英文标题：
《Closed-form Solutions of Relativistic Black-Scholes Equations》
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作者：
Yanlin Qu and Randall R. Rojas
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最新提交年份：
2017
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英文摘要：
  Drawing insights from the triumph of relativistic over classical mechanics when velocities approach the speed of light, we explore a similar improvement to the seminal Black-Scholes (Black and Scholes (1973)) option pricing formula by considering a relativist version of it, and then finding a respective solution. We show that our solution offers a significant improvement over competing solutions (e.g., Romero and Zubieta-Martinez (2016)), and obtain a new closed-form option pricing formula, containing the speed limit of information transfer c as a new parameter. The new formula is rigorously shown to converge to the Black-Scholes formula as c goes to infinity. When c is finite, the new formula can flatten the standard volatility smile which is more consistent with empirical observations. In addition, an alternative family of distributions for stock prices arises from our new formula, which offer a better fit, are shown to converge to lognormal, and help to better explain the volatility skew.
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中文摘要：
当速度接近光速时，从相对论战胜经典力学的经验中，我们探索了对开创性的Black-Scholes（Black and Scholes（1973））期权定价公式的类似改进，方法是考虑其相对论版本，然后找到相应的解。我们证明，我们的解决方案比竞争解决方案（如Romero和Zubieta Martinez（2016））有显著改进，并获得了一个新的封闭形式期权定价公式，其中包含信息传输速度限制c作为新参数。当c趋于无穷大时，新公式被严格证明收敛于Black-Scholes公式。当c为有限时，新公式可以展平标准波动率微笑，这与经验观察结果更为一致。此外，我们的新公式产生了一个股票价格分布的替代族，它提供了更好的拟合，显示收敛于对数正态分布，并有助于更好地解释波动率偏斜。
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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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