arXiv 0912.49732009-12-25q-fin.PR

正收益概率与看涨期权的价值

Probabilities of Positive Returns and Values of Call Options

Guanghui Huang, Jianping Wan

备注：: 14 pages, 4 figures, 2 tables

摘要：

在布莱克-斯科尔斯模型下研究了欧式看涨期权获得正收益的真实概率。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这一概率。我们的数值研究表明，BS公式的偏差与股票价格的增长率相关。提出了欧式看涨期权定价的一种替代方法，该方法采用均衡论的观点，通过正收益概率来确定期权价格。研究发现，对于价外期权，BS值平均大于建议方法的值，而对于价内期权，BS值平均小于建议方法的值。在我们的数值研究中还观察到一个典型的微笑形状的隐含波动率。这些理论观察结果与BS值的经验异常相似，这表明所提出的估值方法可能具有一定的优点。

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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