臺灣博碩士論文加值系統

GARCH是一個相當常見的隨機變異數模型。這個模型成功的描繪了資產報酬的序列相關。這個模型有五個參數，而其中某些參數並沒有直覺的經濟意義，所以如何決定參數是GARCH模型所面臨最重要的問題之一。傳統上最常用的方法是在歷史資料上使用最大概似法來估計，本論文提供了一個有效率的數值演算法以選擇權價格來校對模型參數。

GARCH is one of the most popular stochastic variance models. The model successfully captures the serial correlation of asset return volatilities. The model needs five parameters, and some of them do not have intuitively economic meanings. So how to determine the parameters is one of the most challenging problems facing the GARCH model. Applying the maximum likelihood method to the
historical data is the most common approach to obtaining the parameters. As an alternative, this thesis develops efficient numerical algorithms to calibrate the model with option prices.

Introduction 1
The GARCH model 3
The mean-tracking (MT) tree 5
Calibration based on the di®erential tree 9
Applying the Newton-Raphson method 14
Choices of the products 16
Estimating the parameters 21
Conclusion 24

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