The additive process generalizes the L\'evy process by relaxing its assumption of time-homogeneous increments and hence covers a larger family of stochastic processes. Recent research in option pricing shows that modeling the underlying log price with an additive process has advantages in easier construction of the risk-neural measure, an explicit option pricing formula and characteristic function, and more flexibility to fit the implied volatility surface. Still, the challenge of calibrating an additive model arises from its time-dependent parameterization, for which one has to prescribe parametric functions for the term structure. For this, we propose the neural term structure model to utilize feedforward neural networks to represent the term structure, which alleviates the difficulty of designing parametric functions and thus attenuates the misspecification risk. Numerical studies with S\&P 500 option data are conducted to evaluate the performance of the neural term structure.

翻译：加性过程通过放宽其增量时间齐次的假设，推广了Lévy过程，从而涵盖了一个更广泛的随机过程族。期权定价领域的最新研究表明，使用加性过程对标的资产对数价格进行建模具有多重优势：风险中性测度的构建更为简便，能够获得显式的期权定价公式与特征函数，并且在拟合隐含波动率曲面时具有更高的灵活性。然而，加性模型的校准挑战源于其时间依赖的参数化方式，这要求必须为期限结构预先设定参数化函数。为此，我们提出神经期限结构模型，利用前馈神经网络来表征期限结构，从而减轻了设计参数化函数的困难，并降低了模型设定错误的风险。我们利用标普500指数期权数据进行了数值研究，以评估神经期限结构的性能。