A long-term alternative formula for a stochastic stock price model
A long-term alternative formula for a stochastic stock price model
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随机股票价格模型的长期替代公式
DOI：
10.1007/s42452-022-05176-9
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发表时间：
2022
影响因子：
2.6
通讯作者：
Jin Yoshimura
中科院分区：
文献类型：
--
作者：
Takuya Okabe;Jin Yoshimura
本研究提出了一种股票价格变化的长期替代公式，由基于中位数而不是均值或预期值的几何布朗运动描述。所提出的方法是受到在偏远地区进行的观察的启发，其中赌注对冲或多样化策略的优化是基于与期望值不同的度量（例如几何平均值）来解释的。当可能结果的概率分布显着偏斜时，众所周知，预期值由于其对异常值（罕见发生的极端值）的敏感性而导致错误的图像。由于几何平均值或其对应的对数正态分布中位数没有这个缺点，因此它为我们提供了更合适的度量，特别是用于评估由异常值主导的长期结果。因此，本公式对大波动的长期结果做出了更现实的预测，其概率分布变得明显重尾。
This study presents a long-term alternative formula for stock price variation described by a geometric Brownian motion on the basis of median instead of mean or expected values. The proposed method is motivated by the observation made in remote fields, where optimalizty of bet-hedging or diversification strategies is explained based on a measure different from expected value, like geometric mean. When the probability distribution of possible outcomes is significantly skewed, it is generally known that expected value leads to an erroneous picture owing to its sensitivity to outliers, extreme values of rare occurrence. Since geometric mean, or its counterpart median for the log-normal distribution, does not suffer from this drawback, it provides us with a more appropriate measure especially for evaluating long-term outcomes dominated by outliers. Thus, the present formula makes a more realistic prediction for long-term outcomes of a large volatility, for which the probability distribution becomes conspicuously heavy-tailed.