一种用于欧式期权定价的阻尼SWIFT方法：系数衰减、截断与误差分析
A Damped SWIFT Method for European Option Pricing: Coefficients Decay, Truncation, and Error Analysis
AI总结：
研究利用香农小波逆傅里叶技术的阻尼变体对欧式期权定价，通过对收益应用指数阻尼变换及分析傅里叶系数衰减，推导误差分解并给出实用规则，经实验验证该方法能提高精度、减少系数数量且保持稳定。
AI中文摘要：
当基础模型的特征函数可用时，我们引入了香农小波逆傅里叶技术（SWIFT）的阻尼变体来对欧式期权定价。关键思想是对收益应用指数阻尼变换，能在频域直接计算傅里叶系数而无需引入额外的物理域截断参数。通过利用相关傅里叶变换的奇异性结构，我们对这些系数的衰减进行了严格分析。对于轻尾模型，得到高斯型衰减估计；对于具有极点、代数分支点或对数分支点奇异性的半重尾和重尾模型，导出了带有显式多项式前置因子的指数衰减界。由此得到的精确界使得截断傅里叶级数无需依赖基础密度的累积量，而累积量在实际中往往不可用或难以计算。我们进一步推导了误差分解，分离出投影、截断和求积误差，并将分析转化为选择阻尼参数、分辨率水平和截断范围的实用规则。数值实验表明，该方法在需要显著更少的傅里叶系数的情况下持续提高了原始SWIFT方法的精度，并且在无阻尼方法恶化的情况下保持稳定。
英文摘要：
We introduce a damped variant of the Shannon Wavelet Inverse Fourier Technique (SWIFT) for pricing European options when the characteristic function of the underlying model is available. The key idea is to apply an exponential damping transformation to the payoff, which enables the direct computation of Fourier coefficients in the frequency domain without introducing an additional physical-domain truncation parameter. We provide a rigorous analysis of the decay of these coefficients by exploiting the singularity structure of the associated Fourier transforms. For light-tailed models, we obtain Gaussian-type decay estimates, while for semi-heavy and heavy-tailed models whose singularities are poles, algebraic branch points, or logarithmic branch points, we derive exponential decay bounds with explicit polynomial prefactors. The resulting sharp bounds make it possible to truncate the Fourier series without relying on the cumulants of the underlying density, which are often unavailable or difficult to compute in practice. We further derive an error decomposition separating projection, truncation, and quadrature errors, and translate the analysis into practical rules for selecting the damping parameter, resolution level, and truncation range. Numerical experiments demonstrate that the proposed approach consistently improves the accuracy of the original SWIFT method while requiring a significantly smaller number of Fourier coefficients and remaining stable in cases where the undamped method deteriorates.
