|摘要: ||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。|
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.