GARCH選擇權評價模型之複雜性研究

Abstract

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.