摘要翻译：
在Black-Scholes模型下，研究了欧式看涨期权实现正收益的真实概率。研究发现，除了股票价格的增长率外，BS公式中出现的市场因素也决定了股票价格的变动概率。我们的数值研究表明，BS公式的偏差与股票价格的增长率有关。提出了一种欧式看涨期权定价的替代方法，该方法采用均衡论元，通过正收益概率确定期权价格。结果表明，对于货币外期权，其BS值平均大于本文提出的方法的值，而对于货币内期权，其BS值平均小于本文提出的方法的值。在数值研究中，我们还观察到隐含波动率的一个典型的微笑形状。这些理论观测与BS值的经验异常相似，表明所提出的估值方法可能有一定的优点。
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英文标题：
《Probabilities of Positive Returns and Values of Call Options》
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作者：
Guanghui Huang, Jianping Wan
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最新提交年份：
2009
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分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Pricing of Securities        证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/0912.4973