臺灣博碩士論文加值系統

在信用風險管理的文獻上，KMV模型是最被廣泛應用於Merton (1974)模型的方法之一。然而，KMV估計值的分配性質仍未被廣泛瞭解及探討，而MLE估計值則是具有良好的統計性質，進而對估計的參數進行統計推論。本篇文章在Duan et al. (2004)的架構下，利用蒙地卡羅模擬來驗證KMV及MLE的估計結果是相近的。我們同時利用台灣市場的資料來驗證KMV及MLE方法在Merton (1974)模型下對公司違約機率估計的正確率。雖然用實證資料在兩個方法下計算出來的違約機率略有不同，但所預測的正確率是相近的。我們發現不論在KMV或MLE方法下，Merton (1974)的模型正確率可達60%。然而，這是在違約前一季做預測所需的公司資料並未完整的結果，若可取得完整的資料，我們預期模型正確率將可進一步提高。

KMV method is a popular commercial implementation of Merton''s (1974) structural credit risk model. It is found in recent academic papers, but it is not clear as to whether it is statistically sound. Unlike the MLE method, the KMV method is speechless with the distributional properties of the estimates and it is unsuited for statistical inference. We follow Duan et al. (2004) to verify that the KMV estimate is identical to the MLE estimate in Merton''s (1974) model. Moreover, we perform the Monte Carlo simulation to show that the estimations of KMV and MLE are alike. We also use the data from Taiwan market to examine the accuracy of Merton''s (1974) model by both KMV and MLE methods. We find that Merton''s (1974) model provides about 60% of accuracy ratio no matter the KMV or MLE method is emplyed in predicting the default probabilities of Taiwan companies. It is notable that our result is somehow driven by the incompleteness for one-quarter prediction. If we are able to complement the missing data, we could expect to have an accuracy ratio higher than 60%.

1 Introduction…………………………………………………………1
2 The KMV and maximum likelihood estimates (MLE) under Merton''s (1974)Model…………………………………………………3
2.1 Merton (1974) model……………………………………………3
2.2 The KMV estimation………………………………………………6
2.3 The transformed-data maximum likelihood estimation (MLE)……………………………………………………………………8
2.4 The simulation of the KMV and MLE methods………………12
2.4.1 The KMV method………………………………………………13
2.4.2 The MLE method………………………………………………14
2.4.3 The comparison of the KMV and MLE method……………15
2.4.4 The simulation results of the KMV and MLE method…16
3 Data description and empirical methods……………………18
3.1 Data description………………………………………………18
3.2 Empirical methods and the testing design………………20
3.3 Evaluation of Probability Forecasts………………………21
4 Empirical results and discussion……………………………22
4.1 Analyses of model accuracy…………………………………22
4.1.1 Empirical results of the KMV method……………………22
4.1.2 Empirical comparison between KMV and MLE methods…26
4.2 Analyses of model fitness……………………………………29
5 Conclusions…………………………………………………………31
References……………………………………………………………32
Appendix………………………………………………………………34

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