相依結構對多資產選擇權定價之模擬分析

Bivariate Options Pricing with Copula-GARCH Model- Simulation Analysis

游明翰(Ming-Han Yu)

指導教授 ： 王耀輝

國立臺灣大學/管理學院/財務金融學研究所/碩士(2009年)

https://doi.org/10.6342/NTU.2009.00081

摘要

二元選擇權是由兩個標的資產所衍生出的選擇權，其價格會與兩個資產的變動與相依結構有很大的相關性。但由於其市場透明度不高，平常很難於公開市場觀察二元選擇權的價格。本篇論文將取三種市場上較廣為被交易的二元選擇權來評價，利用copula-GARCH模型來檢測在不同的邊際分配參數設定下，二元選擇權價格對copula函數選擇的敏感度。
我們的研究結果可整理為三大結論，首先，Frank copula模型常常會產生較其他copula模型差異較大之評價結果。第二點，二元彩虹選擇權的價格，對copula模型的選擇最為敏感。最後，copula-GARCH的二元選擇權評價模型中，對殘插值的分配設定會嚴重影響評價的結果。總結來說，相依結構的設定對二元選擇權的價格會產生顯著的影響，是在評價二元選擇權時不可被忽略的一環。

關鍵字

二元選擇權 ； 多資產選擇權 ； 相依結構

並列摘要

Bivariate option is the contingent claims derives from a pair of underlying assets. The underlying assets can be equity, commodities, foreign exchange rate, interest rate or any index with quotations. In this paper, we present a copula-GARCH model and the Monte Carlo simulation method base on the model. We examine the pricing result of three kinds of bivariate options - digital, rainbow and spread option, in many different cases and find that the choosing of pricing copula may cause a significant difference of the pricing result. Furthermore, the pricing result of rainbow option is most sensitive to the choosing of copulas in the three kinds of bivariate options.

並列關鍵字

Bivariate Option ； Copula ； Dependent Structure ； GARCH ； Monte Carlo

參考文獻

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