论文标题
有效评估Lévy过程及其极值功能功能的期望
Efficient evaluation of expectations of functions of a Lévy process and its extremum
论文作者
论文摘要
我们证明了简单的一般公式，可以期望列维工艺的功能及其运行的极值。在其他条件下，我们使用傅立叶/拉普拉斯反转和维也纳-HOPF分解得出分析公式，并讨论实现这些公式的有效数值方法。作为应用程序，计算了该过程的累积概率分布函数及其运行最大值以及以其最大值交换股票功率的期权的价格。最有效的数值方法使用SINH加速技术和简化的梯形规则。在具有中等特征的MAC上运行的MATLAB中的程序可以在几毫秒内获得精度E-7，并且在几秒钟内获得了更好的E-7。
We prove simple general formulas for expectations of functions of a Lévy process and its running extremum. Under additional conditions, we derive analytical formulas using the Fourier/Laplace inversion and Wiener-Hopf factorization, and discuss efficient numerical methods for realization of these formulas. As applications, the cumulative probability distribution function of the process and its running maximum and the price of the option to exchange the power of a stock for its maximum are calculated. The most efficient numerical methods use the sinh-acceleration technique and simplified trapezoid rule. The program in Matlab running on a Mac with moderate characteristics achieves the precision E-7 and better in several milliseconds, and E-14 - in a fraction of a second.
