用GARCH Copula LSM法評價雙資產美式選擇權

Bivariate American Option Pricing Using GARCH Copula LSM Method

沈國曄(Kuo-Yeh Shen)

指導教授 ： 呂育道

國立臺灣大學/管理學院/財務金融學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.00995

摘要

本篇論文介紹一個新的美式雙資產選擇權評價技術。此評價技術用到GARCH、copula以及最小平方蒙地卡羅法(least squares Monte-Carlo)理論。其中個別資產報酬率的統計模型以GARCH模型描述；而各資產間的相關性則由建立GARCH殘差項的聯合機率分配來描述。其各資產殘差項的聯合機率分配可由各種不同的copula模型以及傳統的二元常態分配模擬。最後，美式雙資產選擇權價格可由最小平方蒙地卡羅法計算。本篇論文呈現美式雙資產買權的數值分析結果。結果發現GARCH copula模型與傳統的二元常態模型算出的美式雙資產買權價格有本質上的差異，使用傳統的二元常態模型將會高估美式雙資產買權的價值。

關鍵字

雙資產美式選擇權 ； GARCH ； Copula ； LSM

並列摘要

A bivariate American option is an option with two underlying assets. In this thesis, a new pricing technique for bivariate American option pricing is presented. The pricing technique is implemented using GARCH, copula and the least squares Monte-Carlo (LSM) algorithm. The individual asset return process is described using the GARCH model. The correlation between the underlying assets’ returns is represented by modeling the joint distribution of the innovations of their respective GARCH processes. The joint distribution of the innovations is modeled by different copula models and traditional bivariate normal setting. Finally, the bivariate American option price is calculated by the LSM method. The numerical results of bivariate basket American call option are presented. Different copula models and bivariate normal model of innovations are provided. The results show that American option prices implied by GARCH-copula-LSM models can differ substantially from the prices implied by traditional bivariate normal model. The traditional bivariate normal innovations setting will overestimate the value of the bivariate American call options.

並列關鍵字

Bivariate American option ； GARCH ； copula ； least squares Monte-Carlo (LSM)

參考文獻

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