@article {Kwok28,
author = {Kwok, Yue Kuen and Lau, Ka Wo},
title = {Pricing Algorithms for Options with Exotic Path-Dependence},
volume = {9},
number = {1},
pages = {28--38},
year = {2001},
doi = {10.3905/jod.2001.319167},
publisher = {Institutional Investor Journals Umbrella},
abstract = {Path-dependent derivatives present a major challenge to standard valuation algorithms. Closed-form solutions are available for a handful of simple cases like {\textquotedblleft}out{\textquotedblright} options with continuously monitored barriers, or odd special cases like Asian options based on the geometric average. Basic lattice techniques can work for a somewhat larger subset of instruments, such as discretely monitored barrier options. But as the variety of options traded in the marketplace expands, seemingly without bound, the path-dependency problem quickly becomes formidable. For some important cases, lattice-based solutions have been devised that involve carrying an auxiliary variable through the asset price tree to keep track of the current state of the path at each price node, a technique known as a {\textquotedblleft}Forward Shooting Grid.{\textquotedblright} In this article, Kwok and Lau demonstrate how to set one up and provide several examples to illustrate its use, pricing Parisian options, both standard and exotic (e.g., a {\textquotedblleft}cumulative Parisian{\textquotedblright} contract), with complex dependence on the asset price path. The convergence rate in the examples is shown to be proportional to the square root of the number of time steps.},
issn = {1074-1240},
URL = {https://jod.pm-research.com/content/9/1/28},
eprint = {https://jod.pm-research.com/content/9/1/28.full.pdf},
journal = {The Journal of Derivatives}
}