We use intraday data to construct measures of the realized volatility of bitcoin returns. We then construct measures that focus exclusively on relatively large realizations of returns to assess the tail shape of the return distribution, and use the heterogeneous autoregressive realized volatility (HAR-RV) model to study whether these measures help to forecast subsequent realized volatility. We find that mainly forecasters suffering a higher loss in case of an underprediction of realized volatility (than in case of an overprediction of the same absolute size) benefit from using the tail measures as predictors of realized volatility, especially at a short and intermediate forecast horizon. This result is robust controlling for jumps and realized skewness and kurtosis, and it also applies to downside (bad) and upside (good) realized volatility.

我们使用日内数据来衡量比特币回报的实际波动率。然后，我们构建了专门针对相对较大的收益实现的度量来评估收益分布的尾部形状，并使用异构自回归实现波动率 (HAR-RV) 模型来研究这些度量是否有助于预测随后的实现波动率。我们发现，在实际波动率被低估的情况下（比在相同绝对规模的高估的情况下）遭受更高损失的主要预测者受益于使用尾部测量作为实际波动率的预测因子，特别是在短期和中期预测范围内. 这个结果是对跳跃和实现的偏度和峰度的稳健控制，它也适用于下行（坏）和上行（好）的实现波动。