臺灣博碩士論文加值系統

Abstract
In general, the implied correlation is higher for equity and most senior tranches than for mezzanine tranches, which is known as the correlation smile. This paper uses Gaussian Copula and One-Factor Gaussian Copula methods to price CDO products, and compares two methods to examine why correlation smile occurs. We change different correlation dependency structures, and different copula functions in this paper. We want to test if the loss distribution or the correlation structures led to correlation smiles. We will use Base Correlation to solve this problem, and use implied correlation and base correlation in Taiwan product.

Abstract
In general, the implied correlation is higher for equity and most senior tranches than for mezzanine tranches, which is known as the correlation smile. This paper uses Gaussian Copula and One-Factor Gaussian Copula methods to price CDO products, and compares two methods to examine why correlation smile occurs. We change different correlation dependency structures, and different copula functions in this paper. We want to test if the loss distribution or the correlation structures led to correlation smiles. We will use Base Correlation to solve this problem, and use implied correlation and base correlation in Taiwan product.

Contents
1. Introduction 2
2. Literature Review 5
3. Methodology 7
3.1 Gaussian Copula 7
3.1.1 Survival Function 7
3.1.2 Hazard Rate Function 8
3.1.3 Simulation method for Gaussian Copula 9
3.2 Factor Copula 10
3.2.1 Factor-based Model 10
3.2.2 Factor Model and Copula Function 10
3.2.3 Implementation of the Model 12
3.3 Pricing CDO tranches 13
3.4 Measures of Implied correlation 15
3.4.1 Compound Correlations 15
3.4.2 Base Correlations 15
4. Empirical Results 16
4.1 Homogeneous CDO 16
4.2 Heterogeneous CDO 20
4.3 Different Copulas 27
4.4 Base correlation 28
4.5 Numerical Results 30
5. Conclusion 31
References ………………………………………………………………………….33

References
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