Bitcoin Volatility Estimate Applying Rogers and Satchell Range Model

Eloisa Cadenas · International Journal of Finance, Insurance and Risk Management · Febrero de 2022

Eloisa Cadenas-Morales y Edgar Ortiz (Universidad Nacional Autónoma de México). International Journal of Finance, Insurance and Risk Management, vol. XII, núm. 1, 2022, pp. 49–79. Artículo en inglés; aquí se reproducen el resumen, la introducción y las conclusiones.

Abstract

The objectives of this paper are, first, to synthesize the main events that have influenced the development and volatility of bitcoin, and second to present and apply the Rogers and Satchell range model (1993) for the measurement of bitcoin volatility. The findings support risk management and portfolio diversification; further studies extending it, considering leptokurtosis and other moments of the distribution of the series, would be beneficial. The work emphasizes the need for regulation of cryptocurrencies and proposes creating additional IMF Special Drawing Rights as a global cryptocurrency alternative.

Keywords: Bitcoin volatility, Rogers and Satchell, range models, cryptocurrencies, central bank digital currencies. JEL: C01, C13, C58, D53, F37.

Introduction

The daring innovations of bitcoin and ulterior altcurrencies –decentralized, non-fiat currencies based on blockchain technique– came immediately to the attention of investors, regulation authorities, entrepreneurs, consumers, and the academia leading to controverted points of view and research. Their detractors stressed their lack of legality, scalability vs. other forms of digital payments (mainly credit cards), unknown security against hackers, misuse to hide illicit operations like money laundering, excessive volatility, lack of inherent value, and the lack of regulations.

Their defenders welcomed their appearance even though their original characteristics were limited and unknown. They stressed the possibility of peer-to-peer faster transactions, smaller transaction fees, greater confidentiality of transactions, easing of international trade, individual control of one's account, and the potential alternative for new and greater investment and credit opportunities.

Strong debates took place particularly in the professional and academic worlds. Due to its initial reduced acceptance and limited knowledge about their market behavior bitcoin and other cryptocurrencies were mostly considered as volatile speculative investments, far from becoming fully currencies assets accepted worldwide for local and international transactions and as mean of exchange.

Indeed, the road full of favorable and unfavorable situations paved the way to these currencies' volatility. Considering their importance of this intricate path of development of bitcoin, the first objective and contribution of this paper is to highlight some facts related to the erratic behavior of bitcoin's prices and returns. The second objective and contribution of this work is to present and apply a novel method to measure the volatility of financial assets, Rogers and Satchel range model (1993). This methodology has been practically ignored to measure the volatility of bitcoin.

Concluding Remarks

The volatility of bitcoin has been subject to various events related to either its acceptation or rejection as a full financial asset. Considering the complex behavior of that asset's volatility, this work presents and applies Rogers and Satchell range model. A revision of the literature reveals that range cryptocurrencies volatilities have mostly studied using diverse GARCH type but stressing comparative approaches and limited to closing prices series, which might lead to some erroneous volatility estimation by ignoring abrupt intraday changes. To overcome such limitation high frequency data models have been used.

However, high frequency data analysis does not necessarily offer better volatility estimates. Indeed, Lyócsa et al. (2021) assert that "high-frequency volatility models outperform low-frequency volatility models only for short-term forecasts." Consequently, to GARCH and high-frequency models range models emerged as practical alternatives. However, range models for variance analysis applied to cryptocurrencies have been practically overlooked. These models have been mainly applied to estimate the volatility of stock markets, exchange rates, and commodity exchange traded funds. Few related studies using range models to estimate cryptocurrencies volatility with these models are reported in the literature. No applications of the R&S models are reported in the literature, making this work the first to fully acknowledge and employ it. The evidence confirms its usefulness: R&S is an unbiased estimator regardless of drift and allows the error not to be affected by the high and low values of the series.

Thus, the empirical evidence reveals R&S estimations of both the variance and the standard deviation of bitcoin volatility are higher than those estimated using the conventional volatility formula, overcoming underestimation when normality is assumed. Additionally, as expected, bitcoin in the long run has been higher compared with the S&P's performance. A ten-year variance annualized for the Standard and Poor Depository Receipts Fund is 1.53% versus 1.93% estimated with the R&S model. Finally, in the last quarter of the sample conventional measurements of the variance and covariance of bitcoin are greater than those estimated using the R&S range model. This probably can be attributed to speculation, as well as to outliers present at the beginning of the Covid-19 crisis. This evidence suggests the need to use more advanced GARCH models to capture the complex behavior of bitcoin, particularly during short (speculative) periods.

Finally, an important evidence drawn from key events related to the evolution of bitcoin reveals the need for further and improved regulation of cryptocurrencies, which are definitively evolving to stay and most likely will organize in some collaboration nets. Also, countries are contemplating the creation of Central Banks Digital Currencies which will coexist with private cryptocurrencies. An appealing suggestion is the creation of an IMF global currency. However, negotiations would be very complex and lengthy. A practical solution could be to increment SDRs along with a redistribution of IMF quotas, promoting a greater participation of developing nations. A strengthened international governance would help to overcome the problems created by the covid pandemic, increasing investments and growth. All member countries would retain their control of local monetary policies.

Future research should extend R&S model considering leptokurtosis, other moments of the distribution, additional distributions, and short and long run volatility estimates.

Publicado originalmente en International Journal of Finance, Insurance and Risk Management, febrero de 2022. Leer el artículo completo ↗