合成式擔保債務憑證內非標準型分劵之定價與避險

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姓名

許恆杰(Heng-Chieh Hsu) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

合成式擔保債務憑證內非標準型分劵之定價與避險
(Pricing and Hedging Non-Standardized Synthetic CDO Tranches)

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摘要(中)

隨著合成式擔保債務憑證內標準型分劵的興起發展，為了能迎合不同投資人的風現偏好，透過結合合成式擔保債務憑證內標準型分劵的市場報價，我們嘗試對合成式擔保債務憑證內非標準型分劵進行定價與避險。在本篇論文中，我們會選定一組標準型DJ iTraxx Europe分劵的市場報價，利用HLPGC模型對照各分劵的市場報價求出各分劵的複合相關性及基點相關性。更進一步我們可以利用求出的基點相關性對任何非標準型分劵進行定價。至於在非標準型分劵的避險方面，對於第一層風險，我們針對在價差改變的風險並且利用delta避險法建立各非標準型分劵的避險部位。我們也會討論第二層風險像是價差凸性風險。我們發現非標準型低層分劵在經過delta避險後會使投資人從價差凸性發生的情形下獲利。相反地，非標準型高層分劵在經過delta避險後則會使投資人從價差凹性發生的情形下損失。另外我們也利用相關性敏感度來分析非標準型分劵的相關性風險。最後，我們連結違約相關性參數與delta避險值後發現，當違約相關性增加時，價差改變的風險會從非標準型低層分劵轉移到非標準型高層分劵。

摘要(英)

With the development of synthetic CDO standardized tranches, in order to fit in different investors’ risk preference, we try to value and hedge non-standardized tranches which are combined with market quotes of standardized ones. In this paper, we select a set of market quotes of standardized DJ iTraxx Europe tranches and use the Homogeneous Large Pool Gaussian Copula model to find the compound and base correlations of tranches. Moreover, we can value any non-standardized tranches by those base correlations. As to hedge non-standardized tranches, for the first-order risk, we focus on the spread risk and build up hedging positions by tranches’ deltas. We also discuss the second-order risk such as the spread convexity. We discover that the delta-hedged non-standardized equity tranche position can make investors benefit from the spread convexity. By contrast, the delta-hedged non-standardized senior tranche position can make investors suffer from the spread concavity. We also analyze the correlation risk by tranches’ correlation sensitivities. Finally, we connect the default correlation parameter with the deltas and we find that the spread risk is parceled to the senior tranche as the default correlation increases.

關鍵字(中)

★ 基點相關性
★ 價差凸性
★ 合成式擔保債務憑證
★ 標準型分劵
★ 非標準型分劵
★ HLPGC模型
★ 複合相關性

關鍵字(英)

★ Spread Convexity
★ Standardized Tranches
★ Non-Standardized Tranches
★ Homogeneous Large Pool Gaussian Copula model
★ Compound Correlations
★ Base Correlations
★ Synthetic CDO

論文目次

1. Introduction 1
2. Synthetic CDOs 3
2.1. CDS Index 4
2.1.1. CDS Contract 4
2.1.2. CDS Index 4
2.1.3. CDS Index contract 5
2.2. Standardized Synthetic CDO tranches 6
3. Literature review 8
4. Homogeneous Large Pool Gaussian Copula Model 12
4.1. Deriving Expected Loss for a Synthetic CDO tranche 14
4.2. Valuation of a Synthetic CDO Tranche 18
4.2.1. Valuation of a plain-vanilla CDS 19
4.2.2. Valuation of a synthetic CDO tranche 21
4.3. Compound correlations in Synthetic CDO tranches 22
4.3.1. Effect of correlations on Synthetic CDO tranches 22
4.3.2. Concept of Compound correlation 24
4.3.3. Measure of Compound correlation 25
4.3.4 Correlation Smile 26
5. Valuation of Non-Standardized Synthetic CDO tranches 27
5.1. Base correlation 28
5.1.1. Concept of Base correlation 28
5.1.2. Calculation of base correlations 28
5.2. Valuation of Non-Standardized tranches from base correlations 31
6. Hedging with Non-Standardized Synthetic CDO tranches 34
6.1. Spread Sensitivity 34
6.1.1. Delta Hedge 34
6.1.2. Spread Convexity 41
6.2. Correlation Sensitivity 45
7. Conclusion 50
References 52

參考文獻

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指導教授

岳夢蘭(Meng-Lan Yueh)

審核日期

2006-7-10

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