呂育道臺灣大學：資訊工程學研究所許智睿Shea, Chih-JuiChih-JuiShea2007-11-262018-07-052007-11-262018-07-052006http://ntur.lib.ntu.edu.tw//handle/246246/53739This 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.1 Introduction 5 I Barrier Options.....................................5 A Barrier Option Basics...........................5 B Pricing of Barrier Options......................6 2 The Adaptive Mesh Model 10 I Approximation Error in Lattice Models..............10 III Application of the Adaptive Mesh Model to Plain Vanilla Options..........................................14 IV Extending the AMM Model to Discrete Single Barrier Options..................................................18 V Further Extending to Discrete Double Barrier Options..................................................22 3 Numerical Results 29 I Trinomial Lattice Mechanisms.......................29 A The Ritchken Trinomial Tree Mechanism..........29 B The Enhanced Trinomial Tree Mechanism..........31 C Numerical Comparisons..........................32 II The BGK Formula Approach..........................42 A Numerical Comparisons..........................44 III The Quadrature Method............................44 A Pricing Discrete Double Moving Knock-out Options..................................................49 B Numerical Comparisons..........................51 4 Conclusions 58597109 bytesapplication/pdfen-US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Adaptive Mesh Modelnumerical valuation techniquesdiscrete barrier optionsdouble barrier optionstrinomial treesenhanced binomial treesBGK modelquadrature methodoption pricingthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/53739/1/ntu-95-R91922030-1.pdf