NIG-GARCH選擇權訂價模型

Abstract

這篇論文發展了一個誤差項服從由Barndorff-Nielsen (1997) 所提出之Normal Inverse Gaussian分配來做GARCH選擇權訂價模型。這個模型叫做NIG-GARCH 且將包含Duan (1995)之GARCH 選擇權訂價模型為其極限特例。此外吾人也提出另一個可考慮到“槓桿效應”現象之NIG-NGARCH模型，其可以解釋財務時間序列上常發生之資產報酬波動率不對稱的現象。在史坦普爾500指數的實證研究上顯示我們的模型檢驗比Duan (1995) 和 Heston and Nandi (2000)之GARCH模型還要好。而另一個在史坦普爾500指數選擇權訂價上的研究也顯示我們的模型在比較價內的買權時優於其他的GARCH模型。這改善是由於“厚尾分配”假設所致，且因此可以解釋財務時間序列上“超越峰態”的現象。

This thesis develops a GARCH option pricing model with its innovation following a Normal Inverse Gaussian (NIG) distribution as proposed by Barndorff-Nielsen (1997). The model is called NIG-GARCH and will include the GARCH option pricing model of Duan (1995) as a limiting case. In addition, we also consider the “leverage effects” in the model, called NIG-NGARCH, which can explain the asymmetric effect of asset return volatility, observed often in financial time series. Empirical studies on S&P500 index shows that model checking of our models perform better than the GARCH models of Duan (1995) and Heston and Nandi (2000). Studies on pricing S&P500 index options also shows that our model in the out-of-sample performance is superior to other models for at-the-money calls. The improvement is due to the distribution with fat tails and thus can explain excess kurtosis often observed in financial time series.