arXiv 2310.024362023-10-03q-fin.ST

比特币与标普500指数：收益与风险分析

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

A. H. Nzokem

备注：: 26 page, 16 figures
发表信息：: Math. Comput. Appl. 2024, 29(3), 44;
DOI：: 10.3390/mca29030044

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AI总结：

本文通过拟合七参数GTS分布并采用FRFT方案，对比比特币与标普500指数日收益率的分布特征与尾部风险，发现比特币具有重尾性且极端损失严重程度显著高于标普500指数。

摘要：

标普500指数被认为是金融市场中最受欢迎的交易工具。随着过去几年加密货币的兴起，比特币的受欢迎程度和采用率也在不断增长。本文旨在分析比特币和标普500指数的日收益率分布，并通过两种金融风险度量评估其尾部概率。在方法上，我们使用比特币和标普500指数的日收益率数据，拟合七参数广义调和稳定（GTS）分布，所采用的先进快速分数阶傅里叶变换（FRFT）方案由快速分数阶傅里叶（FRFT）算法与12点复合牛顿-柯特斯求积规则相结合而开发。研究结果表明，尖峰性是标普500收益率分布的主要特征，而重尾性是比特币收益率分布的主要特征。GTS分布显示，标普500指数80.05%的收益率位于-1.06%和1.23%之间，而比特币收益率仅有40.32%位于该区间。在风险水平（α）下，分布左侧的损失严重程度（AVaR_α(X)）大于分布右侧的收益严重程度（AVaR_{1-α}(X)）。与标普500指数相比，比特币产生高日收益率（超过1.23%或低于-1.06%）的可能性高出39.73%。严重程度分析表明，在相同风险水平（α）下，比特币收益率的平均风险价值（AVaR(X)）在一个有效数字上是标普500指数收益率的四倍。

英文摘要：

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.

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