離散式障礙選擇權之數值方法評價: 適應性網格模型與其他競爭技術

Valuation of Numerical Methods for Discrete Barrier Options: the Adaptive Mesh Model and Other Competing Techniques

許智睿(Chih-Jui Shea)

指導教授 ： 呂育道

國立臺灣大學/電機資訊學院/資訊工程學研究所/碩士(2006年)

https://doi.org/10.6342/NTU.2006.00152

摘要

無資料

關鍵字

適應性網格模型 ； 數值方法 ； 離散式障礙選擇權 ； 雙障礙選擇權 ； 三元樹 ； BGK模型 ； 微分積分法 ； 選擇權評價

並列摘要

This thesis develops an Adaptive Mesh Model for pricing discrete double barrier options. Adaptive Mesh Model is a trinomial lattice that applies higher resolution to where nonlinearity errors occur. Since an Adaptive Mesh Model was first proposed for discrete single barrier options in 1999 by Ahn, Figlewski, and Gao, no further research in Adaptive Mesh Model has been carried out for pricing discrete barrier options. Furthermore, numerical data of the Adaptive Mesh Model are also scarce in the paper of Ahn et al.. This thesis bases on the lattice structure of Ahn et al. and extends the Adaptive Mesh Model to price discrete double barrier options. Besides, since there is no close-form solution for discrete barrier options, many suggesting methods have been declared to price discrete barrier options fast and accurately, but no one can tell exactly what is the best. We also make a complete comparisons of the Adaptive Mesh Model with other methods no matter in accuracy or in efficiency. Our numerical results show that the Adaptive Mesh Model does not only generally surpass the
other lattice methods and the BGK formula approach, but also
exceed the quadrature method in efficiency with accurate enough outcomes.

並列關鍵字

Adaptive Mesh Model ； numerical valuation techniques ； discrete barrier options ； double barrier options ； trinomial trees ； enhanced binomial trees ； BGK model ； quadrature method ； option pricing

參考文獻

Ahn, Dong-Hyun, Stephen Figlewski, and Bin Gao, 1999, Pricing discrete barrier options with an adaptive mesh model, The Journal of Derivatives

Andricopoulos, Ari D., Martin Widdicks, Peter W. Duck, and David P. Newton, 2003, Universal option valuation using quadrature methods, Journal of Financial Economics 67, 447–471.

Broadie, Mark, Paul Glasserman, and Steven Kou, 1997, A continuity correction for discrete barrier options, Mathematical Finance 7, 325–349.

Broadie, Mark, Paul Glasserman, and Steven Kou, 1999, Connecting discrete and continuous path-dependent options, Finance Stochastics 3, 55–82.

Cheuk, Terry H.F., and Ton C.F. Vorst, 1996, Complex barrier options, The Journal of Derivatives 4, 8–22.