A new method to retrieve the risk-neutral probability measure from observed option prices is developed and a closed form pricing formula for European options is obtained by employing a modified Gram–Charlier series expansion, known as the Gauss–Hermite expansion. This expansion converges for fat-tailed distributions commonly encountered in the study of financial returns. The expansion coefficients can be calibrated from observed option prices and can also be computed, for example, in models with the probability density function or the characteristic function known in closed form. We investigate the properties of the new option pricing model by calibrating it to both real-world and simulated option prices and find that the resulting implied volatility curves provide an accurate approximation for a wide range of strike prices. Based on an extensive empirical study, we conclude that the new approximation method outperforms other methods both in-sample and out-of-sample.

中文翻译：

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通用封闭式期权定价公式

开发了一种从观察到的期权价格中检索风险中性概率测度的新方法，并通过使用改良的Gram-Charlier级数展开式（称为Gauss-Hermite展开式）获得欧洲期权的封闭式定价公式。这种扩展收敛于财务收益研究中经常遇到的胖尾分布。膨胀系数可以从观察到的期权价格中进行校准，也可以在例如具有已知封闭形式的概率密度函数或特征函数的模型中进行计算。通过对新期权定价模型的实际价格和模拟期权价格进行校准，我们研究了新期权定价模型的属性，并发现所得的隐含波动率曲线为广泛的执行价格提供了准确的近似值。