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期权收益、正收益概率与布莱克–斯科尔斯定价偏差

文章 arXiv papers · 作者: Guanghui Huang et al.
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总结

本文档研究在布莱克–斯科尔斯框架下，欧式看涨期权获得正收益的概率。文中指出，该概率取决于模型中的市场输入以及股票增长率，并报告数值定价偏差与该增长率有关。

作者基于均衡论证和获得正收益的概率，提出一种替代的看涨期权估值方法。在数值分析中，与替代估值相比，布莱克–斯科尔斯价格往往对虚值期权定得更高，对实值期权定得更低。分析还得出了常见的隐含波动率微笑。这些理论模式被描述为与观察到的布莱克–斯科尔斯异常相似，但文中没有提供实证数据集、估计流程或样本外验证。因此，应将该估值方法视为一种理论替代方案，而非已确立的标准定价方法替代品。

核心观点

  • 研究考察布莱克–斯科尔斯假设下欧式看涨期权的正收益概率。
  • 报告称，该概率取决于模型市场输入和股票增长率。
  • 一种拟议的均衡方法根据看涨期权获得正收益的概率进行估值。
  • 数值比较显示，虚值和实值看涨期权的相对价格不同。
  • 文中描述的隐含波动率微笑和定价模式属于理论发现。

标签

期权衍生品定价波动率统计学
全文
# Probabilities of Positive Returns and Values of Call Options


# Probabilities of Positive Returns and Values of Call Options









The true probability of a European call option to achieve positive return is investigated under the Black-Scholes model. It is found that the probability is determined by those market factors appearing in the BS formula, besides the growth rate of stock price. Our numerical investigations indicate that the biases of BS formula is correlated with the growth rate of stock price. An alternative method to price European call option is proposed, which adopts an equilibrium argument to determine option price through the probability of positive return. It is found that the BS values are on average larger than the values of proposed method for out-of-the-money options, and smaller than the values of proposed method for in-the-money options. A typical smile shape of implied volatility is also observed in our numerical investigation. These theoretical observations are similar to the empirical anomalies of BS values, which indicates that the proposed valuation method may have some merit.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。