臺灣博碩士論文加值系統

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。

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.

摘要............................................................ i
Abstract........................................................ ii
1 Introduction.................................................. 1
2 Literature Review............................................. 3
3 Bivariate Options............................................. 7
4 Methodology................................................... 9
4.1 GARCH Model................................................. 9
4.2 Copulas Functions........................................... 11
4.3 Monte Carlo Simulation...................................... 13
5 Result Analysis............................................... 14 6 Conclusion.................................................... 37
References...................................................... 39
Appendix A. Common Bivariate Copula Functions................... 43
Appendix B. Kendall’s tau of each Copulas...................... 43
Appendix C. Inverse Function of Cu1() of each Copula Models..... 44

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