标题： 一种用于校准金融模型的空间映射方法及其在Heston模型中的应用 显示英文标题

标题： A Space Mapping approach for the calibration of financial models with the application to the Heston model

摘要： 我们提出了一种新颖的方法，用于对亚式看跌期权定价的Heston模型进行参数校准，即空间映射。由于Heston模型中的少数参数无法直接从真实市场数据中提取，因此对真实市场数据的校准是隐式的，因此是一项具有挑战性的任务。此外，模型中的一些参数是非线性的，这使得在校准过程中难以找到优化问题的全局最小值。我们的方法基于空间映射的思想，利用了一个允许优化的粗略代理模型的残差和一个需要校准的精细模型。在我们的案例中，使用Heston模型SDE对亚式期权进行定价是精细模型，而代理模型被选为对欧式期权进行定价的Heston模型PDE。我们使用来自带有PDE的优化的已知技术，正式推导出一种针对PDE约束校准模型的梯度下降算法。我们的主要目标是提供证据，表明空间映射方法在金融校准任务中有用。数值结果证明了我们方法的可行性。 显示英文摘要

摘要： We present a novel approach for parameter calibration of the Heston model for pricing an Asian put option, namely space mapping. Since few parameters of the Heston model can be directly extracted from real market data, calibration to real market data is implicit and therefore a challenging task. In addition, some of the parameters in the model are non-linear, which makes it difficult to find the global minimum of the optimization problem within the calibration. Our approach is based on the idea of space mapping, exploiting the residuum of a coarse surrogate model that allows optimization and a fine model that needs to be calibrated. In our case, the pricing of an Asian option using the Heston model SDE is the fine model, and the surrogate is chosen to be the Heston model PDE pricing a European option. We formally derive a gradient descent algorithm for the PDE constrained calibration model using well-known techniques from optimization with PDEs. Our main goal is to provide evidence that the space mapping approach can be useful in financial calibration tasks. Numerical results underline the feasibility of our approach.