應用Copula函數於組合型認購權證的評價

Copula Function to the Pricing of Basket Stock Call Warrant

10.29718/TJHSS.201009.0003

李沃牆(Wo-Chiang Lee)；黃佳慧(Chia-Hui Huang)

Copula函數 ； 組合型認購權證 ； CC評價模式 ； copula function ； basket stock call warrant ； CC basket option pricing model

淡江人文社會學刊

43期（2010 / 09 / 01）

49 - 80

繁體中文

本研究將Copula函數加入CC評價模式中，並應用於組合型認購權證訂價。Copula方法可處理多變量的聯合機率分配，近年來已被運用在財務和經濟的領域。實證上利用B-S、CC評價模式以及加入6種Copula函數的CC模型，對國內已下市的二標的股票型組合型認購權證，共14檔進行評價，最後透過MAE、RMSE、MAPE、Theil's U指標評估其績效。 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ArchimedeanCopula的方法比N-copula或t-copula績效好，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模型績效為佳。資產間的報酬實際上並不會符合特定的分配，使用Copula函數更能配適二資產間的最適相關性結構。

This article is aimed at combining the copula functions with CC basket options pricing model, and applying them to the pricing of basket stock call warrants. The Copula function can deal with multivariate joint marginal probability distribution and has been widely used in economics and finance in recent years. In our empirical study, we selected fourteen Taiwan basket stock call warrants with two underlying stock assets. The models include B-S option pricing model, CC basket option pricing model, and six copula functions based on the CC model. Last, we utilize MAE, RMSE, MAPE and Theil's U as criteria for evaluating. Among pricing models based on the copula, the performance of Archimedean copula models always can outperform N-copula or t-copula models. Besides, the performance of underlying assets correlation structure in copula models is better than CC basket and B-S option pricing models. In fact, the return of assets does not always fit a special distribution, while the copula functions can capture the correlation structure between two assets more precisely.

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