呂育道Lyuu, Yuh-Dauh臺灣大學:資訊管理學研究所陳盈潔YUH-DAUH LYUU2010-05-052018-06-292010-05-052018-06-292009U0001-0901200916210000http://ntur.lib.ntu.edu.tw//handle/246246/179932建立樹狀模型評價選擇權時，我們通常以增加一日的切割數，n，來增進評價的正確性，但增加 n 的同時也降低了評價的效率性。在LGARCH下，樹狀模型隨著 n 增加會導致樹上之總點數呈指數型成長。Lyuu and Wu (2005)發現，在LGARCH下，樹狀模型上之總點數呈指數型成長與否和 n 有關。但並非所有的GARCH模型皆同。我們發現，LGARCH、NGARCH、GJR-GARCH、TS-GARCH和TGARCH有類似之性質，而在Heston-Nandi和VGARCH下，樹狀模型上之總點數呈指數型成長與否則與 n 無關。When building trees to price options, we often increase the number of partitions per day, n , to improve accuracy. But increasing n often lowers efficiency. Under LARCH, raising n makes the GARCH tree grow exponentially. Lyuu and Wu (2005) prove that the criteria for explosion and non-explosion under LGARCH depend on n . Surprisingly, not all GARCH models share the same property. This thesis proves that LGARCH, NGARCH, GJR-GARCH, TS-GARCH and TGARCH share this property, but the Heston-Nandi model and VAGRCH do not.Chapter 1 Introduction 1hapter 2 The GARCH Models and the Change of Measure 3hapter 3 The RT Tree 7hapter 4 The Mean-Tracking (MT) Tree 11hapter 5 LGARCH 15.1 The Criterion for Explosion 15.2 The Criterion for Non-Explosion 15.3 Numerical Results under Explosion Conditions 16.4 Numerical Results under Non-Explosion Conditions 17hapter 6 NGARCH 19.1 The Criterion for Explosion 19.2 The Criterion for Non-Explosion 19.3 Numerical Results under Explosion Conditions 20.4 Numerical Results under Non-Explosion Conditions 21hapter 7 GJR-GARCH 23.1 The Criterion for Explosion 23.2 The Criterion for Non-Explosion 24.3 Numerical Results under Explosion Conditions 24.4 Numerical Results under Non-Explosion Conditions 25hapter 8 TS-GARCH 27.1 The Criterion for Explosion 27.2 The Criterion for Non-Explosion 28.3 Numerical Results under Explosion Conditions 30.4 Numerical Results under Non-Explosion Conditions 31hapter 9 TGARCH 32.1 The Criterion for Explosion 32.2 The Criterion for Non-Explosion 33.3 Numerical Results under Explosion Conditions 33.4 Numerical Results under Non-Explosion Conditions 34hapter 10 The Heston-Nandi Model 360.1 The Criterion for Explosion 360.2 The Criterion for Non-Explosion 380.3 Numerical Results under Explosion Conditions 400.4 Numerical Results under Non-Explosion Conditions 42hapter 11 VGARCH 451.1 The Criterion for Explosion 451.2 The Criterion for Non-Explosion 461.3 Numerical Results under Explosion Conditions 481.4 Numerical Results under Non-Explosion Conditions 50hapter 12 Conclusion 52ibliography 53application/pdf1214586 bytesapplication/pdfen-USGARCH路徑相關三元樹選擇權評價path dependencytrinomial treeoption pricinghttp://ntur.lib.ntu.edu.tw/bitstream/246246/179932/1/ntu-98-R95723051-1.pdf