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比特币与标普500收益尾部：截尾稳定模型比较

文章 arXiv papers · 作者: A. H. Nzokem
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总结

这项研究比较比特币和标普500的每日收益分布，重点关注尾部概率以及损失和收益的严重程度。研究采用一种结合快速分数阶傅里叶变换与复合牛顿–柯特斯求积的数值方法，拟合七参数广义截尾稳定分布。报告的分布特征显示，标普500收益分布的峰度更高，而比特币收益的尾部更厚。

拟合模型显示，80.05%的标普500收益落在−1.06%至1.23%之间，相比之下比特币收益为40.32%。模型还估计，比特币每日极端收益出现得更频繁；在所述风险水平下，其平均风险价值约为该指数的四倍。对两种资产，估计的下行损失严重程度均高于上行收益严重程度。这些发现基于每日收益数据的模型估计；摘录未说明样本期、参数不确定性或差异是否能在样本外持续存在。

核心观点

  • 研究使用七参数广义温和稳定分布拟合比特币和标普500的每日收益。
  • 报告显示，标普500收益分布的峰度更高，而比特币收益呈现更厚的尾部。
  • 模型估计，比特币每日大幅波动的发生率高于指数中幅度相当的波动。
  • 对两种资产，估计的下行平均风险价值都高于上行严重程度。
  • 摘录未报告样本期或拟合估计值的不确定性。

标签

加密资产股票统计学风险管理美国市场
全文
# Bitcoin versus S&P 500 Index: Return and Risk Analysis


# Bitcoin versus S&P 500 Index: Return and Risk Analysis









The S&P 500 index is considered the most popular trading instrument in financial markets. With the rise of cryptocurrencies over the past years, Bitcoin has also grown in popularity and adoption. The paper aims to analyze the daily return distribution of the Bitcoin and S&P 500 index and assess their tail probabilities through two financial risk measures. As a methodology, We use Bitcoin and S&P 500 Index daily return data to fit The seven-parameter General Tempered Stable (GTS) distribution using the advanced Fast Fractional Fourier transform (FRFT) scheme developed by combining the Fast Fractional Fourier (FRFT) algorithm and the 12-point rule Composite Newton-Cotes Quadrature. The findings show that peakedness is the main characteristic of the S&P 500 return distribution, whereas heavy-tailedness is the main characteristic of the Bitcoin return distribution. The GTS distribution shows that $80.05\%$ of S&P 500 returns are within $-1.06\%$ and $1.23\%$ against only $40.32\%$ of Bitcoin returns. At a risk level ($α$), the severity of the loss ($AVaR_α(X)$) on the left side of the distribution is larger than the severity of the profit ($AVaR_{1-α}(X)$) on the right side of the distribution. Compared to the S&P 500 index, Bitcoin has $39.73\%$ more prevalence to produce high daily returns (more than $1.23\%$ or less than $-1.06\%$). The severity analysis shows that at a risk level ($α$) the average value-at-risk ($AVaR(X)$) of the bitcoin returns at one significant figure is four times larger than that of the S&P 500 index returns at the same risk.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。