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On time-scaling of risk and the square-root-of-time rule

机译:关于风险的时间尺度和时间的平方根规则

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摘要

Many financial applications, such as risk analysis, and derivatives pricing, depend on time scaling of risk. A common method for this purpose is the square-root-of-time rule where an estimated quan-tile of a return distribution is scaled to a lower frequency by the square root of the time horizon. This paper examines time scaling of quantiles when returns follow a jump diffusion process. We demonstrate that when jumps represent losses, the square-root-of-time rule leads to a systematic underestimation of risk, whereby the degree of underestimation worsens with the time horizon, the jump intensity and the confidence level.
机译:许多金融应用程序(例如风险分析和衍生产品定价)取决于风险的时间尺度。用于此目的的常用方法是时间平方根规则,其中,时间分布的平方根将收益分布的估计分位数缩放到较低的频率。本文研究了当收益遵循跳跃扩散过程时分位数的时间缩放。我们证明,当跳跃代表损失时,时间的平方根规则会导致系统地低估风险,因此低估的程度会随着时间范围,跳跃强度和置信度而变差。

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