考慮違約相關性下，以「信用價差違約模型」評價信用衍生性商品

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姓名

游日傑(Jih-Chieh Yu) 查詢紙本館藏

畢業系所

財務金融學系

論文名稱

考慮違約相關性下，以「信用價差違約模型」評價信用衍生性商品
(A Spread-Based Model for Valuing Credit Risk Derivatives under Correlated Defaults)

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摘要(中)

在本論文中，我們將建構一個樹狀模型，能夠用來處理多個公司之間具有「相關性信用風險」的情況。在評價信用衍生性商品時，我們的模型可以納入以下各種考量：（1）有相關性的市場風險與信用風險，（2）相互影響的信用風險結構，（3）交易對手風險。
此外，我們的模型能夠評價以「信用價差」或「倒帳事件」為標的物等不同類型的信用衍生性商品。最後，我們將以「信用價差選擇權」以及「一籃子信用違約交換」等商品為例子來進行評價，並且討論信用風險相關性以及利率波動性結構對於信用衍生性商品價格的影響。

摘要(英)

We develop a lattice model to characterize multi-firms’ correlated credit risk. When valuing credit derivatives, our approach allows one to incorporate not only the correlative market and credit risk, but also takes the interdependent default risk structure and counterparty risk into consideration. Moreover, the lattice carries a rich information set and thus a wide range of products can be priced including credit-spread-based and default-based credit derivatives. For a direct application of our model, we demonstrate the valuation of credit derivatives, such as credit-spread options and first to default basket contracts. At the same time, we also conduct a comparative static analysis to discuss the impact of the default correlation and interest rate volatility term structure to credit derivatives’ prices.

關鍵字(中)

★ 交易對手風險
★ 信用衍生性商品
★ 相關性信用風險
★ 信用風險評價模型

關鍵字(英)

★ Correlated Defaults
★ Credit Model
★ Counterparty Risk
★ Credit Risk Derivatives

論文目次

Contents
1. Introduction ……………………………………………………………1
2. Literature Review …………………………………………………… 5
2.1 Credit Risk Modelling ……………………………………………5
2.2 Default Correlation ………………………………………………6
2.3 Das and Sundaram [2000] Model …………………………………7
2.4 Kamrad and Ritchken [1991] Model …………………………… 8
3. The Model ………………………………………………………………10
3.1 Notations ………………………………………………………… 11
3.2 Stochastic Interest Rate Process ……………………………12
3.3 Dealing with Joint Probabilities In the Lattice ……… 16
3.4 Default Probability …………………………………………… 19
3.5 Recovery Rate …………………………………………………… 20
3.6 The Input Data and Parameters Estimation …………………21
3.7 Implementing the Model …………………………………………23
4. Pricing …………………………………………………………………26
4.1 Credit Spread Options ………………………………………… 27
4.2 First to Default Baskets ………………………………………30
5. Conclusion ………………………………………………………33
6. Appendix …………………………………………………………34
7. Reference ……………………………………………………… 36

參考文獻

References
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Brady, B. and Vazza, D., 2004, “Research: Corporate Defaults in 2003 Recede From Recent Highs,” Standard & Poor’s Investors Service.
Chu, C. C. and Kwok, Y. K., 2003, “No-Arbitrage Approach to Pricing Credit Spread Derivatives,”, Spring, 51-64.
Chen, R. R. and Sopranzetti, B. J., 2003, “The Valuation of Default-Triggered Credit Derivatives,” Journal of financial and quantitative analysis, Vol. 38, No. 2, 359-382.
Das, S. R., 1995, “Credit Risk Derivatives,” The Journal of Derivatives, Vol.2, Spring, 7-23.
Das, S. R., Fong, G. and Geng, G., 2001, “The Impact of Correlated Default Risk on Credit Portfolios,” Journal of Fixed Income, Vol. 11, No. 3, 9-19.
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Hull, J. and White, A., 2001, “Valuing Credit Default Swaps Ⅱ: Modeling Default Correlations,” Journal of Derivatives, Vol. 8, 12-22.
Jarrow, R. and Turnbull, S., 1995, “Pricing Derivatives on Financial Securities Subject to Credit Risk,” Journal of Finance, 50, 53-85.
Jarrow, R., Lando, and Turnbull, S., 1997, ”A Markov Model for the Term Structure of Credit Risk Spreads,” Review of Financial Studies, 10, 481-523.
Jarrow, R. and Yu, F., 2001, “Counterparty Risk and the Pricing of Defaultable Securities,” The Journal of Finance, No.5, 1765-1799.
Kamrad, B. and Ritchken, P., 1991, “Multinomial Approximating Models for Options with K State Variables,” Management Science, Vol.37, No.12, 1640-1652.
Lando, D., 1998, “On Cox Processes and Credit Risky Securities,” Review of Derivatives Research, Vol. 2, 99-120.
Madan, D. and Unal, H., 1993, “Pricing the Risks of Defaults,” Working Paper, Univ. of Maryland.
Merton, R., 1974, “On The Pricing of Corporate Debt: The Risk Structure of Interest Rates,” Journal of Finance, Vol. 29, 449-470.
Schonbucher, P. J., 1999, “A Tree Implementation of a Credit Spread Model for Credit Derivatives,” Working Paper, Bonn University, Department of Statistics.
Schonbucher, P. J., 2000, “The Pricing of Credit Risk and Credit Derivatives,” Working Paper, Bonn University, Department of Statistics.
Zhou, C., 2001, “An Analysis of Default Correlations and Multiple Defaults.” Review of Financial Studies, Vol.14, 555-576.

指導教授

張傳章(Chuang-Chang Chang)

審核日期

2004-7-1

推文