积分逆变换精确算法的金融应用

This research project proposes an inversion algorithm with computable error bounds for two-sided Laplace transforms, with its concrete financial applications within many categories. Enlightened by the celebrated Euler inversion method, this algorithm introduces novel discretization parameters and truncation parameters, in order to efficiently control the approximation error. Based on the computable error bounds, we can select these parameters appropriately to achieve any desired accuracy. Hence this algorithm is particularly useful to provide benchmarks. In many cases, the error bounds decay quickly (e.g., exponentially), making the algorithm very efficient. We would apply this algorithm to price exotic options such as spread options and barrier options under various asset pricing models, evaluate the joint cumulative distribution functions of related state variables, and estimate the parameters for many financial dynamic models. Intensive numerical examples will be provided via numerical experiments in this project, which indicate that the inversion algorithm is accurate, fast and easy to implement.

本研究项目针对双边拉普拉斯变换提出了一个具有误差显式上界的积分逆变换算法，及其许多类具体的金融应用。为了高效地控制逼近误差，此算法借鉴欧拉逆变换的方法，引入了新型的离散化参数和截断参数。根据两种误差的上界，我们可以直接选定合适的算法参数，来使得输出结果达到任意预先制定的精度。因此，本算法尤其适合为后续研究与应用提供参照标准数据。很多情况下，我们的误差上界迅速下降（比如以指数速度），使得本算法非常高效。我们将把此新算法应用于多种模型下奇异期权的定价（如差异期权与障碍期权），一些金融状态变量的联合分布函数的估值，以及多种金融动态模型的参数估计。本项目的数值实验将提供大量的数值运算范例，来表明新算法在金融应用中准确、快速并易于实现。