- 學位論文
結合D-CRR, GARCH, 及均值對稱方法評價CDOs
Pricing CDOs with Defaultable Trinomial Trees under GARCH Processes
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摘要
擔保債權憑證(Collateralized Debt Obligation: CDO)近年來發展迅速，尤其在2007年的次貸危機以及2008年的金融風暴後，更顯出正確的評價CDOs的重要性。而目前評價信用衍生性金融商品有兩大主流方法-其一是結構式模型；其二是縮減式模型，本論文建立在結合結構式模型(structural model)與縮減式模型(reduced form model)的可破產二元樹模型(Defaultable Cox, Ross and Rubinstein model: D-CRR model)之上，並利用mean-tracking方法修正D-CRR模型中股價上漲及下跌機率跳出0與1範圍的問題，之後針對D-CRR模型中的破產強度做修改，使之能對駝峰型CDS的價差結構能作出更好的解釋能力、以及更能符合結構式模型的精神，最後基於許多文獻都證實了廣義自我迴歸條件異質變異模型 (Generalized Autoregressive Conditional Heteroskedasticity: GARCH) 較符合實務上股價的表現，加上GARCH模型以考慮股價波動性對違約強度的影響，於是成就了本論文之「結合D-CRR, GARCH, 及均值對稱方法評價CDOs」的在GARCH架構下，可考慮破產之三元樹，評價CDOs的模型。
並列摘要
Finding an effective pricing model for Collateralized Debt Obligations (CDOs) has become more important in these days, especially after the Subprime Mortgage Crisis in 2007 and the Financial Tsunami in 2008. Das and Sundaram (2004) and Bandreddi, Das and Fan (2007) introduce the Defaultable CRR binomial tree model (D-CRR model) to combine the structural and the reduced form model. However, some problems still exist in the D-CRR model to be solved. In order to fix the probabilities problem in D-CRR model and restrict the probabilities staying within 0 and 1, the mean-tracking method is added into the model in this thesis. In addition, the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) process is employed to capture the empirical characteristics such as clustering volatilities, leptokurtic or fatter tails stock returns. Moreover, both of the impacts of the stock price and the volatilities are considered in the default intensity. Modifications are done to the default intensity equation for not only better performance in the case of hump shaped, but also better fitting with the reality.
參考文獻
Bandreddi, S., S. Das, and R. Fan, 2007, Correlated Default Modeling with a Forest of Binomial Trees, Journal of Fixed Income, Vol. 17, No. 3, pp.38–56.
Black, F. and J. C. Cox, 1976, Valuing Corporate Securities: Some Effects of Bond Indenture Provisions, Journal of Finance, Vol. 31, No. 2, pp. 351–367.
Black, F. and M. Scholes, 1973, The pricing of options and corporate liabilities, Journal of Political Economy, Vol. 81, pp. 637-659.
Bollerslev T, 1986, Generalized Autoregressive Conditional Heteroskedasticity, Journal of Econometrics, 31, pp. 307-28.
Burtschell, X., J. Gregory, and J. P. Laurent, 2008, A Comparative Analysis of CDO Pricing Models, working paper.