結構改變下Black-Scholes與Hull-White評價模型之應用－以台灣股價指數選擇權為例

Evaluating Black-Scholes and Hull-White Assess Models on TAIEX Options with Structure Changes

陳文典(Wen-Den Chen) ； 陳依兌(Yi-Tui Chen) ； 張東生(Dong-Shang Chang) ； 林慧芳(Hwei-Fang Lin)

《中華管理學報》 10卷1期 (2009/03) Pp. 93-106

https://doi.org/10.30053/CHJM.200903.0004

摘要

Black-Scholes模型之波動不變的假設並無法貼切說明實際市場，Hull-White模型因此提出了隨機波動的假設，大幅降低因假設不符合實際造成估計誤差過高的困擾。但Hull-White模型未考慮到市場價格容易受到外部事件衝擊而改變價格的波動路徑因而造成估計誤差；本文以不同的波動假設重新對Black-Scholes 與 Hull-White模型進行探討。
本文以Black-Scholes與Hull-White兩模型分別搭配歷史波動與GARCH模型，並分別以F-test與Wald-test進行結構性改變檢定，藉由檢定找出結構變動時間點，重新區分各子區間，並以適合各子區的波動對價格進行估計，分析估計誤差是否有降低，結果發現結構性改變檢定將可找出較適合各子區間的波動，使估計結果更為準確，且在維持Black-Scholes與Hull-White模型的原本假設下，模型的估計誤差明顯減少，甚至在價平、價外及深價外的情況下，Black-Scholes模型的估計誤差低於Hull-White模型的估計誤差，此結果改變過去Hull-White模型優於Black-Scholes模型的說法。

關鍵字

台指選擇權 ； 結構性改變 ； Black-Scholes模型 ； Hull-White模型 ； GARCH模型

並列摘要

In traditional approaches the parameters of a volatility model are usually assumed to be constant during an empirical study period, which implies that the market structure has not changed over the time. In practice, one can see that the structure change easily happens in a financial (options) market. This phenomenon is intriguing. In conventional approaches we usually remedy the models to improve the performances, and therefore many complex models have been developed, but in practice their improvements are often restricted.
This article focuses on the structure change point and provides an alternative thinking to enhance performance. The empirical study shows that even the simple Black-Scholes model can improve its performance radically.
This research applies Black-Scholes and Hull-White models on TAIEX options, in which the historical volatility model and GARCH model are used for estimation. The Black-Scholes model's performance is significantly better than when the model did not consider a structure change, especially for deep-out-the-money pricing of call options. The reason could be that the buyers are more sensible than before. In the GARCH model we find one change point. Similar to the historical volatility model, these models which have considered a structure change are significantly better than the others.

並列關鍵字

TAIEX Options ； Structure Change ； Black-Scholes Model ； Hull-White Model ； GARCH Model