應用馬可夫鏈-蒙地卡羅模擬法於新巴賽爾資本協定中資產報酬相關係數之估計

The Application of Markov Chain Monte Carlo Simulations to Estimate Asset Return Correlation in Basel II

陳志遠(Chih-Yuan Chen)

指導教授 ： 鍾麗英

國立臺北大學/商學院/統計學系/碩士(2008年)

摘要

資產報酬相關係數在新巴賽爾資本協定的信用風險模型中，扮演相當重要的角色。且推導信用風險模型時，假設資產報酬為常態分配。然而，輿論指出資產報酬的分配其實比常態分配有更厚尾的情況。在本研究中，將用貝氏統計方法估計在T分配下的資產報酬相關係數，基於非常見的後驗機率分配的關係，馬可夫鏈-蒙地卡羅模擬中的兩種方法－Gibbs抽樣法以及Slice抽樣法，用來估計參數。除此之外，厚尾對資本計提的效果也將被探討。結果指出在T分配下，資產報酬相關係數與資產規模、違約機率的關連性依然與常態分配下是一致的。同時也將調查在不同評等以及不同的資產規模下，資本計提差異的大小。

關鍵字

資產報酬相關係數 ； 新巴賽爾資本協定 ； 貝氏統計方法 ； 馬可夫鏈-蒙地卡羅模擬法 ； 資本計提

並列摘要

The asset return correlation plays an important role in the credit risk model of Basel II. The asset return is assumed to be normally distributed in deriving models for credit risk. However, there is consensus that the distribution of asset return has tails that are fatter than those of normal distribution. In this study, Bayesian method is applied to estimate asset return correlation under t distributions. Due to the unknown posterior distribution, two methods of Markov Chain Monte Carlo simulations, Gibbs Sampler and Slice Sampler, are used to estimate parameters. Besides, the effect of fat-tailed dependence to the capital requirement is also explored. The result suggests that the relationship between asset return correlation, firm size and default probability under t distribution is the same as that for normal distribution. The magnitudes of differences in capital requirement among different ratings and firm sizes are also investigated.

並列關鍵字

Asset return correlation ； Basel II ； Bayesian method ； Markov chain Monte Carlo simulations ； Capital requirement.

參考文獻

Altman, E.I., 1968. Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Journal of Finance, 23:589-609.

Basel Committee on Banking Supervision, 2004. An Explanatory Note on the Basel II IRB Risk Weight Functions. Consultative Document.

Burtschell, X., Gregory, J., Laurent, J. P., 2005. A Comparative Analysis of CDO Pricing Models. Working Paper, BNP Paribas.

C´espedes, G., Carlos, J., Herrero, J. A., Kreinin, A., Rosen, D., 2006. A Simple Multi-Factor ”Factor Adjustment” for the Treatment of Diversification.

Dietsch, M., Petey, J., 2004. Should SME Exposures Be Treated as Retail or Corporate Exposures? A Comparative Analysis of Default Probabilities and Asset Correlations in French and German SMEs. Journal of Banking and Finance,