偏度、峰度及信用風險考量下之轉換公司債訂價研究

On the Valuation of Convertible Bonds with respect to Skewness, Kurtosis and Credit Risk

余冠廷(kuan-Ting Yu)

指導教授 ： 李存修

國立臺灣大學/管理學院/財務金融學研究所/碩士(2007年)

https://doi.org/10.6342/NTU.2007.01698

摘要

在實務上，轉換公司債是用於融資和投資的一項重要金融工具。雖然在過去的數十年間已有不少商品訂價模式提出，但是卻缺少了對於標的資產價格機率分配之偏度及峰度於轉換公司債訂價的研究。本篇論文欲針對此面向檢驗該參數對於轉換公司債價格的影響。在信用風險的考量上，我們考慮了更貼近現實的轉換公司債發行者破產過程，意即破產過程可能為信用等級連續向下調整的結果。
結果顯示，一般而言正偏對於五年期轉換公司債價格有正向的影響；反之，負偏則有負向的價格影響。因為轉換公司債的存續期間會相對大於一般的個股買權，這樣的結果也與偏度對於個股買權價格的影響不同。峰度的影響則是較小的。除此之外，存續期間和標的資產價格波動度也會改變偏度和峰度影響轉換公司債價格的形式。另一方面，初期的信用等級也會對於轉換公司債價格有影響；特別是對於賣回條款、贖回條款和重設條款之價值產生影響。
我們亦利用了2001年至2006年間台灣市場所發行的轉換公司債資料以檢驗初期發行訂價之效率性。根據所得到的結果，有充分的證據顯示初期發行的轉換公司債容易被發行者低估價值。若轉換公司債市場之流動性大，此不效率性將會被消除。

關鍵字

信用等級 ； 隱含選擇權 ； 馬可夫鏈模型 ； 非常態性 ； 路徑相依

並列摘要

Convertible bond is an important financial instrument used as the funding or investment tool in practice. Over the past few decades, there are numerous valuation models proposed, however, the one with direct consideration about skewness and kurtosis of underlying stock return is lacking. This research intends to examine the effects of these parameters on the convertible bond value. For credit risk modeling, we consider that default event of convertibles issuer may occur after the successive rating downgrades, which coincides with the reality.
The general finding indicates that positive skewness contributes positive influence and negative skewness contributes negative influence on the value of convertible bond with five years maturity. Since convertibles are usually with longer maturity, this result is in the different pattern with that of relative short term call options. The effect of kurtosis is slightly small. In addition, maturity and volatility will alter the pattern skewness and kurtosis influence convertible bond value. On the other hand, the initial credit rating also have the effects on the value of convertible bond, particularly, on the value of provisions such as put provision, call provision, and reset provision.
To examine the efficiency of initial offering pricing of convertibles issues, we conduct the empirical investigation in the period from 2001 to 2006 in Taiwan CB market. Based on the results, there is an evidence that initially offering prices of convertibles tends to be undervalued by issuers. Such inefficiency will be eliminated as long as liquidity of convertibles trading is large.

並列關鍵字

Credit rating ； Embedded options ； Markov chain model ； Non-normality ； Path dependent

參考文獻

8.Chung, S.-L., H.-W. Lai, S.-Y. Lin, and G. Shyy (2004), CB Asset Swaps and CB Options : Structure and Pricing, Academic Economic Papers 32: 23-51.

19.Jarrow, R.A., D. Lando, and S. M. Turnbull (1997), A Markov Model for the Term Structure of Credit Risk Spreads, The Review of Financial Studies 10: 481-523.

1.Ammann, M., A. Kind, and C. Wilde (2007), Simulation Based Pricing of Convertible Bonds, Journal of Empirical Finance, forthcoming.

2.Ayache, E., P.A. Forsyth, and K.R. Vetzal (2003), Valuation of Convertible Bonds with Credit Risk, Journal of Derivatives 11: 9-29.

3.Black, F., and M. Scholes (1973), The Pricing of Options and Corporate Liabilities, Journal of Political Economy 18: 637-659.