應用Copula函數於組合型認購權證的評價

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Title:	應用Copula函數於組合型認購權證的評價
Other Titles:	Applying Copula function to the pricing of basket stock call warrant
Authors:	黃佳慧;Huang, Chia-hui
Contributors:	淡江大學財務金融學系碩士班李沃牆
Keywords:	Copula;組合型認購權證;CC評價模式;Copula;Basket option pricing model;CC basket option pricing model
Date:	2010
Issue Date:	2010-09-23 15:25:00 (UTC+8)
Abstract:	本研究之目的是將Copula函數加入CC評價模式中，應用在組合型認購權證定價，並加入績效指標衡量各種模型之績效表現以及在各種模型評價下的相關係數。Copula方法可以簡化處理多變量的聯合機率分配，將邊際分配及相關性結構分開處理，近年來被運用在財務和經濟的領域上。實驗設計B-S、CC評價模式和加入各種Copula函數於CC模型中共八種模型，對國內已下市組合型認購權證，標的股為二檔個股的資料共十四筆做定價，找出相關係數，並用MAE、RMSE、MAPE、Theil’s U這四個績效指標評估哪一個模型表現最好。研究結果發現CC-Frank-copula-CCC-BiGARCH模型的績效表現最好，其次是CC-Gumbel-copula-CCC-BiGARCH，在所有加入Copula函數模型中，使用Archimedean Copula的方法比N-copula或t-copula績效較好，而使用Copula函數去衡量資產報酬相關性結構的績效也比CC評價模型和B-S模型績效好。資產間的報酬實際上是不會符合特定的分配，使用Copula函數更能準確的找出二資產間的相關性結構，不需要在常態或特定某分配的假設下，此研究結果符合預期結果。另外就動態相關係數模型而言，在相關係數固定下，當距到期日愈近(遠)時，權證價格愈低(高)。 The purpose of this study is to join the Copulas to the CC basket options pricing model, which is used to determine the price of basket stock call warrants. We use four kinds of performance indicators MAE, RMSE, MAPE and Theil’s U. These indicators measure the performance of various models and evaluate the correlation coefficient. In our empirical study, we use Taiwan basket stock call warrants, which are no longer for sale, and two underlying stock assets as empirical objects. The eight models, including B-S option pricing model, CC basket option pricing model, and six kinds of copula functions joined into the CC model, are constructed in order to determine the price of the fourteen basket call warrants and to find the correlation coefficient. In all Copulas models, the performance of Archimedean copulas models is better than N-copula or t-copula models. Besides, the performance of underlying assets correlation structure in copula models is better than the performance observed in CC basket options pricing model and B-S option pricing model. In fact, the return of assets does not fit within a certain distribution, however, the Copulas are able to describe the correlation structure between two assets more precisely without taking into consideration all the assumptions of normal or other distributions. Our empirical study confirms what was expected. Furthermore, under fixed correlation coefficient, the prices of warrants are lower and lower when warrants are near the time to maturity. In the contrary, when the time to maturity is far, the prices are higher.
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