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    Please use this identifier to cite or link to this item: http://nccur.lib.nccu.edu.tw/handle/140.119/76175

    Title: 狀態轉換漸進極值因子模型下擔保債權憑證之評價與避險
    Pricing and Hedging of CDOs under a Regime Switching Asymptotic Single Factor Model
    Authors: 賴冠宇
    Lai, Kuan Yu
    Contributors: 江彌修
    Chiang, Mi Hsiu
    Lai, Kuan Yu
    Keywords: 狀態轉換
    Regime Switching
    Asymptotic Single Factor Model
    Date: 2014
    Issue Date: 2015-07-01 14:45:58 (UTC+8)
    Abstract: 本篇論文使用了LHP的近似方法去評價擔保債權憑證,並推導出漸進極值因子模型,又稱單因子copula模型,單因子copula模型被廣泛運用在CDO之風險管理與一些風險因子模擬之應用,但由於2008年之金融海嘯造成市場標準模型Gaussian copula model會有評價上的誤差,所以為了能在市場不穩定時能更精確的求算出分券價差,我們必須找到一個更簡單且快速捕捉到市場不穩定性的模型。在這篇論文中,我們引用了Anna Schloesser在2009年所提出以NIG copula model為基礎的兩個延伸,讓模型更穩健和且擁有良好的性質去進行模擬,NIG Regime-Switch 模型有兩大特色: (i)可以用一致的方法去評價不同到期日的分券,放寬了同一分券必須是相同到期日的假設,和(ii)有不同的相關係數狀態,對於金融風暴來說,狀態轉換可以有效地降低市場不穩定所帶來的評價誤差。本文也對不同模型下的CDO進行風險分析與避險,分券的期望損失廣泛被信評公司視為一項審定信用評等重要的風險衡量指標,但是並無法真實反映出擔保債權憑證分券之間相對風險之大小,因此本文採用期望損失率的觀念,利用期望損失佔本金的比例來比較各分券之相對風險,且本文也求算出CDO之避險參數,讓投資人了解對合成行擔保債權憑證分券避險時所需之避險部位,分券持有人也可依據所要規避的風險類型,選擇市場上現有的信用違約交換指數或是單一資產之信用違約交換(single-name credit default swap)來進行避險。
    This paper presents the Large Homogeneous Portfolio (LHP) approach to the pricing of CDOs and we derive the one-factor copula model. It is popular that the one-factor copula models are very useful for risk management and measurement applications involving the generation of scenarios for the complete universe of risk factors. However, since the financial crisis in 2008 induces some errors in the valuation by Gaussian copula model, which is originally adopted by credit rating firms, it is necessary to have a simple and fast model that can capture the market unstableness. In this paper we apply two extensions of the NIG copula model, which are first present by Anna Schloesser (2009), since they make the model well defined and powerful for scenario simulation. The NIG Regime-Switch copula model allows for two important features: (i) tranches with different maturities modeled in a consistent way, and (ii) different correlation regimes. The regime-switching component of the NIG copula model is especially important in view of the financial crisis. This paper also targets on different models to conduct risk analysis and hedging strategy. The expected loss of tranches is widely used by credit rating organizations as one of the important indicators for risk measurement. However, it can’t reflect the relative risk level between CDO’s tranches. Therefore, our research adopts the concept of expected loss rate, which use the proportion of expected loss to total principal amount to compare the relative risk of each tranche. Moreover, when we want to hedge the spread risk of synthetic CDO tranches, the holders of tranches can choose the existing CDS index or the single-name CDS based on different risks types to hedge. The employment of the NIG Regime-Switch copula model not only has more precise estimation for the spread of tranches but also possess more stable hedge ratio to hedge.
    Reference: 1. Anderson, W. (1991), Continuous-Time Markov chains, Springer Verlag.
    2. Andersen, L. & Sidenius, J. (2005), Extensions to the Gaussian copula: random recovery and random factor loadings, Journal of credit risk 1(1).
    3. Anna, K., Bernd, S. & Ralf, W. (2005), The Normal Inverse Gaussian Distribution for Synthetic CDO Pricing. Working paper.
    4. Anna, S. & Rudi, Z. (2009), Crash-NIG copula model: regime-switching credit portfolio modeling through the crisis.
    5. Barndorff-Nielsen, Ole E. (2007), Normal Inverse Gaussian Distributions and Stochastic Volatility Modeling, Journal of Statistics.
    6. Bluhm, C., Laurent, J.-P. & Gregory, J. (2005), A comparative analysis of CDO pricing models. Working paper, BNP-Paribas.
    7. Burtschell, X., J. Gregory & J-P. Laurent, 2005, A Comparative Analysis of CDO Pricing Models. Working paper, ISFA Actuarial School, University of Lyon & BNP-Paribas.
    8. Duffie, D. & Singleton, K. (1999), Modeling term structures of defaultable bonds, Review of Financial Studies 12, 687-720.
    9. Hull, J. & White, A. (2004), Valuation of a CDO and an n-th to default CDS without a Monte Carlo simulation, Journal of Derivatives.
    10. Hull, J., Predescu, M. & White, A. (2005), The valuation of correlation-dependent credit derivatives using a structural model. Working paper.
    11. Jarrow, R., Lando, D. & Turnbull, S. (1997), A Markov model for the term structure of credit spread, Review of Financial Studies 10, 481-523.
    12. Li, D. X. (2000), On default correlation: A copula function approach, Journal of Fixed Income 9(4), 43-54.
    13. Max S. (2011), Calibration of multi-period single-factor Gaussian copula models for CDO pricing, University of Toronto.
    14. Merton, R. (1974), On the pricing of corporate debt: The risk structure of interest rates. Journal of Finance 29(2), 449-470.
    15. Nelsen, R.B. (2005), An Introduction to Copulas. Springer. Second Edition.
    16. O'Kane, D. & Schloegl, L. (2003), An analytical portfolio credit model with tail dependence, Quantitative credit research. Lehman Brothers.
    17. Vasicek, O. (1987), Probability of loss on loan portfolio. Memo, KMV corporation.
    18. Yan ya, C. (2007), Pricing CDOs with One Factor Double Mixture Distribution Copula Model.
    Description: 碩士
    Source URI: http://thesis.lib.nccu.edu.tw/record/#G0102352031
    Data Type: thesis
    Appears in Collections:[Department of Money and Banking] Theses

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