GARCH選擇權評價模型之複雜性研究

The Complexity of GARCH Option Pricing Models

陳盈潔(Ying-Chieh Chen)

指導教授 ： 呂育道

國立臺灣大學/管理學院/資訊管理學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00589

摘要

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。

關鍵字

GARCH ； 路徑相關 ； 三元樹 ； 選擇權評價

並列摘要

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.

並列關鍵字

GARCH ； path dependency ； trinomial tree ； option pricing

參考文獻

[1] Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31, pp. 307–327.

[2] Cakici, N., and Topyan, K. (2000) The GARCH Option Pricing Model: A Lattice Approach. Journal of Computational Finance, 3(4), pp. 71–85.

[3] Duan, J.-C. (1995) The GARCH Option Pricing Model. Mathematical Finance, 5(1), pp. 13–32.

[4] Engle, R. (1993) Measuring and Testing the Impact of News on Volatility. Journal of Finance, 48, pp. 1749–1778.

[5] Glosten. L., Jagannathan, R., and Runkle, D. (1993) On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks. Journal of Finance 48, pp. 1779–1801.