這篇論文是分別探討Black-Scholes模型與GARCH(1,1)模型的選擇權避險部位,當標的物的對數報酬率呈現GARCH(1,1)的過程.
結果顯示Black-Scholes模型與GARCH模型的其中一個避險參數,delta值,在接近價平時是相似的;在深入價外時,Black-Scholes模型的選擇權delta值會大於GARCH模型;在深入價內時,Black-Scholes模型的選擇權delta值會小於GARCH模型.
我們也會呈現GARCH(1,1)與Black-Sholes模型的模擬避險過程,其結果也支持我們的發現.

This article examines the hedging positions derived from the Black-Scholes(B-S) model
and the GARCH(1,1) models, respectively, when the log returns of underlying asset exhibits
GARCH(1,1) process.
The result shows that Black-Scholes and GARCH options deltas, one of the hedging
parameters, are similar for near-the-money options, and Black-Scholes options delta is
higher then GARCH delta in absolute terms when the options are deep out-of-money, and
Black-Scholes options delta is lower then GARCH delta in absolute terms when the options
are deep in-the-money.
Simulation study of hedging procedure of GARCH(1,1) and B-S models are performed,
which also support the above findings.

1 Introduction..................1
2 Preliminaries.................4
3 Literature Review............11
4 The GARCH(1,1) Model.........15
5 Main Result..................21
6 Simulation Study.............29
7 Conclusion...................36
References.....................37
Figure 1~3.....................39
Table 1........................40
Table 2........................41
Table 3........................42
Table 4........................43
Table 5........................44
Table 6........................45

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