This research investigates pricing financial options based on the traditional martingale theory of arbitrage pricing applied to neural SDEs. We treat neural SDEs as universal It\^o process approximators. In this way we can lift all assumptions on the form of the underlying price process, and compute theoretical option prices numerically. We propose a variation of the SDE-GAN approach by implementing the Wasserstein distance metric as a loss function for training. Furthermore, it is conjectured that the error of the option price implied by the learnt model can be bounded by the very Wasserstein distance metric that was used to fit the empirical data.

中文翻译：

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神经期权定价

本研究基于应用于神经 SDE 的套利定价的传统鞅理论来研究定价金融期权。我们将神经 SDE 视为通用的 It\^o 过程逼近器。通过这种方式，我们可以取消对标的价格过程形式的所有假设，并以数值方式计算理论期权价格。我们通过将 Wasserstein 距离度量作为训练的损失函数来提出 SDE-GAN 方法的变体。此外，据推测，学习模型所隐含的期权价格的误差可以由用于拟合经验数据的 Wasserstein 距离度量来限制。