A Wavelet Analysis of Bitcoin Price Volatility Dynamic
Authors: Mohamed BEN ABDALLAH , Omar TALBI 
Published: February 2024

The cryptocurrency market has experienced significant growth in international finance in recent years, attracting a large number of investors. This has led to a substantial increase in the overall trading volume[1], surpassing 1.2 trillion USD in July2023. Bitcoin in particular, has garnered significant interest from both advanced and emerging economies. Notably, Bitcoin is legal tender in El Salvador and the Central African Republic. The cryptocurrency market possesses distinct characteristics that set it apart from traditional markets such as exchanges, commodities, and equities. Its decentralization, facilitated by Blockchain technology, stands as a key differentiating factor. This technology enables anonymous trading of cryptocurrencies, with the identities of market participants, account holders, and electronic wallet managers remaining unknown. Consequently, there is an inherent ambiguity when it comes to characterizing the behavior of these investors or determining their preferred trading horizons. In this context, an important question arises: how do investors in the cryptocurrency market navigate price volatility? Furthermore, how do their trading strategies, which are inherently tied to their investment horizons, impact each other and consequently influence market prices? The heterogeneity hypothesis, which is a prevalent assumption in financial markets, is particularly relevant when exploring how investors in the cryptocurrency market navigate price volatility. The diverse trading strategies and approaches to handling price fluctuations among heterogeneous investors impact and influence the overall volatility and price dynamics of cryptocurrencies. The heterogeneity market hypothesis[2] refers to the existence of differences among investors or traders regarding their beliefs, information, risk preferences, investment strategies, and time horizons. In a heterogeneous market, investors, traders and financial institutions have varying views and expectations about the future performance of assets. These differences can manifest in various ways, such as market information access, market liquidity provision, trading strategies and market structure. While numerous empirical studies have explored the concept of market heterogeneity in relation to traditional assets such as those conducted by Müller et al. (1993;1997), Lux and Marchesi (2000), LeBaron (2000), Dacorogna et al. (2001) and Benhmad (2011), there is a paucity of research on this topic specifically focusing on cryptocurrencies. This paper aims to contribute to the existing literature that investigates the hypothesis of investor heterogeneity in traditional markets, including forex, stocks, and commodities. Specifically, we focus on the cryptocurrency market, which is predominantly dominated by Bitcoin. As of November 2021[3], Bitcoin holds the distinction of being the most actively traded cryptocurrency, with a market capitalization exceeding 1.2 trillion USD. Given its significance, Bitcoin garners substantial interest from investors across various categories. Therefore, this research seeks to uncover potential synergies among participants[4] in the cryptocurrency market and identify investor types and investment horizons prevalent in this market. By understanding these factors, we can gain insights into the dynamic volatility displayed by Bitcoin’s price. To tackle this issue, we investigate Bitcoin’s price volatility, analyzing causal relationships among short-term, medium and long-term traders by using wavelet transform to decompose volatility at different trading frequency scales[5] considered, then Granger causality test will be employed to determine if changes in one scale impact others. Furthermore, we extend this analysis by employing the nonlinear causality test proposed by Hmamouche. Y (2020). This nonlinear causality test goes beyond the limitations of the linear causality test and helps identifying potential nonlinear causal effects that may exist between the volatilities at different frequency scales, which could be overlooked by the linear causality test. The rest of this paper is organized as follows: Section 2 presents the theoretical framework relatively to the heterogeneity market hypothesis. Section 3 focuses on the empirical review. Section 4 and 5 turns to the data and methodology. Section 6 provides the empirical findings. Section 7 concludes.