英文标题：
《A new median-based formula for the Black-Scholes-Merton Theory》
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作者：
Takuya Okabe and Jin Yoshimura
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最新提交年份：
2019
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英文摘要：
The Black-Scholes-Merton (BSM) theory for price variation has been well established in mathematical financial engineering. However, it has been recognized that long-term outcomes in practice may divert from the Black-Scholes formula, which is the expected value of the stochastic process of price changes. While the expected value is expected for the long-run average of infinite realizations of the same stochastic process, it may give an erroneous picture of nearly every realization when the probability distribution is skewed, as is the case for prices. Here we propose a new formula of the BSM theory, which is based on the median of the stochastic process. This formula makes a more realistic prediction for the long-term outcomes than the current Black-Scholes formula.
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中文摘要：
布莱克-斯科尔斯-默顿（Black-Scholes-Merton，BSM）价格变动理论在数学金融工程中已得到很好的应用。然而，人们已经认识到，实践中的长期结果可能会偏离Black-Scholes公式，该公式是价格变化随机过程的预期值。虽然预期值是针对同一随机过程的无限实现的长期平均值，但当概率分布发生偏差时，它可能会给出几乎所有实现的错误图片，如价格情况。本文提出了一个新的基于随机过程中值的BSM理论公式。该公式比当前的Black-Scholes公式对长期结果做出了更现实的预测。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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