2010)," Anais do XL Encontro Nacional de Economia [Proceedings of the 40th Brazilian Economics Meeting] 110, ANPEC - Associação Nacional dos Centros de Pós-Graduação em Economia [Brazilian Association of Graduate Programs in Economics].
    13. Alaoui, Marwane El & Bouri, Elie & Roubaud, David, 2019. "Bitcoin price–volume: A multifractal cross-correlation approach," Finance Research Letters, Elsevier, vol. 31(C).
    14. Panagiotidis, Theodore & Papapanagiotou, Georgios & Stengos, Thanasis, 2022. "On the volatility of cryptocurrencies," Research in International Business and Finance, Elsevier, vol. 62(C).
    15. T. Takaishi, 2021. "Power-Law Return-Volatility Cross Correlations of Bitcoin," Papers 2102.08187, arXiv.org.
    16. López-Martín, Carmen & Arguedas-Sanz, Raquel & Muela, Sonia Benito, 2022. "A cryptocurrency empirical study focused on evaluating their distribution functions," International Review of Economics & Finance, Elsevier, vol. 79(C), pages 387-407.
    17. Caporale, Guglielmo Maria & Zekokh, Timur, 2019. "Modelling volatility of cryptocurrencies using Markov-Switching GARCH models," Research in International Business and Finance, Elsevier, vol. 48(C), pages 143-155.
    18. Eom, Cheoljun & Kaizoji, Taisei & Kang, Sang Hoon & Pichl, Lukas, 2019. "Bitcoin and investor sentiment: Statistical characteristics and predictability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 511-521.
    19. Delson Chikobvu & Thabani Ndlovu, 2023. "The Generalised Extreme Value Distribution Approach to Comparing the Riskiness of BitCoin/US Dollar and South African Rand/US Dollar Returns," JRFM, MDPI, vol. 16(4), pages 1-16, April.
    20. Zhuhua Jiang & Walid Mensi & Seong-Min Yoon, 2023. "Risks in Major Cryptocurrency Markets: Modeling the Dual Long Memory Property and Structural Breaks," Sustainability, MDPI, vol. 15(3), pages 1-15, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jdataj:v:8:y:2023:i:7:p:122-:d:1201466. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.