论文标题
有效评估双屏障选项和莱维过程的联合CPDF及其两个极端
Efficient evaluation of double-barrier options and joint cpdf of a Lévy process and its two extrema
论文作者
论文摘要
在本文中，我们开发了一种非常快速，准确的方法，用于通过在各种莱维模型中进行连续监视的双重障碍选项。计算在双重空间中，使用维纳 - hopf分解。对于参数空间中的宽区域，可以在几秒钟内实现$ 10^{ - 15} $的顺序，而$ 10^{ - 9} -9} -10^{ - 8} $的顺序在一秒钟内。使用集成线的sinh形式，变量的相应变化和简化的梯形规则来计算定价公式中的Wiener-HOPF因子和重复积分。如果Bromwich积分是使用Gaver-Wynn Rho加速而不是SINH-ACCELERANION计算的，则CPU时间通常较小，但精度为$ 10^{ - 9} -9} -10^{ - 6} $。显式定价算法和数值示例用于无触摸选项，数字（等效地，对于Lévy过程的联合分布函数及其最高和最高过程）以及呼叫选项。产生了几种图表来解释使用状态空间中时间离散化和基于插值的计算来准确定价的基本困难。
In the paper, we develop a very fast and accurate method for pricing double barrier options with continuous monitoring in wide classes of Lévy models; the calculations are in the dual space, and the Wiener-Hopf factorization is used. For wide regions in the parameter space, the precision of the order of $10^{-15}$ is achievable in seconds, and of the order of $10^{-9}-10^{-8}$ - in fractions of a second. The Wiener-Hopf factors and repeated integrals in the pricing formulas are calculated using sinh-deformations of the lines of integration, the corresponding changes of variables and the simplified trapezoid rule. If the Bromwich integral is calculated using the Gaver-Wynn Rho acceleration instead of the sinh-acceleration, the CPU time is typically smaller but the precision is of the order of $10^{-9}-10^{-6}$, at best. Explicit pricing algorithms and numerical examples are for no-touch options, digitals (equivalently, for the joint distribution function of a Lévy process and its supremum and infimum processes), and call options. Several graphs are produced to explain fundamental difficulties for accurate pricing of barrier options using time discretization and interpolation-based calculations in the state space.
