This paper proposes an efficient method for calculating European option prices under local, stochastic, and fractional volatility models. Instead of directly calculating the density function of a target underlying asset, we replicate it from a simpler diffusion process with a known analytical solution for the European option. For this purpose, we derive six functions that characterize the density function of a diffusion process, for both the original and simpler processes and match these functions so that the latter mimics the former. Using the analytical formula, we then approximate the option price of the target asset. By comparison with previous works and numerical experiments, we show that the accuracy of our approximation is high, and the calculation is fast enough for practical purposes; hence, it is suitable for calibration purposes.

中文翻译：

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欧洲期权定价的复制方案

本文提出了一种在局部、随机和部分波动率模型下计算欧式期权价格的有效方法。我们不是直接计算目标标的资产的密度函数，而是从更简单的扩散过程中复制它，并使用已知的欧式期权分析解。为此，我们推导出六个函数来表征扩散过程的密度函数，用于原始过程和更简单的过程，并匹配这些函数，以便后者模仿前者。使用分析公式，我们然后近似目标资产的期权价格。通过与以前的工作和数值实验的比较，我们表明我们的近似精度很高，计算速度足够快，可以满足实际用途；因此，它适用于校准目的。