障礙選擇權違約風險模型之績效與應用

Performance and Application of the Default Risk Model Based on Barrier Option Framework

10.6504/JOM.2009.26.03.03

周恆志(Heng-Chih Chou)

違約風險 ； 障礙選擇權 ； 違約機率 ； 違約門檻值 ； 信用評分法 ； Default Risk ； Barrier Option ； Default Probability ； Default Barrier ； Credit Ratings

管理學報

26卷3期（2009 / 04 / 01）

275 - 289

繁體中文

鑒於Merton模型對於違約點的不當假設與Ronn and Verma (1986)參數估計法的缺點，本文採用障礙選擇權架構建立違約風險模型，並採用Duan (1994, 2000)的資料轉換最大概似估計法推估樣本公司的資產價值、資產飄移項、資產價值波動度與違約門檻值。本文以台灣證交所的上市公司為配適對象，實證結果發現樣本公司的違約門檻值顯著存在，支持障礙選擇權模型在評估公司違約風險的適用性。相較於以會計資訊為基礎的信用評分法（Zscore模型與Zeta模型）與同屬於結構式模型的Merton模型，障礙選擇權違約風險模型的違約判定績效較佳。最後，在障礙選擇權違約風險模型的架構下，本文發現股價報酬率顯著具有公司違約風險的資訊內涵，支持Vassalouand Xing (2004)的推論。

Default risk modeling has gained increasing prominence over the years. Most of the interest is motivated by new regulatory, the Basel Ⅱ, which provide strong incentives for financial institutions to quantify the credit risk of their portfolios. Much of the literature follows Merton's (1974) model by explicitly linking the risk of a firm's default process to the variability in the firm's asset value and viewing the market value of firm's equity as the standard call option on the market value of the firm's asset with strike price equal to the promised payment of corporate liabilities. These insights have a profound impact on financial economics, but many researches have been stimulated to criticize the approach. One obvious weakness of the approach is that default only occurs at maturity of the deb. Brockman and Turtle (2003) propose to incorporate a default barrier on the market value of firms' asset for triggering default prior to the maturity. As a result, the down and-out call option is proposed to model the firm's equity value, and the default risk can be estimated from the barrier option pricing model. Brockman and Turtle provide empirical validation of the barrier option framework by estimating the default barriers from the market value of firm's equity and showing that implied default barriers are statistically and economically significant for a large cross-section of industrial firms. They, however, adopt the sum of the market value of firm's equity and the book value of firm's liability as a proxy for the market value of firm's asset in their tests. Obviously this proxy is not appropriate. Duan, Gauthier and Simonato (2005) utilize Duan's (1994, 2000) transformed-data maximum likelihood estimation (MLE hereafter) to directly estimate the market value of firm's asset along with the asset value volatility and the default barrier from the market value of firm's equity. The benefits of using MLE method are well understood in statistics and econometrics, and many studies demonstrate that the MLE method dominates the estimation approach by Ronn and Verma (1986) in the context of structural credit risk models. Due to the weakness of the Merton's model and estimation approach by Ronn and Verma, the article constructs a default risk model based on a barrier option pricing framework with a data-transformation MLE approach. The market data of the listed firms in TAIEX over the period of 2002 to 2004 are used to test the performance of the default risk model. We investigate the validity of the framework by testing the statistical significance of the implied default barriers. We then apply the framework for default prediction and compare its prediction performance to the commonly adopted models, Merton's model, the Z-score model and the ZETA model. We also test the n-year-ahead prediction performance of the framework. Finally, because Vassalou and Xing (2004) show that size and book-to-market factors appear to contain no significant price information related to default risk, we also assess the effect of estimated default risks on equity returns. The empirical results show that a positive default barrier level exists significantly for each firm, implying that the barrier option framework is suitable for the measurement of default risk. Meanwhile, the default risk model based on barrier option is a better measure for default prediction when comparing with Altman's Z-score and Zeta model, and also Merton’s model. Finally, our results show that beta, size, book-to-market and default probability are all valuable explanatory variables of equity returns. The estimated coefficients are statistically significant at the 5% level. The signs of the estimated coefficients show that high-beta firms earn higher returns than low-beta firms, small firms earn higher returns than big firms, growth stocks (low book-to-market) earn higher returns than value stocks (high book-to-market), and low-default-risk firms earn higher returns than high-default-risk firms. The results further show that the inclusion of default probability in the Fama–French model increases the adjusted R^2 relative to other models in isolation, and show that default probability is statistically significant at the 5% level. Thus, we find evidence that default risk is able to explain equity returns, and that default risk is a variable worth considering in asset-pricing tests, above and beyond size and bookto-market. Our evidence is consistent with the finding from Vassalou and Xing.

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